rfc9690.original.xml   rfc9690.xml 
<?xml version='1.0' encoding='utf-8'?> <?xml version='1.0' encoding='UTF-8'?>
<!DOCTYPE rfc [ <!DOCTYPE rfc [
<!ENTITY nbsp "&#160;"> <!ENTITY nbsp "&#160;">
<!ENTITY zwsp "&#8203;"> <!ENTITY zwsp "&#8203;">
<!ENTITY nbhy "&#8209;"> <!ENTITY nbhy "&#8209;">
<!ENTITY wj "&#8288;"> <!ENTITY wj "&#8288;">
]> ]>
<?xml-stylesheet type="text/xsl" href="rfc2629.xslt" ?>
<!-- generated by https://github.com/cabo/kramdown-rfc version 1.7.11 (Ruby 3.2. <rfc xmlns:xi="http://www.w3.org/2001/XInclude" ipr="trust200902" docName="draft
4) --> -ietf-lamps-rfc5990bis-10" number="9690" category="std" consensus="true" submiss
<rfc xmlns:xi="http://www.w3.org/2001/XInclude" ipr="trust200902" docName="draft ionType="IETF" updates="" obsoletes="5990" tocInclude="true" sortRefs="true" sym
-ietf-lamps-rfc5990bis-10" category="std" consensus="true" submissionType="IETF" Refs="true" version="3" xml:lang="en">
obsoletes="5990" tocInclude="true" sortRefs="true" symRefs="true" version="3">
<!-- xml2rfc v2v3 conversion 3.21.0 -->
<front> <front>
<title abbrev="RSA-KEM with CMS KEMRecipientInfo">Use of the RSA-KEM Algorit hm in the Cryptographic Message Syntax (CMS)</title> <title abbrev="RSA-KEM with CMS KEMRecipientInfo">Use of the RSA-KEM Algorit hm in the Cryptographic Message Syntax (CMS)</title>
<seriesInfo name="Internet-Draft" value="draft-ietf-lamps-rfc5990bis-10"/> <seriesInfo name="RFC" value="9690"/>
<author initials="R." surname="Housley" fullname="Russ Housley"> <author initials="R." surname="Housley" fullname="Russ Housley">
<organization abbrev="Vigil Security">Vigil Security, LLC</organization> <organization abbrev="Vigil Security">Vigil Security, LLC</organization>
<address> <address>
<postal> <postal>
<street>516 Dranesville Road</street> <street>516 Dranesville Road</street>
<city>Herndon, VA</city> <city>Herndon</city>
<region>VA</region>
<code>20170</code> <code>20170</code>
<country>US</country> <country>United States of America</country>
</postal> </postal>
<email>housley@vigilsec.com</email> <email>housley@vigilsec.com</email>
</address> </address>
</author> </author>
<author initials="S." surname="Turner" fullname="Sean Turner"> <author initials="S." surname="Turner" fullname="Sean Turner">
<organization>sn3rd</organization> <organization>sn3rd</organization>
<address> <address>
<email>sean@sn3rd.com</email> <email>sean@sn3rd.com</email>
</address> </address>
</author> </author>
<date year="2024" month="June" day="05"/> <date year="2025" month="January"/>
<area>Security</area>
<workgroup>Limited Additional Mechanisms for PKIX and SMIME</workgroup> <area>SEC</area>
<workgroup>lamps</workgroup>
<keyword>Key Encapsulation Mechanism (KEM)</keyword> <keyword>Key Encapsulation Mechanism (KEM)</keyword>
<keyword>KEMRecipientInfo</keyword> <keyword>KEMRecipientInfo</keyword>
<abstract> <abstract>
<?line 138?>
<t>The RSA Key Encapsulation Mechanism (RSA-KEM) Algorithm is a one-pass <t>The RSA Key Encapsulation Mechanism (RSA-KEM) algorithm is a one-pass
(store-and-forward) cryptographic mechanism for an originator to securely (store-and-forward) cryptographic mechanism for an originator to securely
send keying material to a recipient using the recipient's RSA public key. send keying material to a recipient using the recipient's RSA public key.
The RSA-KEM Algorithm is specified in Clause 11.5 of ISO/IEC: 18033-2:2006. The RSA-KEM algorithm is specified in Clause 11.5 of ISO/IEC: 18033-2:2006.
This document specifies the conventions for using the RSA-KEM Algorithm as a This document specifies the conventions for using the RSA-KEM algorithm as a
standalone KEM algorithm and the conventions for using the RSA-KEM Algorithm standalone KEM algorithm and the conventions for using the RSA-KEM algorithm
with the Cryptographic Message Syntax (CMS) using KEMRecipientInfo as with the Cryptographic Message Syntax (CMS) using KEMRecipientInfo as
specified in RFC XXXX. This document obsoletes RFC 5990.</t> specified in RFC 9629. This document obsoletes RFC 5990.</t>
<t>RFC EDITOR: Please replace XXXX with the RFC number assigned to draft-i
etf-lamps-cms-kemri.</t>
</abstract> </abstract>
<note removeInRFC="true">
<name>About This Document</name>
<t>
Status information for this document may be found at <eref target="https
://datatracker.ietf.org/doc/draft-ietf-lamps-rfc5990bis/"/>.
</t>
<t>
Discussion of this document takes place on the
Limited Additional Mechanisms for PKIX and SMIME Working Group mailing l
ist (<eref target="mailto:spasm@ietf.org"/>),
which is archived at <eref target="https://mailarchive.ietf.org/arch/bro
wse/spasm/"/>.
Subscribe at <eref target="https://www.ietf.org/mailman/listinfo/spasm/"
/>.
</t>
</note>
</front> </front>
<middle> <middle>
<?line 151?>
<section anchor="introduction"> <section anchor="introduction">
<name>Introduction</name> <name>Introduction</name>
<t>The RSA Key Encapsulation Mechanism (RSA-KEM) Algorithm is a one-pass <t>The RSA Key Encapsulation Mechanism (RSA-KEM) algorithm is a one-pass
(store-and-forward) cryptographic mechanism for an originator to securely (store-and-forward) cryptographic mechanism for an originator to securely
send keying material to a recipient using the recipient's RSA public key. send keying material to a recipient using the recipient's RSA public key.
The RSA-KEM Algorithm is specified in Clause 11.5 of <xref target="ISO18033-2"/> The RSA-KEM algorithm is specified in Clause 11.5 of <xref target="ISO18033-2"/>
.</t> .</t>
<t>The RSA-KEM Algorithm takes a different approach than other RSA key <t>The RSA-KEM algorithm takes a different approach than other RSA key
transport mechanisms <xref target="RFC8017"/>, with the goal of providing higher transport mechanisms <xref target="RFC8017"/> with the goal of providing higher
security assurance while also satisfying the KEM interface. The security assurance while also satisfying the KEM interface. The
RSA-KEM Algorithm encrypts a random integer with the recipient's RSA-KEM algorithm encrypts a random integer with the recipient's
RSA public key, and derives a shared secret from the random integer. The RSA public key and derives a shared secret from the random integer. The
originator and recipient can derive a symmetric key from the shared originator and recipient can derive a symmetric key from the shared
secret. For example, a key-encryption key can be derived from the shared secret. For example, a key-encryption key (KEK) can be derived from the shared
secret to wrap a content-encryption key.</t> secret to wrap a content-encryption key (CEK).</t>
<t>In the Cryptographic Message Syntax (CMS) <xref target="RFC5652"/> usin g <t>In the Cryptographic Message Syntax (CMS) <xref target="RFC5652"/> usin g
KEMRecipientInfo <xref target="I-D.ietf-lamps-cms-kemri"/>, the shared secret va KEMRecipientInfo <xref target="RFC9629"/>, the shared-secret value
lue is input to a key derivation function (KDF) to compute a key-encryption key and
is input to a key-derivation function to compute a key-encryption key, and
wrap a symmetric content-encryption key with the key-encryption key. In wrap a symmetric content-encryption key with the key-encryption key. In
this way, the originator and the recipient end up with the same this way, the originator and the recipient end up with the same
content-encryption key.</t> content-encryption key.</t>
<t>For completeness, a specification of the RSA-KEM Algorithm is given in <t>For completeness, a specification of the RSA-KEM algorithm is given in
Appendix A of this document; ASN.1 syntax is given in Appendix B.</t> <xref target="app-alg" format="default"/> of this document. ASN.1 syntax is give
n in <xref target="app-asn1" format="default"/>.</t>
<section anchor="rsa-kem-algorithm-rationale"> <section anchor="rsa-kem-algorithm-rationale">
<name>RSA-KEM Algorithm Rationale</name> <name>RSA-KEM Algorithm Rationale</name>
<t>The RSA-KEM Algorithm provides higher security assurance than other <t>The RSA-KEM algorithm provides higher security assurance than other
variants of the RSA cryptosystem for two reasons. First, the input to the variants of the RSA cryptosystem for two reasons. First, the input to
underlying RSA operation is a string-encoded random integer between 0 and n-1, the underlying RSA operation is a string-encoded random integer
where n is the RSA modulus, so it does not have any structure that could be between 0 and n-1, where n is the RSA modulus, so it does not have any
exploited by an adversary. Second, the input is independent of the keying structure that could be exploited by an adversary. Second, the input
material so the result of the RSA decryption operation is not directly is independent of the keying material, so the result of the RSA
available to an adversary. As a result, the RSA-KEM Algorithm enjoys a decryption operation is not directly available to an adversary. As a
"tight" security proof in the random oracle model. (In other padding result, the RSA-KEM algorithm enjoys a "tight" security proof in the
schemes, such as PKCS #1 v1.5 <xref target="RFC8017"/>, the input has structure random oracle model. (In other padding schemes, such as PKCS #1 v1.5
and/or <xref target="RFC8017"/>, the input has structure and depends on the
depends on the keying material, and the provable security assurances are not keying material. Additionally, the provable security assurances are
as strong.)</t> not as strong.)</t>
<t>The approach is also architecturally convenient because the <t>The approach is also architecturally convenient because the
public-key operations are separate from the symmetric operations on the public-key operations are separate from the symmetric operations on the
keying material. Another benefit is that the length of the keying material keying material. Another benefit is that the length of the keying material
is determined by the symmetric algorithms, not the size of the RSA modulus.</t> is determined by the symmetric algorithms, not the size of the RSA modulus.</t>
</section> </section>
<section anchor="rsa-kem-algorithm-summary"> <section anchor="rsa-kem-algorithm-summary">
<name>RSA-KEM Algorithm Summary</name> <name>RSA-KEM Algorithm Summary</name>
<t>All KEM algorithms provide three functions: KeyGen(), Encapsulate(), <t>All KEM algorithms provide three functions: KeyGen(), Encapsulate(),
and Decapsulate().</t> and Decapsulate().</t>
<t>The following summarizes these three functions for RSA-KEM:</t> <t>The following summarizes these three functions for RSA-KEM:</t>
<t>KeyGen() -&gt; (pk, sk):</t>
<ul empty="true"> <dl spacing="normal" newline="true">
<li> <dt>KeyGen() -&gt; (pk, sk):</dt>
<t>Generate the public key (pk) and a private key (sk) as described <dd><t>Generate the public key (pk) and a private key (sk) as
in <xref section="3" sectionFormat="of" target="RFC8017"/>.</t> described in <xref section="3" sectionFormat="of"
</li> target="RFC8017"/>.</t></dd>
</ul> <dt>Encapsulate(pk) -&gt; (ct, SS):</dt>
<t>Encapsulate(pk) -&gt; (ct, SS):</t> <dd>
<ul empty="true"> <t>Given the recipient's public key (pk), produce a ciphertext
<li> (ct) to be passed to the recipient and a shared secret (SS) for
<t>Given the recipient's public key (pk), produce a ciphertext (ct) use by the originator as follows:</t>
to be <ol type="1" spacing="normal">
passed to the recipient and a shared secret (SS) for use by the originator, <li>Generate a random integer z between 0 and n-1.</li>
as follows:</t> <li><t>Encrypt the integer z with the recipient's RSA public key t
</li> o obtain the ciphertext:</t>
</ul>
<ul empty="true">
<li>
<t>1. Generate a random integer z between 0 and n-1.</t>
</li>
</ul>
<ul empty="true">
<li>
<t>2. Encrypt the integer z with the recipient's RSA public key to o
btain the ciphertext:</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
ct = z^e mod n ct = z^e mod n]]></artwork>
]]></artwork> </li>
<ul empty="true"> <li><t>Derive a shared secret from the integer z using a Key
<li> Derivation Function (KDF):</t>
<t>3. Derive a shared secret from the integer z using a Key Derivati
on Function (KDF):</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
SS = KDF(Z, ssLen) SS = KDF(Z, ssLen)]]></artwork>
]]></artwork> </li>
<ul empty="true"> <li><t>The ciphertext and the shared secret are returned by the
<li> function. The originator sends the ciphertext to the
<t>4. The ciphertext and the shared secret are returned by the funct recipient.</t>
ion. The </li>
originator sends the ciphertext to the recipient.</t> </ol>
</li> </dd>
</ul> <dt>Decapsulate(sk, ct) -&gt; SS:</dt>
<t>Decapsulate(sk, ct) -&gt; SS:</t> <dd><t>Given the private key (sk) and the ciphertext (ct), produce
<ul empty="true"> the shared secret (SS) for the recipient as follows:</t>
<li> <ol type="1" spacing="normal">
<t>Given the private key (sk) and the ciphertext (ct), produce the <li><t>Decrypt the ciphertext with the recipient's RSA private
shared secret (SS) for the recipient as follows:</t> key to obtain the random integer z:</t>
</li>
</ul>
<ul empty="true">
<li>
<t>1. Decrypt the ciphertext with the recipient's RSA private key
to obtain the random integer z:</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
z = ct^d mod n z = ct^d mod n]]></artwork>
]]></artwork> </li>
<ul empty="true"> <li><t>Derive a shared secret from the integer z:</t>
<li>
<t>2. Derive a shared secret from the integer z:</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
SS = KDF(Z, ssLen) SS = KDF(Z, ssLen)]]></artwork>
]]></artwork> </li>
<t>3. The shared secret is returned by the function.</t> <li><t>The shared secret is returned by the function.</t></li>
</ol>
</dd>
</dl>
</section> </section>
<section anchor="cms-kemrecipientinfo-processing-summary"> <section anchor="cms-kemrecipientinfo-processing-summary">
<name>CMS KEMRecipientInfo Processing Summary</name> <name>CMS KEMRecipientInfo Processing Summary</name>
<t>To support the RSA-KEM algorithm, the CMS originator <bcp14>MUST</bcp <t>To support the RSA-KEM algorithm, the CMS originator
14> implement <bcp14>MUST</bcp14> implement Encapsulate().</t>
Encapsulate().</t> <t>Given a content-encryption key CEK, the RSA-KEM algorithm
<t>Given a content-encryption key CEK, the RSA-KEM Algorithm processing processing by the originator to produce the values that are carried in
by the the CMS KEMRecipientInfo can be summarized as follows:</t>
originator to produce the values that are carried in the CMS KEMRecipientInfo
can be summarized as:</t> <ol type="1" spacing="normal">
<ul empty="true">
<li> <li>
<t>1. Obtain the shared secret using the Encapsulate() function of <t>Obtain the shared secret using the Encapsulate() function of
the the RSA-KEM algorithm and the recipient's RSA public key:</t>
RSA-KEM algorithm and the recipient's RSA public key:</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
(ct, SS) = Encapsulate(pk) (ct, SS) = Encapsulate(pk)]]></artwork>
]]></artwork> </li>
<ul empty="true">
<li> <li>
<t>2. Derive a key-encryption key KEK from the shared secret:</t> <t>Derive a key-encryption key KEK from the shared secret:</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
KEK = KDF(SS, kekLength, otherInfo) KEK = KDF(SS, kekLength, otherInfo)]]></artwork>
]]></artwork> </li>
<ul empty="true">
<li> <li>
<t>3. Wrap the CEK with the KEK to obtain wrapped keying material W <t>Wrap the CEK with the KEK to obtain wrapped keying material WK:</
K:</t> t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
WK = WRAP(KEK, CEK) WK = WRAP(KEK, CEK)
]]></artwork> ]]></artwork>
<ul empty="true"> </li>
<li> <li>
<t>4. The originator sends the ciphertext and WK to the recipient in <t>The originator sends the ciphertext and WK to the recipient in
the CMS the CMS KEMRecipientInfo structure.</t>
KEMRecipientInfo structure.</t>
</li> </li>
</ul> </ol>
<t>To support the RSA-KEM algorithm, the CMS recipient <bcp14>MUST</bcp1
4> implement <t>To support the RSA-KEM algorithm, the CMS recipient
Decapsulate().</t> <bcp14>MUST</bcp14> implement Decapsulate().</t>
<t>The RSA-KEM algorithm recipient processing of the values obtained fro <t>The RSA-KEM algorithm recipient processing of the values obtained
m the from the KEMRecipientInfo structure is summarized as follows:</t>
KEMRecipientInfo structure can be summarized as:</t>
<ul empty="true"> <ol type="1" spacing="normal">
<li> <li>
<t>1. Obtain the shared secret using the Decapsulate() function of <t>Obtain the shared secret using the Decapsulate() function of
the the RSA-KEM algorithm and the recipient's RSA private key:</t>
RSA-KEM algorithm and the recipient's RSA private key:</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
SS = Decapsulate(sk, ct) SS = Decapsulate(sk, ct)]]></artwork>
]]></artwork> </li>
<ul empty="true">
<li> <li>
<t>2. Derive a key-encryption key KEK from the shared secret:</t> <t>Derive a key-encryption key KEK from the shared secret:</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
KEK = KDF(SS, kekLength, otherInfo) KEK = KDF(SS, kekLength, otherInfo)]]></artwork>
]]></artwork> </li>
<ul empty="true">
<li> <li>
<t>3. Unwrap the WK with the KEK to obtain content-encryption key C <t>Unwrap the WK with the KEK to obtain the content-encryption key C
EK:</t> EK:</t>
</li>
</ul>
<artwork><![CDATA[ <artwork><![CDATA[
CEK = UNWRAP(KEK, WK) CEK = UNWRAP(KEK, WK)]]></artwork>
]]></artwork> </li>
</ol>
<t>Note that the KDF used to process the KEMRecipientInfo structure <bcp 14>MAY</bcp14> be <t>Note that the KDF used to process the KEMRecipientInfo structure <bcp 14>MAY</bcp14> be
different from the KDF used to derive the shared secret in the RSA-KEM different from the KDF used to derive the shared secret in the RSA-KEM
algorithm.</t> algorithm.</t>
</section> </section>
<section anchor="conventions-and-definitions"> <section anchor="conventions-and-definitions">
<name>Conventions and Definitions</name> <name>Conventions and Definitions</name>
<t>The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp <t>
14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp14>REQU
NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>RECO IRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL
MMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>", NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>
"<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to be i RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>",
nterpreted as "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to
described in BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and be interpreted as
only when, they described in BCP&nbsp;14 <xref target="RFC2119"/> <xref target="RFC8174"/>
appear in all capitals, as shown here.</t> when, and only when, they appear in all capitals, as shown here.
<?line -18?> </t>
</section>
</section>
<section anchor="asn1"> <section anchor="asn1">
<name>ASN.1</name> <name>ASN.1</name>
<t>CMS values are generated using ASN.1 <xref target="X.680"/>, which us es the Basic <t>CMS values are generated using ASN.1 <xref target="X.680"/>, which us es the Basic
Encoding Rules (BER) and the Distinguished Encoding Rules (DER) <xref target="X. 690"/>.</t> Encoding Rules (BER) and the Distinguished Encoding Rules (DER) <xref target="X. 690"/>.</t>
</section> </section>
<section anchor="changes-since-rfc-5990"> <section anchor="changes-since-rfc-5990">
<name>Changes Since RFC 5990</name> <name>Changes Since RFC 5990</name>
<t>RFC 5990 <xref target="RFC5990"/> specified the conventions for using the RSA-KEM Algorithm <t>RFC 5990 <xref target="RFC5990"/> specified the conventions for using the RSA-KEM algorithm
in CMS as a key transport algorithm. That is, it used KeyTransRecipientInfo <xr ef target="RFC5652"/> in CMS as a key transport algorithm. That is, it used KeyTransRecipientInfo <xr ef target="RFC5652"/>
for each recipient. Since the publication of RFC 5990, a new KEMRecipientInfo for each recipient. Since the publication of RFC 5990, a new KEMRecipientInfo
structure <xref target="I-D.ietf-lamps-cms-kemri"/> has been defined to support KEM structure <xref target="RFC9629"/> has been defined to support KEM
algorithms. When the id-rsa-kem algorithm identifier appears in the algorithms. When the id-rsa-kem algorithm identifier appears in the
SubjectPublicKeyInfo field of a certificate, the complex parameter structure SubjectPublicKeyInfo field of a certificate, the complex parameter structure
defined in RFC 5990 can be omitted; however, the parameters are allowed for defined in RFC 5990 can be omitted; however, the parameters are allowed for
backward compatibility. Also, to avoid visual confusion with id-kem-rsa, backward compatibility. Also, to avoid visual confusion with id-kem-rsa,
id-rsa-kem-spki is introduced as an alias for id-rsa-kem.</t> id-rsa-kem-spki is introduced as an alias for id-rsa-kem.</t>
<t>RFC 5990 used EK as the EncryptedKey, which is the concatenation of <t>RFC 5990 used EK as the EncryptedKey, which is the concatenation of
the ciphertext C and the wrapped key WK, EK = (C || WK). The use of EK was the ciphertext C and the wrapped key WK, EK = (C || WK). The use of EK was
necessary to align with the KeyTransRecipientInfo structure. In this necessary to align with the KeyTransRecipientInfo structure. In this
document, the ciphertext and the wrapped key are sent in separate fields of document, the ciphertext and the wrapped key are sent in separate fields of
the KEMRecipientInfo structure. In particular, the ciphertext is carried in the KEMRecipientInfo structure. In particular, the ciphertext is carried in
the kemct field, and wrapped key is carried in the encryptedKey the kemct field, and the wrapped key is carried in the encryptedKey
field. See <xref target="app-alg"/> for details about the computation of the ci phertext.</t> field. See <xref target="app-alg"/> for details about the computation of the ci phertext.</t>
<t>RFC 5990 included support for Camellia and Triple-DES block ciphers; <t>RFC 5990 included support for Camellia and Triple-DES block ciphers;
discussion of these block ciphers is removed from this document, but discussion of these block ciphers does not appear in this document, but
the algorithm identifiers remain in the ASN.1 Module <xref target="app-asn1-modu the algorithm identifiers remain in the ASN.1 module (see <xref target="app-asn1
le"/>.</t> -module"/>).</t>
<t>RFC 5990 included support for SHA-1 hash function; discussion of this <t>RFC 5990 included support for SHA-1 hash function; discussion of this
hash function is removed from this document, but the algorithm identifier hash function does not appear this document, but the algorithm identifier
remains in the ASN.1 module <xref target="app-asn1-module"/>.</t> remains in the ASN.1 module (see <xref target="app-asn1-module"/>).</t>
<t>RFC 5990 required support for the KDF3 key-derivation function <xref <t>RFC 5990 required support for the KDF3 key derivation function
target="ANS-X9.44"/>; <xref target="ANS-X9.44"/>; this document continues to require
this document continues to require support for the KDF3 key-derivation function, support for the KDF3 key derivation function, but it requires support
but it requires support for SHA-256 <xref target="SHS"/> as the hash function.</ for SHA-256 <xref target="SHS"/> as the hash function.</t>
t>
<t>RFC 5990 recommended support for alternatives to KDF3 and AES-Wrap-12 8; <t>RFC 5990 recommended support for alternatives to KDF3 and AES-Wrap-12 8;
this document simply states that other key-derivation functions and other this document simply states that other key derivation functions and other
key-encryption algorithms <bcp14>MAY</bcp14> be supported.</t> key-encryption algorithms <bcp14>MAY</bcp14> be supported.</t>
<t>RFC 5990 supported the future definition of additional KEM algorithms that <t>RFC 5990 supported the future definition of additional KEM algorithms that
use RSA; this document supports only one, and it is identified by the use RSA; this document supports only one, and it is identified by the
id-kem-rsa object identifier.</t> id-kem-rsa object identifier.</t>
<t>RFC 5990 included an ASN.1 module; this document provides an alternat ive <t>RFC 5990 included an ASN.1 module; this document provides an alternat ive
ASN.1 module that follows the conventions established in <xref target="RFC5911"/ >, ASN.1 module that follows the conventions established in <xref target="RFC5911"/ >,
<xref target="RFC5912"/>, and <xref target="RFC6268"/>. The new ASN.1 module <x ref target="app-asn1-module"/> <xref target="RFC5912"/>, and <xref target="RFC6268"/>. The new ASN.1 module (< xref target="app-asn1-module"/>)
produces the same bits-on-the-wire as the one in RFC 5990.</t> produces the same bits-on-the-wire as the one in RFC 5990.</t>
</section> </section>
</section> </section>
<section anchor="use-of-the-rsa-kem-algorithm-in-cms"> <section anchor="use-of-the-rsa-kem-algorithm-in-cms">
<name>Use of the RSA-KEM Algorithm in CMS</name> <name>Use of the RSA-KEM Algorithm in CMS</name>
<t>The RSA-KEM Algorithm <bcp14>MAY</bcp14> be employed for one or more re cipients in the <t>The RSA-KEM algorithm <bcp14>MAY</bcp14> be employed for one or more re cipients in the
CMS enveloped-data content type <xref target="RFC5652"/>, the CMS authenticated- data CMS enveloped-data content type <xref target="RFC5652"/>, the CMS authenticated- data
content type <xref target="RFC5652"/>, or the CMS authenticated-enveloped-data content type <xref target="RFC5652"/>, or the CMS authenticated-enveloped-data
content type <xref target="RFC5083"/>. In each case, the KEMRecipientInfo content type <xref target="RFC5083"/>. In each case, the KEMRecipientInfo
<xref target="I-D.ietf-lamps-cms-kemri"/> is used with the RSA-KEM Algorithm <xref target="RFC9629"/> is used with the RSA-KEM algorithm
to securely transfer the content-encryption key from the originator to to securely transfer the content-encryption key from the originator to
the recipient.</t> the recipient.</t>
<section anchor="mandatory-to-implement"> <section anchor="mandatory-to-implement">
<name>Mandatory To Implement</name> <name>Mandatory To Implement</name>
<t>A CMS implementation that supports the RSA-KEM Algorithm <bcp14>MUST< /bcp14> support at <t>A CMS implementation that supports the RSA-KEM algorithm <bcp14>MUST< /bcp14> support at
least the following underlying components:</t> least the following underlying components:</t>
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t>For the key-derivation function, an implementation <bcp14>MUST</b cp14> support <t>For the key derivation function, an implementation <bcp14>MUST</b cp14> support
KDF3 <xref target="ANS-X9.44"/> with SHA-256 <xref target="SHS"/>.</t> KDF3 <xref target="ANS-X9.44"/> with SHA-256 <xref target="SHS"/>.</t>
</li> </li>
<li> <li>
<t>For key-wrapping, an implementation <bcp14>MUST</bcp14> support t he <t>For key-wrapping, an implementation <bcp14>MUST</bcp14> support t he
AES-Wrap-128 <xref target="RFC3394"/> key-encryption algorithm.</t> AES-Wrap-128 <xref target="RFC3394"/> key-encryption algorithm.</t>
</li> </li>
</ul> </ul>
<t>An implementation <bcp14>MAY</bcp14> also support other key-derivatio <t>An implementation <bcp14>MAY</bcp14> also support other key derivatio
n functions and n functions and
other key-encryption algorithms as well.</t> other key-encryption algorithms.</t>
</section> </section>
<section anchor="recipientinfo-conventions"> <section anchor="recipientinfo-conventions">
<name>RecipientInfo Conventions</name> <name>RecipientInfo Conventions</name>
<t>When the RSA-KEM Algorithm is employed for a recipient, the <t>When the RSA-KEM algorithm is employed for a recipient, the
RecipientInfo alternative for that recipient <bcp14>MUST</bcp14> be RecipientInfo alternative for that recipient <bcp14>MUST</bcp14> be
OtherRecipientInfo using the KEMRecipientInfo structure OtherRecipientInfo using the KEMRecipientInfo structure
<xref target="I-D.ietf-lamps-cms-kemri"/>. The fields of the <xref target="RFC9629"/>. The fields of the
KEMRecipientInfo <bcp14>MUST</bcp14> have the following values:</t> KEMRecipientInfo <bcp14>MUST</bcp14> have the following values:</t>
<ul empty="true">
<li> <ul spacing="normal">
<t>version is the syntax version number; it <bcp14>MUST</bcp14> be 0 <li>version is the syntax version number; it <bcp14>MUST</bcp14> be
.</t> 0.</li>
</li>
</ul> <li>rid identifies the recipient's certificate or public key.</li>
<ul empty="true">
<li> <li>kem identifies the KEM algorithm; it <bcp14>MUST</bcp14> contain
<t>rid identifies the recipient's certificate or public key.</t> id-kem-rsa.</li>
</li>
</ul> <li>kemct is the ciphertext produced for this recipient;
<ul empty="true"> it contains C from steps 1 and 2 of Originator's Operations in
<li> <xref target="app-alg"/>.</li>
<t>kem identifies the KEM algorithm; it <bcp14>MUST</bcp14> contain
id-kem-rsa.</t> <li>kdf identifies the key derivation function (KDF).
</li> Note that the KDF used for CMS RecipientInfo process
</ul> <bcp14>MAY</bcp14> be different than the KDF used within the
<ul empty="true"> RSA-KEM algorithm.</li>
<li>
<t>kemct is the ciphertext produced for this recipient; it contains <li>kekLength is the size of the key-encryption key in octets.</li>
C from steps 1 and 2 of Originator's Operations in <xref target="app-alg"/>.</t>
</li> <li>ukm is an optional random input to the key derivation function.<
</ul> /li>
<ul empty="true">
<li> <li>wrap identifies a key-encryption algorithm used to
<t>kdf identifies the key-derivation function (KDF). Note that the encrypt the keying material.</li>
KDF used for CMS RecipientInfo process <bcp14>MAY</bcp14> be different than the
KDF <li>encryptedKey is the result of encrypting the keying material wit
used within the RSA-KEM Algorithm.</t> h the
</li>
</ul>
<ul empty="true">
<li>
<t>kekLength is the size of the key-encryption key in octets.</t>
</li>
</ul>
<ul empty="true">
<li>
<t>ukm is an optional random input to the key-derivation function.</
t>
</li>
</ul>
<ul empty="true">
<li>
<t>wrap identifies a key-encryption algorithm used to encrypt the
keying material.</t>
</li>
</ul>
<ul empty="true">
<li>
<t>encryptedKey is the result of encrypting the keying material with
the
key-encryption key. When used with the CMS enveloped-data content key-encryption key. When used with the CMS enveloped-data content
type <xref target="RFC5652"/>, the keying material is a content-encryption key. When type <xref target="RFC5652"/>, the keying material is a content-encryption key. When
used with the CMS authenticated-data content type <xref target="RFC5652"/>, the used with the CMS authenticated-data content type <xref target="RFC5652"/>, the
keying material is a message-authentication key. When used with the keying material is a message-authentication key. When used with the
CMS authenticated-enveloped-data content type <xref target="RFC5083"/>, the CMS authenticated-enveloped-data content type <xref target="RFC5083"/>, the
keying material is a content-authenticated-encryption key.</t> keying material is a content-authenticated-encryption key (CAEK).</li>
</li> </ul>
</ul> <t>NOTE: For backward compatibility, implementations <bcp14>MAY</bcp14> also sup
<t>NOTE: For backward compatibility, implementations <bcp14>MAY</bcp14> port
also support the RSA-KEM Key Transport algorithm, identified by id-rsa-kem-spki, which uses
RSA-KEM Key Transport Algorithm, identified by id-rsa-kem-spki, which uses
KeyTransRecipientInfo as specified in <xref target="RFC5990"/>.</t> KeyTransRecipientInfo as specified in <xref target="RFC5990"/>.</t>
</section> </section>
<section anchor="certificate-conventions"> <section anchor="certificate-conventions">
<name>Certificate Conventions</name> <name>Certificate Conventions</name>
<t>The conventions specified in this section augment RFC 5280 <xref targ et="RFC5280"/>.</t> <t>The conventions specified in this section augment RFC 5280 <xref targ et="RFC5280"/>.</t>
<t>A recipient who employs the RSA-KEM Algorithm <bcp14>MAY</bcp14> iden tify the public key <t>A recipient who employs the RSA-KEM algorithm <bcp14>MAY</bcp14> iden tify the public key
in a certificate by the same AlgorithmIdentifier as for the in a certificate by the same AlgorithmIdentifier as for the
PKCS #1 v1.5 algorithm, that is, using the rsaEncryption object PKCS #1 v1.5 algorithm, that is, using the rsaEncryption object
identifier <xref target="RFC8017"/>. The fact that the recipient will accept RS A-KEM identifier <xref target="RFC8017"/>. The fact that the recipient will accept RS A-KEM
with this public key is not indicated by the use of this object with this public key is not indicated by the use of this object
identifier. The willingness to accept the RSA-KEM Algorithm <bcp14>MAY</bcp14> be identifier. The willingness to accept the RSA-KEM algorithm <bcp14>MAY</bcp14> be
signaled by the use of the SMIMECapabilities Attribute as specified in signaled by the use of the SMIMECapabilities Attribute as specified in
<xref section="2.5.2." sectionFormat="of" target="RFC8551"/> or the SMIMECapabil ities certificate <xref section="2.5.2" sectionFormat="of" target="RFC8551"/> or the SMIMECapabili ties certificate
extension as specified in <xref target="RFC4262"/>.</t> extension as specified in <xref target="RFC4262"/>.</t>
<t>If the recipient wishes only to employ the RSA-KEM Algorithm with a g iven <t>If the recipient wishes only to employ the RSA-KEM algorithm with a g iven
public key, the recipient <bcp14>MUST</bcp14> identify the public key in the cer tificate public key, the recipient <bcp14>MUST</bcp14> identify the public key in the cer tificate
using the id-rsa-kem-spki object identifier; see <xref target="app-asn1"/>. The use using the id-rsa-kem-spki object identifier; see <xref target="app-asn1"/>. The use
of the id-rsa-kem-spki object identifier allows certificates that were of the id-rsa-kem-spki object identifier allows certificates that were
issued to be compatible with RSA-KEM Key Transport to also be used with issued to be compatible with RSA-KEM Key Transport to also be used with
this specification. When the id-rsa-kem-spki object identifier appears this specification. When the id-rsa-kem-spki object identifier appears
in the SubjectPublicKeyInfo algorithm field of the certificate, the in the SubjectPublicKeyInfo algorithm field of the certificate, the
parameters field from AlgorithmIdentifier <bcp14>SHOULD</bcp14> be absent. That is, the parameters field from AlgorithmIdentifier <bcp14>SHOULD</bcp14> be absent. That is, the
AlgorithmIdentifier <bcp14>SHOULD</bcp14> be a SEQUENCE of one component, the AlgorithmIdentifier <bcp14>SHOULD</bcp14> be a SEQUENCE of one component, the
id-rsa-kem-spki object identifier. With absent parameters, the KDF3 id-rsa-kem-spki object identifier. With absent parameters, the KDF3
key-derivation function <xref target="ANS-X9.44"/> with SHA-256 <xref target="SH S"/> are used to key derivation function <xref target="ANS-X9.44"/> with SHA-256 <xref target="SH S"/> are used to
derive the shared secret.</t> derive the shared secret.</t>
<t>When the AlgorithmIdentifier parameters are present, the <t>When the AlgorithmIdentifier parameters are present, the
GenericHybridParameters <bcp14>MUST</bcp14> be used. Within the kem element, th e algorithm GenericHybridParameters <bcp14>MUST</bcp14> be used. Within the kem element, th e algorithm
identifier <bcp14>MUST</bcp14> be set to id-kem-rsa, and RsaKemParameters <bcp14 >MUST</bcp14> be included. identifier <bcp14>MUST</bcp14> be set to id-kem-rsa, and RsaKemParameters <bcp14 >MUST</bcp14> be included.
As described in <xref target="smimecap"/>, the GenericHybridParameters constrain the values As described in <xref target="smimecap"/>, the GenericHybridParameters constrain the values
that can be used with the RSA public key for the kdf, kekLength, and wrap that can be used with the RSA public key for the kdf, kekLength, and wrap
fields of the KEMRecipientInfo structure.</t> fields of the KEMRecipientInfo structure.</t>
<t>Regardless of the AlgorithmIdentifier used, the RSA public key <bcp14 >MUST</bcp14> be <t>Regardless of the AlgorithmIdentifier used, the RSA public key <bcp14 >MUST</bcp14> be
carried in the subjectPublicKey BIT STRING within the SubjectPublicKeyInfo carried in the subjectPublicKey BIT STRING within the SubjectPublicKeyInfo
field of the certificate using the RSAPublicKey type defined in <xref target="RF C8017"/>.</t> field of the certificate using the RSAPublicKey type defined in <xref target="RF C8017"/>.</t>
<t>The intended application for the public key <bcp14>MAY</bcp14> be ind icated in the key usage <t>The intended application for the public key <bcp14>MAY</bcp14> be ind icated in the key usage
certificate extension as specified in <xref section="4.2.1.3" sectionFormat="of" target="RFC5280"/>. If the certificate extension as specified in <xref section="4.2.1.3" sectionFormat="of" target="RFC5280"/>. If the
keyUsage extension is present in a certificate that conveys an RSA public key keyUsage extension is present in a certificate that conveys an RSA public key
with the id-rsa-kem-spki object identifier as discussed above, then the key with the id-rsa-kem-spki object identifier as discussed above, then the key
usage extension <bcp14>MUST</bcp14> contain only the following value:</t> usage extension <bcp14>MUST</bcp14> contain only the following value:</t>
<ul empty="true"> <t indent="3">keyEncipherment</t>
<li>
<t>keyEncipherment</t>
</li>
</ul>
<t>Other keyUsage extension values <bcp14>MUST NOT</bcp14> be <t>Other keyUsage extension values <bcp14>MUST NOT</bcp14> be
present. That is, a public key intended to be employed only with the present. That is, a public key intended to be employed only with the
RSA-KEM Algorithm <bcp14>MUST NOT</bcp14> also be employed for data encryption o r RSA-KEM algorithm <bcp14>MUST NOT</bcp14> also be employed for data encryption o r
for digital signatures. Good cryptographic practice employs a given RSA for digital signatures. Good cryptographic practice employs a given RSA
key pair in only one scheme. This practice avoids the risk that vulnerability key pair in only one scheme. This practice avoids the risk that vulnerability
in one scheme may compromise the security of the other, and may be essential in one scheme may compromise the security of the other and may be essential
to maintain provable security.</t> to maintain provable security.</t>
</section> </section>
<section anchor="smimecap"> <section anchor="smimecap">
<name>SMIMECapabilities Attribute Conventions</name> <name>SMIMECapabilities Attribute Conventions</name>
<t><xref section="2.5.2" sectionFormat="of" target="RFC8551"/> defines t he SMIMECapabilities attribute to <t><xref section="2.5.2" sectionFormat="of" target="RFC8551"/> defines t he SMIMECapabilities attribute to
announce a partial list of algorithms that an S/MIME implementation can announce a partial list of algorithms that an S/MIME implementation can
support. When constructing a CMS signed-data content type <xref target="RFC5652 "/>, support. When constructing a CMS signed-data content type <xref target="RFC5652 "/>,
a compliant implementation <bcp14>MAY</bcp14> include the SMIMECapabilities attr ibute a compliant implementation <bcp14>MAY</bcp14> include the SMIMECapabilities attr ibute
that announces support for the RSA-KEM Algorithm.</t> that announces support for the RSA-KEM algorithm.</t>
<t>The SMIMECapability SEQUENCE representing the RSA-KEM Algorithm <bcp1 <t>The SMIMECapability SEQUENCE representing the RSA-KEM algorithm <bcp1
4>MUST</bcp14> 4>MUST</bcp14>
include the id-rsa-kem-spki object identifier in the capabilityID field; include the id-rsa-kem-spki object identifier in the capabilityID field;
see <xref target="app-asn1"/> for the object identifier value, and see <xref tar get="app-example"/> see <xref target="app-asn1"/> for the object identifier value and <xref target=" app-example"/>
for examples. When the id-rsa-kem-spki object identifier appears in the for examples. When the id-rsa-kem-spki object identifier appears in the
capabilityID field and the parameters are present, then the parameters capabilityID field and the parameters are present, then the parameters
field <bcp14>MUST</bcp14> use the GenericHybridParameters type.</t> field <bcp14>MUST</bcp14> use the GenericHybridParameters type.</t>
<artwork><![CDATA[
<sourcecode type="asn.1">
GenericHybridParameters ::= SEQUENCE { GenericHybridParameters ::= SEQUENCE {
kem KeyEncapsulationMechanism, kem KeyEncapsulationMechanism,
dem DataEncapsulationMechanism } dem DataEncapsulationMechanism }</sourcecode>
]]></artwork>
<t>The fields of the GenericHybridParameters type have the following mea nings:</t> <t>The fields of the GenericHybridParameters type have the following mea nings:</t>
<ul empty="true"> <ul>
<li> <li>
<t>kem is an AlgorithmIdentifer. The algorithm field <bcp14>MUST</b cp14> be set to id-kem-rsa, <t>kem is an AlgorithmIdentifer. The algorithm field <bcp14>MUST</b cp14> be set to id-kem-rsa,
and the parameters field <bcp14>MUST</bcp14> be RsaKemParameters, which is a SEQ UENCE of an and the parameters field <bcp14>MUST</bcp14> be RsaKemParameters, which is a SEQ UENCE of an
AlgorithmIdentifier that identifies the supported key-derivation function AlgorithmIdentifier that identifies the supported key derivation function
and a positive INTEGER that identifies the length of the key-encryption and a positive INTEGER that identifies the length of the key-encryption
key in octets.</t> key in octets.</t>
</li> </li>
</ul>
<ul empty="true">
<li> <li>
<t>dem is an AlgorithmIdentifier. The algorithm field <bcp14>MUST</ bcp14> be present, and it <t>dem is an AlgorithmIdentifier. The algorithm field <bcp14>MUST</ bcp14> be present, and it
identifies the key-encryption algorithm. The parameters are optional. If the identifies the key-encryption algorithm. The parameters are optional. If the
GenericHybridParameters are present, then the provided dem value <bcp14>MUST</bc p14> be GenericHybridParameters are present, then the provided dem value <bcp14>MUST</bc p14> be
used in the wrap field of KEMRecipientInfo.</t> used in the wrap field of KEMRecipientInfo.</t>
</li> </li>
</ul> </ul>
<t>If the GenericHybridParameters are present, then the provided kem val ue <bcp14>MUST</bcp14> <t>If the GenericHybridParameters are present, then the provided kem val ue <bcp14>MUST</bcp14>
be used as the key-derivation function in the kdf field of KEMRecipientInfo, be used as the key derivation function in the kdf field of KEMRecipientInfo
and the provided key length <bcp14>MUST</bcp14> be used in the kekLength of KEMR ecipientInfo.</t> and the provided key length <bcp14>MUST</bcp14> be used in the kekLength of KEMR ecipientInfo.</t>
</section> </section>
</section> </section>
<section anchor="security-considerations"> <section anchor="security-considerations">
<name>Security Considerations</name> <name>Security Considerations</name>
<t>The RSA-KEM Algorithm should be considered as a replacement for the key transport portion of the <t>The RSA-KEM algorithm should be considered as a replacement for the key transport portion of the
widely implemented PKCS #1 v1.5 <xref target="RFC8017"/> for new applications widely implemented PKCS #1 v1.5 <xref target="RFC8017"/> for new applications
that use CMS to avoid potential vulnerabilities to chosen-ciphertext that use CMS to avoid potential vulnerabilities to chosen-ciphertext
attacks and gain a tighter security proof; however, the RSA-KEM Algorithm attacks and gain a tighter security proof. However, the RSA-KEM algorithm
has the disadvantage of slightly longer encrypted keying material. With has the disadvantage of slightly longer encrypted keying material. With
PKCS #1 v1.5, the originator encrypts the key-encryption key directly with PKCS #1 v1.5, the originator encrypts the key-encryption key directly with
the recipient's RSA public key. With the RSA-KEM, the key-encryption key the recipient's RSA public key. With the RSA-KEM, the key-encryption key
is encrypted separately.</t> is encrypted separately.</t>
<t>The security of the RSA-KEM Algorithm can be shown to be tightly relate <t> The security of the RSA-KEM algorithm can be shown to be tightly related
d to the difficulty of either solving the RSA problem or breaking the underlying
to the difficulty of either solving the RSA problem, or breaking the symmetric key-encryption algorithm if the underlying key derivation function
underlying symmetric key-encryption algorithm, if the underlying is modeled as a random oracle, assuming that the symmetric key-encryption
key-derivation function is modeled as a random oracle, and assuming that algorithm satisfies the properties of a data encapsulation mechanism <xref
the symmetric key-encryption algorithm satisfies the properties of a target="SHOUP"/>. While in practice a random-oracle result does not provide
data encapsulation mechanism <xref target="SHOUP"/>. While in practice a random an actual security proof for any particular key derivation function, the
-oracle result does provide assurance that the general construction is reasonable; a
result does not provide an actual security proof for any particular key derivation function would need to be particularly weak to lead to an
key-derivation function, the result does provide assurance that the general attack that is not possible in the random-oracle model.</t>
construction is reasonable; a key-derivation function would need to be
particularly weak to lead to an attack that is not possible in the
random-oracle model.</t>
<t>The RSA key size and the underlying components need to be selected <t>The RSA key size and the underlying components need to be selected
consistent with the desired security level. Several security levels consistent with the desired security level. Several security levels
have been identified in the NIST SP 800-57 Part 1 <xref target="NISTSP800-57pt1r 5"/>. For example, one way have been identified in the NIST SP 800-57 Part 1 <xref target="NISTSP800-57pt1r 5"/>. For example, one way
to achieve 128-bit security, the RSA key size would be at least 3072 bits, to achieve 128-bit security, the RSA key size would be at least 3072 bits,
the key-derivation function would be SHA-256, and the symmetric the key derivation function would be SHA-256, and the symmetric
key-encryption algorithm would be AES Key Wrap with a 128-bit key.</t> key-encryption algorithm would be AES Key Wrap with a 128-bit key.</t>
<t>Implementations <bcp14>MUST</bcp14> protect the RSA private key, the ke y-encryption key, <t>Implementations <bcp14>MUST</bcp14> protect the RSA private key, the ke y-encryption key,
the content-encryption key, message-authentication key, and the the content-encryption key, message-authentication key, and the
content-authenticated-encryption key. Disclosure of the RSA private key content-authenticated-encryption key. Disclosure of the RSA private key
could result in the compromise of all messages protected with that key. could result in the compromise of all messages protected with that key.
Disclosure of the key-encryption key, the content-encryption key, or the Disclosure of the key-encryption key, the content-encryption key, or the
content-authenticated-encryption key could result in compromise of the content-authenticated-encryption key could result in compromise of the
associated encrypted content. Disclosure of the key-encryption key, the associated encrypted content. Disclosure of the key-encryption key, the
message-authentication key, or the content-authenticated-encryption key message-authentication key, or the content-authenticated-encryption key
could allow modification of the associated authenticated content.</t> could allow modification of the associated authenticated content.</t>
<t>Additional considerations related to key management may be found in <t>Additional considerations related to key management may be found in
<xref target="NISTSP800-57pt1r5"/>.</t> <xref target="NISTSP800-57pt1r5"/>.</t>
<t>The security of the RSA-KEM Algorithm depends on a quality random numbe r <t>The security of the RSA-KEM algorithm depends on a quality random numbe r
generator. For further discussion on random number generation, generator. For further discussion on random number generation,
see <xref target="RFC4086"/>.</t> see <xref target="RFC4086"/>.</t>
<t>The RSA-KEM Algorithm does not use an explicit padding scheme; instead, <t>The RSA-KEM algorithm does not use an explicit padding scheme. Instead,
an encoded random value (z) between zero and the RSA modulus minus one (n-1) an encoded random value (z) between zero and the RSA modulus minus one (n-1)
is directly encrypted with the recipient's RSA public key. The is directly encrypted with the recipient's RSA public key. The
IntegerToString(z, nLen) encoding produces a string that is the full length of IntegerToString(z, nLen) encoding produces a string that is the full length of
the RSA modulus. In addition, the random value is passed through a key-derivati the RSA modulus. In addition, the random value is passed through a
on KDF to reduce possible harm from a poorly implemented random number
function (KDF) to reduce possible harm from a poorly implemented random number
source or a maliciously chosen random value (z). Implementations <bcp14>MUST NO T</bcp14> source or a maliciously chosen random value (z). Implementations <bcp14>MUST NO T</bcp14>
use z directly for any purpose.</t> use z directly for any purpose.</t>
<t>As long as a fresh random integer z is chosen as part of each invocatio n <t>As long as a fresh random integer z is chosen as part of each invocatio n
of the Encapsulate() function, RSA-KEM does not degrade as the number of of the Encapsulate() function, RSA-KEM does not degrade as the number of
ciphertexts increases. Since RSA encryption provides a bijective map, ciphertexts increases. Since RSA encryption provides a bijective map,
a collision in the KDF is the only way that RSA-KEM can produce more than a collision in the KDF is the only way that RSA-KEM can produce more than
one ciphertext that encapsulates the same shared secret.</t> one ciphertext that encapsulates the same shared secret.</t>
<t>The RSA-KEM Algorithm provides a fixed-length ciphertext. The recipien t <bcp14>MUST</bcp14> <t>The RSA-KEM algorithm provides a fixed-length ciphertext. The recipien t <bcp14>MUST</bcp14>
check that the received byte string is the expected length and the length check that the received byte string is the expected length and the length
corresponds to an integer in the expected range prior to attempting decryption corresponds to an integer in the expected range prior to attempting decryption
with their RSA private key as described in Steps 1 and 2 of <xref target="app-al g-decap"/>.</t> with their RSA private key as described in Steps 1 and 2 of <xref target="app-al g-decap"/>.</t>
<t>Implementations <bcp14>SHOULD NOT</bcp14> reveal information about inte rmediate <t>Implementations <bcp14>SHOULD NOT</bcp14> reveal information about inte rmediate
values or calculations, whether by timing or other "side channels", values or calculations, whether by timing or other "side channels";
otherwise an opponent may be able to determine information about otherwise, an opponent may be able to determine information about
the keying data and/or the recipient's private key. Although not all the keying data and/or the recipient's private key. Although not all
intermediate information may be useful to an opponent, it is intermediate information may be useful to an opponent, it is
preferable to conceal as much information as is practical, unless preferable to conceal as much information as is practical, unless
analysis specifically indicates that the information would not be analysis specifically indicates that the information would not be
useful to an opponent.</t> useful to an opponent.</t>
<t>Generally, good cryptographic practice employs a given RSA key pair <t>Generally, good cryptographic practice employs a given RSA key pair
in only one scheme. This practice avoids the risk that vulnerability in only one scheme. This practice avoids the risk that vulnerability
in one scheme may compromise the security of the other, and may be in one scheme may compromise the security of the other, and may be
essential to maintain provable security. RSA public keys have often essential to maintain provable security. RSA public keys have often
been employed for multiple purposes such as key transport and digital been employed for multiple purposes such as key transport and digital
signature without any known bad interactions; however, such combined use signature without any known bad interactions; however, such combined use
of an RSA key pair is <bcp14>NOT RECOMMENDED</bcp14> in the future (unless the d ifferent of an RSA key pair is <bcp14>NOT RECOMMENDED</bcp14> in the future (unless the d ifferent
schemes are specifically designed to be used together).</t> schemes are specifically designed to be used together).</t>
<t>Accordingly, an RSA key pair used for the RSA-KEM Algorithm <bcp14>SHOU LD NOT</bcp14> <t>Accordingly, an RSA key pair used for the RSA-KEM algorithm <bcp14>SHOU LD NOT</bcp14>
also be used for digital signatures. Indeed, the Accredited Standards also be used for digital signatures. Indeed, the Accredited Standards
Committee X9 (ASC X9) requires such a separation between key pairs used Committee X9 (ASC X9) requires such a separation between key pairs used
for key establishment and key pairs used for digital signature for key establishment and key pairs used for digital signature
<xref target="ANS-X9.44"/>. Continuing this principle of key separation, a key pair <xref target="ANS-X9.44"/>. Continuing this principle of key separation, a key pair
used for the RSA-KEM Algorithm <bcp14>SHOULD NOT</bcp14> be used with other key used for the RSA-KEM algorithm <bcp14>SHOULD NOT</bcp14> be used with other key
establishment schemes, or for data encryption, or with more establishment schemes, or for data encryption, or with more
than one set of underlying algorithm components.</t> than one set of underlying algorithm components.</t>
<t>It is acceptable to use the same RSA key pair for RSA-KEM Key Transport <t>It is acceptable to use the same RSA key pair for RSA-KEM Key Transport
as specified in <xref target="RFC5990"/> and this specification. This is accept able as specified in <xref target="RFC5990"/> and this specification. This is accept able
because the operations involving the RSA public key and the RSA private because the operations involving the RSA public key and the RSA private
key are identical in the two specifications.</t> key are identical in the two specifications.</t>
<t>Parties can gain assurance that implementations are correct through <t>Parties can gain assurance that implementations are correct through
formal implementation validation, such as the NIST Cryptographic formal implementation validation, such as the NIST Cryptographic
Module Validation Program (CMVP) <xref target="CMVP"/>.</t> Module Validation Program (CMVP) <xref target="CMVP"/>.</t>
</section> </section>
<section anchor="iana-considerations"> <section anchor="iana-considerations">
<name>IANA Considerations</name> <name>IANA Considerations</name>
<t>For the ASN.1 Module in <xref target="app-asn1-module"/>, IANA is reque sted to assign an <t>For the ASN.1 Module in <xref target="app-asn1-module"/>, IANA has assi gned an
object identifier (OID) for the module identifier. The OID for the module object identifier (OID) for the module identifier. The OID for the module
should be allocated in the "SMI Security for S/MIME Module Identifier" has been allocated in the "SMI Security for S/MIME Module Identifier"
registry (1.2.840.113549.1.9.16.0), and the Description for the new OID registry (1.2.840.113549.1.9.16.0), and the Description for the new OID
should be set to "id-mod-cms-rsa-kem-2023".</t> has been set to "id-mod-cms-rsa-kem-2023".</t>
<t>IANA is requested to update the id-alg-rsa-kem entry in the SMI Security for <t>IANA has updated the id-alg-rsa-kem entry in the "SMI Security for S/MIME Alg
S/MIME Algorithms (1.2.840.113549.1.9.16.3) repository to refer to this document orithms (1.2.840.113549.1.9.16.3)" repository to refer to this document. In add
. In addition, IANA is requested to add the following note to the registry:</t> ition, IANA has added the following note to the registry:</t>
<t>Value 14, "id-alg-rsa-kem," is also referred to as "id-rsa-kem-spki."</t> <t>Value 14, "id-alg-rsa-kem," is also referred to as "id-rsa-kem-spki."</t>
</section> </section>
</middle> </middle>
<back> <back>
<references> <references>
<name>References</name> <name>References</name>
<references anchor="sec-normative-references"> <references anchor="sec-normative-references">
<name>Normative References</name> <name>Normative References</name>
<reference anchor="I-D.ietf-lamps-cms-kemri" target="https://datatracker <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.96
.ietf.org/doc/html/draft-ietf-lamps-cms-kemri-08" xml:base="https://bib.ietf.org 29.xml"/>
/public/rfc/bibxml3/reference.I-D.ietf-lamps-cms-kemri.xml">
<front> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.33
<title>Using Key Encapsulation Mechanism (KEM) Algorithms in the Cry 94.xml"/>
ptographic Message Syntax (CMS)</title> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.50
<author fullname="Russ Housley" initials="R." surname="Housley"> 83.xml"/>
<organization>Vigil Security, LLC</organization> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.52
</author> 80.xml"/>
<author fullname="John Gray" initials="J." surname="Gray"> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.56
<organization>Entrust</organization> 52.xml"/>
</author> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.59
<author fullname="Tomofumi Okubo" initials="T." surname="Okubo"> 11.xml"/>
<organization>DigiCert, Inc.</organization> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.59
</author> 12.xml"/>
<date day="6" month="February" year="2024"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.62
<abstract> 68.xml"/>
<t>The Cryptographic Message Syntax (CMS) supports key transport a <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.80
nd key agreement algorithms. In recent years, cryptographers have been specifyin 17.xml"/>
g Key Encapsulation Mechanism (KEM) algorithms, including quantum-secure KEM alg <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.85
orithms. This document defines conventions for the use of KEM algorithms by the 51.xml"/>
originator and recipients to encrypt and decrypt CMS content. This document upda
tes RFC 5652.</t>
</abstract>
</front>
<seriesInfo name="Internet-Draft" value="draft-ietf-lamps-cms-kemri-08
"/>
</reference>
<reference anchor="RFC3394" target="https://www.rfc-editor.org/info/rfc3
394" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3394.xml">
<front>
<title>Advanced Encryption Standard (AES) Key Wrap Algorithm</title>
<author fullname="J. Schaad" initials="J." surname="Schaad"/>
<author fullname="R. Housley" initials="R." surname="Housley"/>
<date month="September" year="2002"/>
</front>
<seriesInfo name="RFC" value="3394"/>
<seriesInfo name="DOI" value="10.17487/RFC3394"/>
</reference>
<reference anchor="RFC5083" target="https://www.rfc-editor.org/info/rfc5
083" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5083.xml">
<front>
<title>Cryptographic Message Syntax (CMS) Authenticated-Enveloped-Da
ta Content Type</title>
<author fullname="R. Housley" initials="R." surname="Housley"/>
<date month="November" year="2007"/>
<abstract>
<t>This document describes an additional content type for the Cryp
tographic Message Syntax (CMS). The authenticated-enveloped-data content type is
intended for use with authenticated encryption modes. All of the various key ma
nagement techniques that are supported in the CMS enveloped-data content type ar
e also supported by the CMS authenticated-enveloped-data content type. [STANDARD
S-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5083"/>
<seriesInfo name="DOI" value="10.17487/RFC5083"/>
</reference>
<reference anchor="RFC5280" target="https://www.rfc-editor.org/info/rfc5
280" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5280.xml">
<front>
<title>Internet X.509 Public Key Infrastructure Certificate and Cert
ificate Revocation List (CRL) Profile</title>
<author fullname="D. Cooper" initials="D." surname="Cooper"/>
<author fullname="S. Santesson" initials="S." surname="Santesson"/>
<author fullname="S. Farrell" initials="S." surname="Farrell"/>
<author fullname="S. Boeyen" initials="S." surname="Boeyen"/>
<author fullname="R. Housley" initials="R." surname="Housley"/>
<author fullname="W. Polk" initials="W." surname="Polk"/>
<date month="May" year="2008"/>
<abstract>
<t>This memo profiles the X.509 v3 certificate and X.509 v2 certif
icate revocation list (CRL) for use in the Internet. An overview of this approac
h and model is provided as an introduction. The X.509 v3 certificate format is d
escribed in detail, with additional information regarding the format and semanti
cs of Internet name forms. Standard certificate extensions are described and two
Internet-specific extensions are defined. A set of required certificate extensi
ons is specified. The X.509 v2 CRL format is described in detail along with stan
dard and Internet-specific extensions. An algorithm for X.509 certification path
validation is described. An ASN.1 module and examples are provided in the appen
dices. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5280"/>
<seriesInfo name="DOI" value="10.17487/RFC5280"/>
</reference>
<reference anchor="RFC5652" target="https://www.rfc-editor.org/info/rfc5
652" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5652.xml">
<front>
<title>Cryptographic Message Syntax (CMS)</title>
<author fullname="R. Housley" initials="R." surname="Housley"/>
<date month="September" year="2009"/>
<abstract>
<t>This document describes the Cryptographic Message Syntax (CMS).
This syntax is used to digitally sign, digest, authenticate, or encrypt arbitra
ry message content. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="STD" value="70"/>
<seriesInfo name="RFC" value="5652"/>
<seriesInfo name="DOI" value="10.17487/RFC5652"/>
</reference>
<reference anchor="RFC5911" target="https://www.rfc-editor.org/info/rfc5
911" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5911.xml">
<front>
<title>New ASN.1 Modules for Cryptographic Message Syntax (CMS) and
S/MIME</title>
<author fullname="P. Hoffman" initials="P." surname="Hoffman"/>
<author fullname="J. Schaad" initials="J." surname="Schaad"/>
<date month="June" year="2010"/>
<abstract>
<t>The Cryptographic Message Syntax (CMS) format, and many associa
ted formats, are expressed using ASN.1. The current ASN.1 modules conform to the
1988 version of ASN.1. This document updates those ASN.1 modules to conform to
the 2002 version of ASN.1. There are no bits-on-the-wire changes to any of the f
ormats; this is simply a change to the syntax. This document is not an Internet
Standards Track specification; it is published for informational purposes.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5911"/>
<seriesInfo name="DOI" value="10.17487/RFC5911"/>
</reference>
<reference anchor="RFC5912" target="https://www.rfc-editor.org/info/rfc5
912" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5912.xml">
<front>
<title>New ASN.1 Modules for the Public Key Infrastructure Using X.5
09 (PKIX)</title>
<author fullname="P. Hoffman" initials="P." surname="Hoffman"/>
<author fullname="J. Schaad" initials="J." surname="Schaad"/>
<date month="June" year="2010"/>
<abstract>
<t>The Public Key Infrastructure using X.509 (PKIX) certificate fo
rmat, and many associated formats, are expressed using ASN.1. The current ASN.1
modules conform to the 1988 version of ASN.1. This document updates those ASN.1
modules to conform to the 2002 version of ASN.1. There are no bits-on-the-wire c
hanges to any of the formats; this is simply a change to the syntax. This docume
nt is not an Internet Standards Track specification; it is published for informa
tional purposes.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5912"/>
<seriesInfo name="DOI" value="10.17487/RFC5912"/>
</reference>
<reference anchor="RFC6268" target="https://www.rfc-editor.org/info/rfc6
268" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.6268.xml">
<front>
<title>Additional New ASN.1 Modules for the Cryptographic Message Sy
ntax (CMS) and the Public Key Infrastructure Using X.509 (PKIX)</title>
<author fullname="J. Schaad" initials="J." surname="Schaad"/>
<author fullname="S. Turner" initials="S." surname="Turner"/>
<date month="July" year="2011"/>
<abstract>
<t>The Cryptographic Message Syntax (CMS) format, and many associa
ted formats, are expressed using ASN.1. The current ASN.1 modules conform to the
1988 version of ASN.1. This document updates some auxiliary ASN.1 modules to co
nform to the 2008 version of ASN.1; the 1988 ASN.1 modules remain the normative
version. There are no bits- on-the-wire changes to any of the formats; this is s
imply a change to the syntax. This document is not an Internet Standards Track s
pecification; it is published for informational purposes.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="6268"/>
<seriesInfo name="DOI" value="10.17487/RFC6268"/>
</reference>
<reference anchor="RFC8017" target="https://www.rfc-editor.org/info/rfc8
017" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8017.xml">
<front>
<title>PKCS #1: RSA Cryptography Specifications Version 2.2</title>
<author fullname="K. Moriarty" initials="K." role="editor" surname="
Moriarty"/>
<author fullname="B. Kaliski" initials="B." surname="Kaliski"/>
<author fullname="J. Jonsson" initials="J." surname="Jonsson"/>
<author fullname="A. Rusch" initials="A." surname="Rusch"/>
<date month="November" year="2016"/>
<abstract>
<t>This document provides recommendations for the implementation o
f public-key cryptography based on the RSA algorithm, covering cryptographic pri
mitives, encryption schemes, signature schemes with appendix, and ASN.1 syntax f
or representing keys and for identifying the schemes.</t>
<t>This document represents a republication of PKCS #1 v2.2 from R
SA Laboratories' Public-Key Cryptography Standards (PKCS) series. By publishing
this RFC, change control is transferred to the IETF.</t>
<t>This document also obsoletes RFC 3447.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="8017"/>
<seriesInfo name="DOI" value="10.17487/RFC8017"/>
</reference>
<reference anchor="RFC8551" target="https://www.rfc-editor.org/info/rfc8
551" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8551.xml">
<front>
<title>Secure/Multipurpose Internet Mail Extensions (S/MIME) Version
4.0 Message Specification</title>
<author fullname="J. Schaad" initials="J." surname="Schaad"/>
<author fullname="B. Ramsdell" initials="B." surname="Ramsdell"/>
<author fullname="S. Turner" initials="S." surname="Turner"/>
<date month="April" year="2019"/>
<abstract>
<t>This document defines Secure/Multipurpose Internet Mail Extensi
ons (S/MIME) version 4.0. S/MIME provides a consistent way to send and receive s
ecure MIME data. Digital signatures provide authentication, message integrity, a
nd non-repudiation with proof of origin. Encryption provides data confidentialit
y. Compression can be used to reduce data size. This document obsoletes RFC 5751
.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="8551"/>
<seriesInfo name="DOI" value="10.17487/RFC8551"/>
</reference>
<reference anchor="SHS"> <reference anchor="SHS">
<front> <front>
<title>Secure Hash Standard</title> <title>Secure Hash Standard</title>
<author> <author>
<organization>National Institute of Standards and Technology</orga nization> <organization>National Institute of Standards and Technology</orga nization>
</author> </author>
<date year="2015" month="July"/> <date year="2015" month="July"/>
</front> </front>
<seriesInfo name="DOI" value="10.6028/nist.fips.180-4"/> <seriesInfo name="NIST FIPS PUB" value="180-4"/>
<seriesInfo name="DOI" value="10.6028/NIST.FIPS.180-4"/>
</reference> </reference>
<reference anchor="X.680" target="https://www.itu.int/rec/T-REC-X.680"> <reference anchor="X.680" target="https://www.itu.int/rec/T-REC-X.680">
<front> <front>
<title>Information technology -- Abstract Syntax Notation One (ASN.1 ): Specification of basic notation</title> <title>Information technology - Abstract Syntax Notation One (ASN.1) : Specification of basic notation</title>
<author> <author>
<organization>ITU-T</organization> <organization>ITU-T</organization>
</author> </author>
<date year="2021" month="February"/> <date year="2021" month="February"/>
</front> </front>
<seriesInfo name="ITU-T Recommendation" value="X.680"/> <seriesInfo name="ITU-T Recommendation" value="X.680"/>
<seriesInfo name="ISO/IEC" value="8824-1:2021"/> <seriesInfo name="ISO/IEC" value="8824-1:2021"/>
</reference> </reference>
<reference anchor="X.690" target="https://www.itu.int/rec/T-REC-X.680">
<reference anchor="X.690" target="https://www.itu.int/rec/T-REC-X.690">
<front> <front>
<title>Information technology -- ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)</title> <title>Information technology - ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)</title>
<author> <author>
<organization>ITU-T</organization> <organization>ITU-T</organization>
</author> </author>
<date year="2021" month="February"/> <date year="2021" month="February"/>
</front> </front>
<seriesInfo name="ITU-T Recommendation" value="X.690"/> <seriesInfo name="ITU-T Recommendation" value="X.690"/>
<seriesInfo name="ISO/IEC" value="8825-1:2021"/> <seriesInfo name="ISO/IEC" value="8825-1:2021"/>
</reference> </reference>
<reference anchor="ANS-X9.44">
<reference anchor="ANS-X9.44" target="https://webstore.ansi.org/standard
s/ascx9/ansix9442007r2017">
<front> <front>
<title>Public Key Cryptography for the Financial Services Industry - - Key Establishment Using Integer Factorization Cryptography</title> <title>Public Key Cryptography for the Financial Services Industry - - Key Establishment Using Integer Factorization Cryptography</title>
<author> <author>
<organization>American National Standards Institute</organization> <organization>American National Standards Institute</organization>
</author> </author>
<date year="2007"/> <date year="2007"/>
</front> </front>
<seriesInfo name="American National Standard" value="X9.44"/> <seriesInfo name="ANSI" value="X9.44-2007 (R2017)"/>
</reference> </reference>
<reference anchor="ISO18033-2" target="https://www.iso.org/standard/3797 1.html"> <reference anchor="ISO18033-2" target="https://www.iso.org/standard/3797 1.html">
<front> <front>
<title>Information technology -- Security techniques -- Encryption a lgorithms -- Part 2: Asymmetric ciphers</title> <title>Information technology -- Security techniques -- Encryption a lgorithms -- Part 2: Asymmetric ciphers</title>
<author> <author>
<organization>ISO/IEC JTC 1/SC 27</organization> <organization>ISO/IEC</organization>
</author> </author>
<date year="2006"/> <date year="2006"/>
</front> </front>
<seriesInfo name="ISO/IEC" value="18033-2:2006"/> <seriesInfo name="ISO/IEC" value="18033-2:2006"/>
</reference> </reference>
<reference anchor="RFC2119" target="https://www.rfc-editor.org/info/rfc2
119" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2119.xml"> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.21
<front> 19.xml"/>
<title>Key words for use in RFCs to Indicate Requirement Levels</tit <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.81
le> 74.xml"/>
<author fullname="S. Bradner" initials="S." surname="Bradner"/>
<date month="March" year="1997"/>
<abstract>
<t>In many standards track documents several words are used to sig
nify the requirements in the specification. These words are often capitalized. T
his document defines these words as they should be interpreted in IETF documents
. This document specifies an Internet Best Current Practices for the Internet Co
mmunity, and requests discussion and suggestions for improvements.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="2119"/>
<seriesInfo name="DOI" value="10.17487/RFC2119"/>
</reference>
<reference anchor="RFC8174" target="https://www.rfc-editor.org/info/rfc8
174" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8174.xml">
<front>
<title>Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words</ti
tle>
<author fullname="B. Leiba" initials="B." surname="Leiba"/>
<date month="May" year="2017"/>
<abstract>
<t>RFC 2119 specifies common key words that may be used in protoco
l specifications. This document aims to reduce the ambiguity by clarifying that
only UPPERCASE usage of the key words have the defined special meanings.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="8174"/>
<seriesInfo name="DOI" value="10.17487/RFC8174"/>
</reference>
</references> </references>
<references anchor="sec-informative-references"> <references anchor="sec-informative-references">
<name>Informative References</name> <name>Informative References</name>
<reference anchor="RFC4086" target="https://www.rfc-editor.org/info/rfc4
086" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.4086.xml"> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.40
<front> 86.xml"/>
<title>Randomness Requirements for Security</title> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.42
<author fullname="D. Eastlake 3rd" initials="D." surname="Eastlake 3 62.xml"/>
rd"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.59
<author fullname="J. Schiller" initials="J." surname="Schiller"/> 90.xml"/>
<author fullname="S. Crocker" initials="S." surname="Crocker"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.61
<date month="June" year="2005"/> 94.xml"/>
<abstract>
<t>Security systems are built on strong cryptographic algorithms t
hat foil pattern analysis attempts. However, the security of these systems is de
pendent on generating secret quantities for passwords, cryptographic keys, and s
imilar quantities. The use of pseudo-random processes to generate secret quantit
ies can result in pseudo-security. A sophisticated attacker may find it easier t
o reproduce the environment that produced the secret quantities and to search th
e resulting small set of possibilities than to locate the quantities in the whol
e of the potential number space.</t>
<t>Choosing random quantities to foil a resourceful and motivated
adversary is surprisingly difficult. This document points out many pitfalls in u
sing poor entropy sources or traditional pseudo-random number generation techniq
ues for generating such quantities. It recommends the use of truly random hardwa
re techniques and shows that the existing hardware on many systems can be used f
or this purpose. It provides suggestions to ameliorate the problem when a hardwa
re solution is not available, and it gives examples of how large such quantities
need to be for some applications. This document specifies an Internet Best Curr
ent Practices for the Internet Community, and requests discussion and suggestion
s for improvements.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="106"/>
<seriesInfo name="RFC" value="4086"/>
<seriesInfo name="DOI" value="10.17487/RFC4086"/>
</reference>
<reference anchor="RFC4262" target="https://www.rfc-editor.org/info/rfc4
262" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.4262.xml">
<front>
<title>X.509 Certificate Extension for Secure/Multipurpose Internet
Mail Extensions (S/MIME) Capabilities</title>
<author fullname="S. Santesson" initials="S." surname="Santesson"/>
<date month="December" year="2005"/>
<abstract>
<t>This document defines a certificate extension for inclusion of
Secure/Multipurpose Internet Mail Extensions (S/MIME) Capabilities in X.509 publ
ic key certificates, as defined by RFC 3280. This certificate extension provides
an optional method to indicate the cryptographic capabilities of an entity as a
complement to the S/MIME Capabilities signed attribute in S/MIME messages accor
ding to RFC 3851. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="4262"/>
<seriesInfo name="DOI" value="10.17487/RFC4262"/>
</reference>
<reference anchor="RFC5990" target="https://www.rfc-editor.org/info/rfc5
990" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5990.xml">
<front>
<title>Use of the RSA-KEM Key Transport Algorithm in the Cryptograph
ic Message Syntax (CMS)</title>
<author fullname="J. Randall" initials="J." surname="Randall"/>
<author fullname="B. Kaliski" initials="B." surname="Kaliski"/>
<author fullname="J. Brainard" initials="J." surname="Brainard"/>
<author fullname="S. Turner" initials="S." surname="Turner"/>
<date month="September" year="2010"/>
<abstract>
<t>The RSA-KEM Key Transport Algorithm is a one-pass (store-and-fo
rward) mechanism for transporting keying data to a recipient using the recipient
's RSA public key. ("KEM" stands for "key encapsulation mechanism".) This docume
nt specifies the conventions for using the RSA-KEM Key Transport Algorithm with
the Cryptographic Message Syntax (CMS). The ASN.1 syntax is aligned with an expe
cted forthcoming change to American National Standard (ANS) X9.44.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5990"/>
<seriesInfo name="DOI" value="10.17487/RFC5990"/>
</reference>
<reference anchor="RFC6194" target="https://www.rfc-editor.org/info/rfc6
194" xml:base="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.6194.xml">
<front>
<title>Security Considerations for the SHA-0 and SHA-1 Message-Diges
t Algorithms</title>
<author fullname="T. Polk" initials="T." surname="Polk"/>
<author fullname="L. Chen" initials="L." surname="Chen"/>
<author fullname="S. Turner" initials="S." surname="Turner"/>
<author fullname="P. Hoffman" initials="P." surname="Hoffman"/>
<date month="March" year="2011"/>
<abstract>
<t>This document includes security considerations for the SHA-0 an
d SHA-1 message digest algorithm. This document is not an Internet Standards Tra
ck specification; it is published for informational purposes.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="6194"/>
<seriesInfo name="DOI" value="10.17487/RFC6194"/>
</reference>
<reference anchor="NISTSP800-57pt1r5"> <reference anchor="NISTSP800-57pt1r5">
<front> <front>
<title>Recommendation for Key Management:Part 1 - General</title> <title>Recommendation for Key Management: Part 1 - General</title>
<author> <author fullname="Elaine Barker">
<organization>National Institute of Standards and Technology</orga nization> <organization>National Institute of Standards and Technology</orga nization>
</author> </author>
<date year="2020" month="May"/> <date year="2020" month="May"/>
</front> </front>
<seriesInfo name="NIST SP" value="800-57, Part 1, Revision 5"/>
<seriesInfo name="DOI" value="10.6028/nist.sp.800-57pt1r5"/> <seriesInfo name="DOI" value="10.6028/nist.sp.800-57pt1r5"/>
</reference> </reference>
<reference anchor="CMVP" target="https://csrc.nist.gov/projects/cryptogr aphic-module-validation-program"> <reference anchor="CMVP" target="https://csrc.nist.gov/projects/cryptogr aphic-module-validation-program">
<front> <front>
<title>Cryptographic Module Validation Program</title> <title>Cryptographic Module Validation Program</title>
<author> <author>
<organization>National Institute of Standards and Technology</orga nization> <organization>National Institute of Standards and Technology</orga nization>
</author> </author>
<date year="2016"/> <date year="2016"/>
</front> </front>
</reference> </reference>
<reference anchor="SHOUP" target="https://eprint.iacr.org/2001/112"> <reference anchor="SHOUP" target="https://eprint.iacr.org/2001/112">
<front> <front>
<title>A Proposal for an ISO Standard for Public Key Encryption</tit le> <title>A Proposal for an ISO Standard for Public Key Encryption</tit le>
<author initials="V." surname="Shoup" fullname="Victor Shoup"> <author initials="V." surname="Shoup" fullname="Victor Shoup">
<organization/> <organization/>
</author> </author>
<date year="2001"/> <date year="2001"/>
</front> </front>
<seriesInfo name="Cryptology ePrint Archive" value="Paper 2001/112"/> <seriesInfo name="Cryptology ePrint Archive" value="Paper 2001/112"/>
</reference> </reference>
</references> </references>
</references> </references>
<?line 665?>
<section anchor="app-alg"> <section anchor="app-alg">
<name>RSA-KEM Algorithm</name> <name>RSA-KEM Algorithm</name>
<t>The RSA-KEM Algorithm is a one-pass (store-and-forward) cryptographic <t>The RSA-KEM algorithm is a one-pass (store-and-forward) cryptographic
mechanism for an originator to securely send keying material to a recipient mechanism for an originator to securely send keying material to a recipient
using the recipient's RSA public key.</t> using the recipient's RSA public key.</t>
<t>With the RSA-KEM Algorithm, an originator encrypts a random integer (z) with <t>With the RSA-KEM algorithm, an originator encrypts a random integer (z) with
the recipient's RSA public key to produce a ciphertext (ct), and the originator the recipient's RSA public key to produce a ciphertext (ct), and the originator
derives a shared secret (SS) from the random integer (z). The originator then derives a shared secret (SS) from the random integer (z). The originator then
sends the ciphertext (ct) to the recipient. The recipient decrypts the sends the ciphertext (ct) to the recipient. The recipient decrypts the
ciphertext (ct) using their private key to recover the random integer (z), ciphertext (ct) using their private key to recover the random integer (z),
and the recipient derives a shared secret (SS) from the random integer(z). In and the recipient derives a shared secret (SS) from the random integer (z). In
this way, originator and recipient obtain the same shared secret (SS).</t> this way, the originator and recipient obtain the same shared secret (SS).</t>
<t>The RSA-KEM Algorithm depends on a key-derivation function (KDF), which <t>The RSA-KEM algorithm depends on a key derivation function (KDF), which
is is
used to derive the shared secret (SS). Many key-derivation functions support used to derive the shared secret (SS). Many key derivation functions support
the inclusion of other information in addition to the shared secret (SS) in the inclusion of other information in addition to the shared secret (SS) in
the input to the function; however, no other information is included as an the input to the function; however, no other information is included as an
input to the KDF by the RSA-KEM Algorithm.</t> input to the KDF by the RSA-KEM algorithm.</t>
<section anchor="app-alg-encap"> <section anchor="app-alg-encap">
<name>Originator's Operations: RSA-KEM Encapsulate()</name> <name>Originator's Operations: RSA-KEM Encapsulate()</name>
<t>Let (n,e) be the recipient's RSA public key; see <xref target="RFC801 7"/> for details.</t> <t>Let (n,e) be the recipient's RSA public key; see <xref target="RFC801 7"/> for details.</t>
<t>Let nLen denote the length in bytes of the modulus n, i.e., the least <t>Let nLen denote the length in bytes of the modulus n, i.e., the least
integer such that 2^(8*nLen) &gt; n.</t> integer such that 2<sup>(8*nLen)</sup> &gt; n.</t>
<t>The originator performs the following operations:</t> <t>The originator performs the following operations:</t>
<ol spacing="normal" type="1"><li> <ol spacing="normal" type="1"><li>
<t>Generate a random integer z between 0 and n-1 (see note), and <t>Generate a random integer z between 0 and n-1 (see NOTE below), a
convert z to a byte string Z of length nLen, most significant byte nd
first: </t> convert z to a byte string Z of length nLen, most significant byte
first: </t>
<artwork><![CDATA[ <artwork><![CDATA[
z = RandomInteger (0, n-1) z = RandomInteger (0, n-1)
Z = IntegerToString (z, nLen) Z = IntegerToString (z, nLen)]]></artwork>
]]></artwork>
</li> </li>
<li> <li>
<t>Encrypt the random integer z using the recipient's RSA public key <t>Encrypt the random integer z using the recipient's RSA public
(n,e), and convert the resulting integer c to a ciphertext C, a key (n,e) and convert the resulting integer c to a ciphertext C,
byte string of length nLen: </t> a byte string of length nLen: </t>
<artwork><![CDATA[ <artwork><![CDATA[
c = z^e mod n c = z^e mod n
ct = IntegerToString (c, nLen) ct = IntegerToString (c, nLen)]]></artwork>
]]></artwork>
</li> </li>
<li> <li>
<t>Derive a symmetric shared secret SS of length ssLen bytes (which <bcp14>MUST</bcp14> be the length of the key-encryption key) from the <t>Derive a symmetric shared secret SS of length ssLen bytes (which <bcp14>MUST</bcp14> be the length of the key-encryption key) from the
byte string Z using the underlying key-derivation function: </t> byte string Z using the underlying key derivation function: </t>
<artwork><![CDATA[ <artwork><![CDATA[
SS = KDF (Z, ssLen) SS = KDF (Z, ssLen)]]></artwork>
]]></artwork>
</li> </li>
<li> <li>
<t>Output the shared secret SS and the ciphertext ct. Send the <t>Output the shared secret SS and the ciphertext ct. Send the
ciphertext ct to the recipient.</t> ciphertext ct to the recipient.</t>
</li> </li>
</ol> </ol>
<t>NOTE: The random integer z <bcp14>MUST</bcp14> be generated independe ntly at random <t>NOTE: The random integer z <bcp14>MUST</bcp14> be generated independe ntly at random
for different encryption operations, whether for the same or different for different encryption operations, whether for the same or different
recipients.</t> recipients.</t>
</section> </section>
skipping to change at line 981 skipping to change at line 711
<t>Let ct be the ciphertext received from the originator.</t> <t>Let ct be the ciphertext received from the originator.</t>
<t>Let nLen denote the length in bytes of the modulus n.</t> <t>Let nLen denote the length in bytes of the modulus n.</t>
<t>The recipient performs the following operations:</t> <t>The recipient performs the following operations:</t>
<ol spacing="normal" type="1"><li> <ol spacing="normal" type="1"><li>
<t>If the length of the encrypted keying material is less than nLen <t>If the length of the encrypted keying material is less than nLen
bytes, output "decryption error", and stop.</t> bytes, output "decryption error", and stop.</t>
</li> </li>
<li> <li>
<t>Convert the ciphertext ct to an integer c, most significant byte <t>Convert the ciphertext ct to an integer c, most significant byte
first (see NOTE below): </t> first (see NOTE below): </t>
<artwork><![CDATA[ <artwork><![CDATA[
c = StringToInteger (ct) c = StringToInteger (ct)]]></artwork>
]]></artwork>
<t> <t>If the integer c is not between 0 and n-1, output "decryption
If the integer c is not between 0 and n-1, output "decryption error", and stop.</t>
error", and stop.</t>
</li> </li>
<li> <li>
<t>Decrypt the integer c using the recipient's private key <t>Decrypt the integer c using the recipient's private key (n,d)
(n,d) to recover an integer z (see NOTE below): </t> to recover an integer z (see NOTE below): </t>
<artwork><![CDATA[ <artwork><![CDATA[
z = c^d mod n z = c^d mod n]]></artwork>
]]></artwork>
</li> </li>
<li> <li>
<t>Convert the integer z to a byte string Z of length nLen, most <t>Convert the integer z to a byte string Z of length nLen, most
significant byte first (see NOTE below): </t> significant byte first (see NOTE below): </t>
<artwork><![CDATA[ <artwork><![CDATA[
Z = IntegerToString (z, nLen) Z = IntegerToString (z, nLen)]]></artwork>
]]></artwork>
</li> </li>
<li> <li>
<t>Derive a shared secret SS of length ssLen bytes from the byte <t>Derive a shared secret SS of length ssLen bytes from the byte
string Z using the key-derivation function (see NOTE below): </t> string Z using the key derivation function (see NOTE below): </t>
<artwork><![CDATA[ <artwork><![CDATA[
SS = KDF (Z, ssLen) SS = KDF (Z, ssLen)
]]></artwork> ]]></artwork>
</li> </li>
<li> <li>
<t>Output the shared secret SS.</t> <t>Output the shared secret SS.</t>
</li> </li>
</ol> </ol>
<t>NOTE: Implementations <bcp14>SHOULD NOT</bcp14> reveal information ab out the <t>NOTE: Implementations <bcp14>SHOULD NOT</bcp14> reveal information ab out the
integer z, the string Z, or about the calculation of the integer z, the string Z, or about the calculation of the
skipping to change at line 1027 skipping to change at line 755
The observable behavior of the implementation <bcp14>SHOULD</bcp14> be the same at The observable behavior of the implementation <bcp14>SHOULD</bcp14> be the same at
these steps for all ciphertexts C that are in range. For example, these steps for all ciphertexts C that are in range. For example,
IntegerToString conversion should take the same amount of time IntegerToString conversion should take the same amount of time
regardless of the actual value of the integer z. The integer z, the regardless of the actual value of the integer z. The integer z, the
string Z, and other intermediate results <bcp14>MUST</bcp14> be securely deleted string Z, and other intermediate results <bcp14>MUST</bcp14> be securely deleted
when they are no longer needed.</t> when they are no longer needed.</t>
</section> </section>
</section> </section>
<section anchor="app-asn1"> <section anchor="app-asn1">
<name>ASN.1 Syntax</name> <name>ASN.1 Syntax</name>
<t>The ASN.1 syntax for identifying the RSA-KEM Algorithm <t>The ASN.1 syntax for identifying the RSA-KEM algorithm
is an extension of the syntax for the "generic hybrid cipher" in is an extension of the syntax for the "generic hybrid cipher" in
ANS X9.44 <xref target="ANS-X9.44"/>.</t> ANS X9.44 <xref target="ANS-X9.44"/>.</t>
<t>The ASN.1 Module is unchanged from RFC 5990. The id-rsa-kem-spki <t>The ASN.1 Module is unchanged from RFC 5990. The id-rsa-kem-spki
object identifier is used in a backward compatible manner object identifier is used in a backward compatible manner
in certificates <xref target="RFC5280"/> and SMIMECapabilities <xref target="RFC 8551"/>. in certificates <xref target="RFC5280"/> and SMIMECapabilities <xref target="RFC 8551"/>.
Of course, the use of the id-kem-rsa object identifier in the Of course, the use of the id-kem-rsa object identifier in the
new KEMRecipientInfo structure <xref target="I-D.ietf-lamps-cms-kemri"/> new KEMRecipientInfo structure <xref target="RFC9629"/>
was not yet defined at the time that RFC 5990 was written.</t> was not yet defined at the time that RFC 5990 was written.</t>
<section anchor="app-asn1-intro"> <section anchor="app-asn1-intro">
<name>Underlying Components</name> <name>Underlying Components</name>
<t>Implementations that conform to this specification <bcp14>MUST</bcp14 > support <t>Implementations that conform to this specification <bcp14>MUST</bcp14 > support
the KDF3 <xref target="ANS-X9.44"/> key-derivation function using SHA-256 <xref the KDF3 <xref target="ANS-X9.44"/> key derivation function using SHA-256 <xref
target="SHS"/>.</t> target="SHS"/>.</t>
<t>KDF2 <xref target="ANS-X9.44"/> and KDF3 are both key-derivation func <t>KDF2 <xref target="ANS-X9.44"/> and KDF3 are both key derivation func
tions based on tions based on
a hash function. The only difference between KDF2 and KDF3 is the order a hash function. The only difference between KDF2 and KDF3 is the order
of the components to be hashed.</t> of the components to be hashed.</t>
<artwork><![CDATA[ <artwork><![CDATA[
KDF2 calculates T as: T = T || Hash (Z || D || otherInfo) KDF2 calculates T as: T = T || Hash (Z || D || otherInfo)
KDF3 calculates T as: T = T || Hash (D || Z || otherInfo) KDF3 calculates T as: T = T || Hash (D || Z || otherInfo)]]></artwork>
]]></artwork>
<t>The object identifier for KDF3 is:</t> <t>The object identifier for KDF3 is:</t>
<artwork><![CDATA[ <sourcecode type="asn.1">
id-kdf-kdf3 OBJECT IDENTIFIER ::= { x9-44-components kdf3(2) } id-kdf-kdf3 OBJECT IDENTIFIER ::= { x9-44-components kdf3(2) }</sourcecode>
]]></artwork>
<t>The KDF3 parameters identify the underlying hash function. For <t>The KDF3 parameters identify the underlying hash function. For
alignment with the ANS X9.44, the hash function <bcp14>MUST</bcp14> be an ASC X9 -approved alignment with ANS X9.44, the hash function <bcp14>MUST</bcp14> be an ASC X9-app roved
hash function. While the SHA-1 hash algorithm is included in the hash function. While the SHA-1 hash algorithm is included in the
ASN.1 definitions, SHA-1 <bcp14>MUST NOT</bcp14> be used. SHA-1 is considered ASN.1 definitions, SHA-1 <bcp14>MUST NOT</bcp14> be used. SHA-1 is considered
to be obsolete; see <xref target="RFC6194"/>. SHA-1 remains in the ASN.1 module for to be obsolete; see <xref target="RFC6194"/>. SHA-1 remains in the ASN.1 module for
compatibility with RFC 5990. In addition, other hash functions <bcp14>MAY</bcp1 4> be compatibility with RFC 5990. In addition, other hash functions <bcp14>MAY</bcp1 4> be
used with CMS.</t> used with CMS.</t>
<artwork><![CDATA[ <sourcecode type="asn.1">
kda-kdf3 KEY-DERIVATION ::= { kda-kdf3 KEY-DERIVATION ::= {
IDENTIFIER id-kdf-kdf3 IDENTIFIER id-kdf-kdf3
PARAMS TYPE KDF3-HashFunction ARE required PARAMS TYPE KDF3-HashFunction ARE required
-- No S/MIME caps defined -- } -- No S/MIME caps defined -- }
KDF3-HashFunction ::= KDF3-HashFunction ::=
AlgorithmIdentifier { DIGEST-ALGORITHM, {KDF3-HashFunctions} } AlgorithmIdentifier { DIGEST-ALGORITHM, {KDF3-HashFunctions} }
KDF3-HashFunctions DIGEST-ALGORITHM ::= { X9-HashFunctions, ... } KDF3-HashFunctions DIGEST-ALGORITHM ::= { X9-HashFunctions, ... }
X9-HashFunctions DIGEST-ALGORITHM ::= { X9-HashFunctions DIGEST-ALGORITHM ::= {
mda-sha1 | mda-sha224 | mda-sha256 | mda-sha384 | mda-sha1 | mda-sha224 | mda-sha256 | mda-sha384 |
mda-sha512, ... } mda-sha512, ... }</sourcecode>
]]></artwork>
<t>Implementations that conform to this specification <bcp14>MUST</bcp14 > support <t>Implementations that conform to this specification <bcp14>MUST</bcp14 > support
the AES Key Wrap <xref target="RFC3394"/> key-encryption algorithm with a 128-bi t the AES Key Wrap <xref target="RFC3394"/> key-encryption algorithm with a 128-bi t
key. There are three object identifiers for the AES Key Wrap, one for key. There are three object identifiers for the AES Key Wrap, one for
each permitted size of the key-encryption key. There are three object each permitted size of the key-encryption key. There are three object
identifiers imported from <xref target="RFC5912"/>, and none of these algorithm identifiers imported from <xref target="RFC5912"/>, and none of these algorithm
identifiers have associated parameters:</t> identifiers have associated parameters:</t>
<artwork><![CDATA[ <sourcecode type="asn.1">
kwa-aes128-wrap KEY-WRAP ::= { kwa-aes128-wrap KEY-WRAP ::= {
IDENTIFIER id-aes128-wrap IDENTIFIER id-aes128-wrap
PARAMS ARE absent PARAMS ARE absent
SMIME-CAPS { IDENTIFIED BY id-aes128-wrap } } SMIME-CAPS { IDENTIFIED BY id-aes128-wrap } }
kwa-aes192-wrap KEY-WRAP ::= { kwa-aes192-wrap KEY-WRAP ::= {
IDENTIFIER id-aes192-wrap IDENTIFIER id-aes192-wrap
PARAMS ARE absent PARAMS ARE absent
SMIME-CAPS { IDENTIFIED BY id-aes192-wrap } } SMIME-CAPS { IDENTIFIED BY id-aes192-wrap } }
kwa-aes256-wrap KEY-WRAP ::= { kwa-aes256-wrap KEY-WRAP ::= {
IDENTIFIER id-aes256-wrap IDENTIFIER id-aes256-wrap
PARAMS ARE absent PARAMS ARE absent
SMIME-CAPS { IDENTIFIED BY id-aes256-wrap } } SMIME-CAPS { IDENTIFIED BY id-aes256-wrap } }</sourcecode>
]]></artwork>
</section> </section>
<section anchor="app-asn1-module"> <section anchor="app-asn1-module">
<name>ASN.1 Module</name> <name>ASN.1 Module</name>
<t>RFC EDITOR: Please replace TBD2 with the value assigned by IANA
during the publication of <xref target="I-D.ietf-lamps-cms-kemri"/>.</t>
<sourcecode type="asn.1" markers="true"><![CDATA[ <sourcecode type="asn.1" markers="true"><![CDATA[
CMS-RSA-KEM-2023 CMS-RSA-KEM-2023
{ iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
pkcs-9(9) smime(16) modules(0) id-mod-cms-rsa-kem-2023(TBD1) } pkcs-9(9) smime(16) modules(0) id-mod-cms-rsa-kem-2023(79) }
DEFINITIONS EXPLICIT TAGS ::= BEGIN DEFINITIONS EXPLICIT TAGS ::= BEGIN
-- EXPORTS ALL -- EXPORTS ALL
IMPORTS IMPORTS
KEM-ALGORITHM KEM-ALGORITHM
FROM KEMAlgorithmInformation-2023 -- [I-D.ietf-lamps-cms-kemri] FROM KEMAlgorithmInformation-2023 -- [I-D.ietf-lamps-cms-kemri]
{ iso(1) identified-organization(3) dod(6) internet(1) { iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-kemAlgorithmInformation-2023(TBD2) } id-mod-kemAlgorithmInformation-2023(109) }
AlgorithmIdentifier{}, PUBLIC-KEY, DIGEST-ALGORITHM, AlgorithmIdentifier{}, PUBLIC-KEY, DIGEST-ALGORITHM,
KEY-DERIVATION, KEY-WRAP, SMIME-CAPS KEY-DERIVATION, KEY-WRAP, SMIME-CAPS
FROM AlgorithmInformation-2009 -- [RFC5912] FROM AlgorithmInformation-2009 -- [RFC5912]
{ iso(1) identified-organization(3) dod(6) internet(1) { iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-algorithmInformation-02(58) } id-mod-algorithmInformation-02(58) }
kwa-aes128-wrap, kwa-aes192-wrap, kwa-aes256-wrap kwa-aes128-wrap, kwa-aes192-wrap, kwa-aes256-wrap
FROM CMSAesRsaesOaep-2009 -- [RFC5911] FROM CMSAesRsaesOaep-2009 -- [RFC5911]
skipping to change at line 1315 skipping to change at line 1042
SMimeCapsSet SMIME-CAPS ::= { SMimeCapsSet SMIME-CAPS ::= {
kema-kem-rsa.&smimeCaps | kema-kem-rsa.&smimeCaps |
kwa-aes128-wrap | kwa-aes128-wrap |
kwa-aes192-wrap | kwa-aes192-wrap |
kwa-aes256-wrap | kwa-aes256-wrap |
kwa-camellia128-wrap.&smimeCaps | kwa-camellia128-wrap.&smimeCaps |
kwa-camellia192-wrap.&smimeCaps | kwa-camellia192-wrap.&smimeCaps |
kwa-camellia256-wrap.&smimeCaps, kwa-camellia256-wrap.&smimeCaps,
... } ... }
END END]]></sourcecode>
]]></sourcecode>
</section> </section>
</section> </section>
<section anchor="app-example"> <section anchor="app-example">
<name>SMIMECapabilities Examples</name> <name>SMIMECapabilities Examples</name>
<t>To indicate support for the RSA-KEM algorithm coupled with the KDF3 <t>To indicate support for the RSA-KEM algorithm coupled with the KDF3
key-derivation function with SHA-256 and the AES Key Wrap symmetric key derivation function with SHA-256 and the AES Key Wrap symmetric
key-encryption algorithm 128-bit key-encryption key, the key-encryption algorithm 128-bit key-encryption key, the
SMIMECapabilities will include the following entry:</t> SMIMECapabilities will include the following entry:</t>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
id-rsa-kem-spki, -- RSA-KEM Algorithm id-rsa-kem-spki, -- RSA-KEM Algorithm
SEQUENCE { -- GenericHybridParameters SEQUENCE { -- GenericHybridParameters
SEQUENCE { -- key encapsulation mechanism SEQUENCE { -- key encapsulation mechanism
id-kem-rsa, -- RSA-KEM id-kem-rsa, -- RSA-KEM
SEQUENCE { -- RsaKemParameters SEQUENCE { -- RsaKemParameters
SEQUENCE { -- key derivation function SEQUENCE { -- key derivation function
id-kdf-kdf3, -- KDF3 id-kdf-kdf3, -- KDF3
SEQUENCE { -- KDF3-HashFunction SEQUENCE { -- KDF3-HashFunction
id-sha256 -- SHA-256; no parameters (preferred) id-sha256 -- SHA-256; no parameters (preferred)
}, },
16 -- KEK length in bytes 16 -- KEK length in bytes
}, },
SEQUENCE { -- data encapsulation mechanism SEQUENCE { -- data encapsulation mechanism
id-aes128-Wrap -- AES-128 Wrap; no parameters id-aes128-Wrap -- AES-128 Wrap; no parameters
} }
} }
} }]]></artwork>
]]></artwork>
<t>This SMIMECapability value has the following DER encoding (in hexadecim al):</t> <t>This SMIMECapability value has the following DER encoding (in hexadecim al):</t>
<artwork><![CDATA[ <artwork><![CDATA[
30 47 30 47
06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e -- id-rsa-kem-spki 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e -- id-rsa-kem-spki
30 38 30 38
30 29 30 29
06 07 28 81 8c 71 02 02 04 -- id-kem-rsa 06 07 28 81 8c 71 02 02 04 -- id-kem-rsa
30 1e 30 1e
30 19 30 19
06 0a 2b 81 05 10 86 48 09 2c 01 02 -- id-kdf-kdf3 06 0a 2b 81 05 10 86 48 09 2c 01 02 -- id-kdf-kdf3
30 0b 30 0b
06 09 60 86 48 01 65 03 04 02 01 -- id-sha256 06 09 60 86 48 01 65 03 04 02 01 -- id-sha256
02 01 10 -- 16 bytes 02 01 10 -- 16 bytes
30 0b 30 0b
06 09 60 86 48 01 65 03 04 01 05 -- id-aes128-Wrap 06 09 60 86 48 01 65 03 04 01 05 -- id-aes128-Wrap]]></artwork>
]]></artwork>
<t>To indicate support for the RSA-KEM algorithm coupled with the KDF3 <t>To indicate support for the RSA-KEM algorithm coupled with the KDF3
key-derivation function with SHA-384 and the AES Key Wrap symmetric key derivation function with SHA-384 and the AES Key Wrap symmetric
key-encryption algorithm 192-bit key-encryption key, the key-encryption algorithm 192-bit key-encryption key, the
SMIMECapabilities will include the following SMIMECapability value SMIMECapabilities will include the following SMIMECapability value
(in hexadecimal):</t> (in hexadecimal):</t>
<artwork><![CDATA[ <artwork><![CDATA[
30 47 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e 30 30 47 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e 30
38 30 29 06 07 28 81 8c 71 02 02 04 30 1e 30 19 38 30 29 06 07 28 81 8c 71 02 02 04 30 1e 30 19
06 0a 2b 81 05 10 86 48 09 2c 01 02 30 0b 06 09 06 0a 2b 81 05 10 86 48 09 2c 01 02 30 0b 06 09
60 86 48 01 65 03 04 02 02 02 01 18 30 0b 06 09 60 86 48 01 65 03 04 02 02 02 01 18 30 0b 06 09
60 86 48 01 65 03 04 01 19 60 86 48 01 65 03 04 01 19]]></artwork>
]]></artwork>
<t>To indicate support for the RSA-KEM algorithm coupled with the KDF3 <t>To indicate support for the RSA-KEM algorithm coupled with the KDF3
key-derivation function with SHA-512 and the AES Key Wrap symmetric key derivation function with SHA-512 and the AES Key Wrap symmetric
key-encryption algorithm 256-bit key-encryption key, the key-encryption algorithm 256-bit key-encryption key, the
SMIMECapabilities will include the following SMIMECapability value SMIMECapabilities will include the following SMIMECapability value
(in hexadecimal):</t> (in hexadecimal):</t>
<artwork><![CDATA[ <artwork><![CDATA[
30 47 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e 30 30 47 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e 30
38 30 29 06 07 28 81 8c 71 02 02 04 30 1e 30 19 38 30 29 06 07 28 81 8c 71 02 02 04 30 1e 30 19
06 0a 2b 81 05 10 86 48 09 2c 01 02 30 0b 06 09 06 0a 2b 81 05 10 86 48 09 2c 01 02 30 0b 06 09
60 86 48 01 65 03 04 02 03 02 01 20 30 0b 06 09 60 86 48 01 65 03 04 02 03 02 01 20 30 0b 06 09
60 86 48 01 65 03 04 01 2d 60 86 48 01 65 03 04 01 2d]]></artwork>
]]></artwork>
</section> </section>
<section anchor="rsa-kem-cms-enveloped-data-example"> <section anchor="rsa-kem-cms-enveloped-data-example">
<name>RSA-KEM CMS Enveloped-Data Example</name> <name>RSA-KEM CMS Enveloped-Data Example</name>
<t>This example shows the establishment of an AES-128 content-encryption <t>This example shows the establishment of an AES-128 content-encryption
key using:</t> key using:</t>
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t>RSA-KEM with a 3072-bit key and KDF3 with SHA-256;</t> <t>RSA-KEM with a 3072-bit key and KDF3 with SHA-256;</t>
</li> </li>
<li> <li>
<t>KEMRecipientInfo key derivation using KDF3 with SHA-256; and</t> <t>KEMRecipientInfo key derivation using KDF3 with SHA-256; and</t>
</li> </li>
<li> <li>
<t>KEMRecipientInfo key wrap using AES-128-KEYWRAP.</t> <t>KEMRecipientInfo Key Wrap using AES-128-KEYWRAP.</t>
</li> </li>
</ul> </ul>
<t>In real-world use, the originator would encrypt the content-encryption <t>In real-world use, the originator would encrypt the content-encryption
key in a manner that would allow decryption with their own private key key in a manner that would allow decryption with their own private key
as well as the recipient's private key. This is omitted in an attempt as well as the recipient's private key. This is omitted in an attempt
to simplify the example.</t> to simplify the example.</t>
<section anchor="originator-rsa-kem-encapsulate-processing"> <section anchor="originator-rsa-kem-encapsulate-processing">
<name>Originator RSA-KEM Encapsulate() Processing</name> <name>Originator RSA-KEM Encapsulate() Processing</name>
<t>Alice obtains Bob's public key:</t> <t>Alice obtains Bob's public key:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
MIIBojANBgkqhkiG9w0BAQEFAAOCAY8AMIIBigKCAYEA3ocW14cxncPJ47fnEjBZ MIIBojANBgkqhkiG9w0BAQEFAAOCAY8AMIIBigKCAYEA3ocW14cxncPJ47fnEjBZ
AyfC2lqapL3ET4jvV6C7gGeVrRQxWPDwl+cFYBBR2ej3j3/0ecDmu+XuVi2+s5JH AyfC2lqapL3ET4jvV6C7gGeVrRQxWPDwl+cFYBBR2ej3j3/0ecDmu+XuVi2+s5JH
Keeza+itfuhsz3yifgeEpeK8T+SusHhn20/NBLhYKbh3kiAcCgQ56dpDrDvDcLqq Keeza+itfuhsz3yifgeEpeK8T+SusHhn20/NBLhYKbh3kiAcCgQ56dpDrDvDcLqq
vS3jg/VO+OPnZbofoHOOevt8Q/roahJe1PlIyQ4udWB8zZezJ4mLLfbOA9YVaYXx vS3jg/VO+OPnZbofoHOOevt8Q/roahJe1PlIyQ4udWB8zZezJ4mLLfbOA9YVaYXx
2AHHZJevo3nmRnlgJXo6mE00E/6qkhjDHKSMdl2WG6mO9TCDZc9qY3cAJDU6Ir0v 2AHHZJevo3nmRnlgJXo6mE00E/6qkhjDHKSMdl2WG6mO9TCDZc9qY3cAJDU6Ir0v
SH7qUl8/vN13y4UOFkn8hM4kmZ6bJqbZt5NbjHtY4uQ0VMW3RyESzhrO02mrp39a SH7qUl8/vN13y4UOFkn8hM4kmZ6bJqbZt5NbjHtY4uQ0VMW3RyESzhrO02mrp39a
uLNnH3EXdXaV1tk75H3qC7zJaeGWMJyQfOE3YfEGRKn8fxubji716D8UecAxAzFy uLNnH3EXdXaV1tk75H3qC7zJaeGWMJyQfOE3YfEGRKn8fxubji716D8UecAxAzFy
FL6m1JiOyV5acAiOpxN14qRYZdHnXOM9DqGIGpoeY1UuD4Mo05osOqOUpBJHA9fS FL6m1JiOyV5acAiOpxN14qRYZdHnXOM9DqGIGpoeY1UuD4Mo05osOqOUpBJHA9fS
whSZG7VNf+vgNWTLNYSYLI04KiMdulnvU6ds+QPz+KKtAgMBAAE= whSZG7VNf+vgNWTLNYSYLI04KiMdulnvU6ds+QPz+KKtAgMBAAE=
-----END PUBLIC KEY----- -----END PUBLIC KEY-----]]></artwork>
]]></artwork>
<t>Bob's RSA public key has the following key identifier:</t> <t>Bob's RSA public key has the following key identifier:</t>
<artwork><![CDATA[ <artwork><![CDATA[
9eeb67c9b95a74d44d2f16396680e801b5cba49c 9eeb67c9b95a74d44d2f16396680e801b5cba49c]]></artwork>
]]></artwork>
<t>Alice randomly generates integer z between 0 and n-1:</t> <t>Alice randomly generates integer z between 0 and n-1:</t>
<artwork><![CDATA[ <artwork><![CDATA[
9c126102a5c1c0354672a3c2f19fc9ddea988f815e1da812c7bd4f8eb082bdd1 9c126102a5c1c0354672a3c2f19fc9ddea988f815e1da812c7bd4f8eb082bdd1
4f85a7f7c2f1af11d5333e0d6bcb375bf855f208da72ba27e6fb0655f2825aa6 4f85a7f7c2f1af11d5333e0d6bcb375bf855f208da72ba27e6fb0655f2825aa6
2b93b1f9bbd3491fed58f0380fa0de36430e3a144d569600bd362609be5b9481 2b93b1f9bbd3491fed58f0380fa0de36430e3a144d569600bd362609be5b9481
0875990b614e406fa6dff500043cbca95968faba61f795096a7fb3687a51078c 0875990b614e406fa6dff500043cbca95968faba61f795096a7fb3687a51078c
4ca2cb663366b0bea0cd9cccac72a25f3f4ed03deb68b4453bba44b943f4367b 4ca2cb663366b0bea0cd9cccac72a25f3f4ed03deb68b4453bba44b943f4367b
67d6cd10c8ace53f545aac50968fc3c6ecc80f3224b64e37038504e2d2c0e2b2 67d6cd10c8ace53f545aac50968fc3c6ecc80f3224b64e37038504e2d2c0e2b2
9d45e46c62826d96331360e4c17ea3ef89a9efc5fac99eda830e81450b6534dc 9d45e46c62826d96331360e4c17ea3ef89a9efc5fac99eda830e81450b6534dc
0bdf042b8f3b706649c631fe51fc2445cc8d447203ec2f41f79cdfea16de1ce6 0bdf042b8f3b706649c631fe51fc2445cc8d447203ec2f41f79cdfea16de1ce6
abdfdc1e2ef2e5d5d8a65e645f397240ef5a26f5e4ff715de782e30ecf477293 abdfdc1e2ef2e5d5d8a65e645f397240ef5a26f5e4ff715de782e30ecf477293
e89e13171405909a8e04dd31d21d0c57935fc1ceea8e1033e31e1bc8c56da0f3 e89e13171405909a8e04dd31d21d0c57935fc1ceea8e1033e31e1bc8c56da0f3
d79510f3f380ff58e5a61d361f2f18e99fbae5663172e8cd1f21deaddc5bbbea d79510f3f380ff58e5a61d361f2f18e99fbae5663172e8cd1f21deaddc5bbbea
060d55f1842b93d1a9c888d0bf85d0af9947fe51acf940c7e7577eb79cabecb3 060d55f1842b93d1a9c888d0bf85d0af9947fe51acf940c7e7577eb79cabecb3]]></artwork>
]]></artwork>
<t>Alice encrypts integer z using the Bob's RSA public key, the result i <t>Alice encrypts integer z using the Bob's RSA public key. The result i
s s
called ct:</t> called ct:</t>
<artwork><![CDATA[ <artwork><![CDATA[
c071fc273af8e7bdb152e06bf73310361074154a43abcf3c93c13499d2065344 c071fc273af8e7bdb152e06bf73310361074154a43abcf3c93c13499d2065344
3eed9ef5d3c0685e4aa76a6854815bb97691ff9f8dac15eea7d74f452bf350a6 3eed9ef5d3c0685e4aa76a6854815bb97691ff9f8dac15eea7d74f452bf350a6
46163d68288e978cbf7a73089ee52712f9a4f49e06ace7bbc85ab14d4e336c97 46163d68288e978cbf7a73089ee52712f9a4f49e06ace7bbc85ab14d4e336c97
c5728a2654138c7b26e8835c6b0a9fbed26495c4eadf745a2933be283f6a88b1 c5728a2654138c7b26e8835c6b0a9fbed26495c4eadf745a2933be283f6a88b1
6695fc06666873cfb6d36718ef3376cefc100c3941f3c494944078325807a559 6695fc06666873cfb6d36718ef3376cefc100c3941f3c494944078325807a559
186b95ccabf3714cfaf79f83bd30537fdd9aed5a4cdcbd8bd0486faed73e9d48 186b95ccabf3714cfaf79f83bd30537fdd9aed5a4cdcbd8bd0486faed73e9d48
6b3087d6c806546b6e2671575c98461e441f65542bd95de26d0f53a64e7848d7 6b3087d6c806546b6e2671575c98461e441f65542bd95de26d0f53a64e7848d7
31d9608d053e8d345546602d86236ffe3704c98ad59144f3089e5e6d527b5497 31d9608d053e8d345546602d86236ffe3704c98ad59144f3089e5e6d527b5497
ba103c79d62e80d0235410b06f71a7d9bd1c38000f910d6312ea2f20a3557535 ba103c79d62e80d0235410b06f71a7d9bd1c38000f910d6312ea2f20a3557535
ad01b3093fb5f7ee507080d0f77d48c9c3b3796f6b7dd3786085fb895123f04c ad01b3093fb5f7ee507080d0f77d48c9c3b3796f6b7dd3786085fb895123f04c
a1f1c1be22c747a8dface32370fb0d570783e27dbb7e74fca94ee39676fde3d8 a1f1c1be22c747a8dface32370fb0d570783e27dbb7e74fca94ee39676fde3d8
a9553d878224736e37e191dab953c7e228c07ad5ca3122421c14debd072a9ab6 a9553d878224736e37e191dab953c7e228c07ad5ca3122421c14debd072a9ab6]]></artwork>
]]></artwork>
<t>Alice derives the shared secret (SS) using KDF3 with SHA-256:</t> <t>Alice derives the shared secret (SS) using KDF3 with SHA-256:</t>
<artwork><![CDATA[ <artwork><![CDATA[
3cf82ec41b54ed4d37402bbd8f805a52 3cf82ec41b54ed4d37402bbd8f805a52]]></artwork>
]]></artwork>
</section> </section>
<section anchor="originator-cms-processing"> <section anchor="originator-cms-processing">
<name>Originator CMS Processing</name> <name>Originator CMS Processing</name>
<t>Alice encodes the CMSORIforKEMOtherInfo structure with the algorithm <t>Alice encodes the CMSORIforKEMOtherInfo structure with the algorithm
identifier for AES-128-KEYWRAP and a key length of 16 octets. identifier for AES-128-KEYWRAP and a key length of 16 octets.
The DER encoding of CMSORIforKEMOtherInfo produces 18 octets:</t> The DER encoding of CMSORIforKEMOtherInfo produces 18 octets:</t>
<artwork><![CDATA[ <artwork><![CDATA[
3010300b0609608648016503040105020110 3010300b0609608648016503040105020110]]></artwork>
]]></artwork>
<t>The CMSORIforKEMOtherInfo structure contains:</t> <t>The CMSORIforKEMOtherInfo structure contains:</t>
<ul empty="true">
<li>
<artwork><![CDATA[ <artwork><![CDATA[
0 16: SEQUENCE { 0 16: SEQUENCE {
2 11: SEQUENCE { 2 11: SEQUENCE {
4 9: OBJECT IDENTIFIER aes128-wrap (2 16 840 1 101 3 4 1 5) 4 9: OBJECT IDENTIFIER aes128-wrap (2 16 840 1 101 3 4 1 5)
: } : }
15 1: INTEGER 16 15 1: INTEGER 16
: } : }]]></artwork>
]]></artwork>
</li>
</ul>
<t>Alice derives the key-encryption key from shared secret produced <t>Alice derives the key-encryption key from shared secret produced
by RSA-KEM Encapsulate() and the CMSORIforKEMOtherInfo structure by RSA-KEM Encapsulate() and the CMSORIforKEMOtherInfo structure
with KDF3 and SHA-256, the KEK is:</t> with KDF3 and SHA-256. The KEK is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
e6dc9d62ff2b469bef604c617b018718 e6dc9d62ff2b469bef604c617b018718]]></artwork>
]]></artwork>
<t>Alice randomly generates a 128-bit content-encryption key:</t> <t>Alice randomly generates a 128-bit content-encryption key:</t>
<artwork><![CDATA[ <artwork><![CDATA[
77f2a84640304be7bd42670a84a1258b 77f2a84640304be7bd42670a84a1258b]]></artwork>
]]></artwork>
<t>Alice uses AES-128-KEYWRAP to encrypt the 128-bit content-encryption <t>Alice uses AES-128-KEYWRAP to encrypt the 128-bit content-encryption
key with the derived key-encryption key:</t> key with the derived key-encryption key:</t>
<artwork><![CDATA[ <artwork><![CDATA[
28782e5d3d794a7616b863fbcfc719b78f12de08cf286e09 28782e5d3d794a7616b863fbcfc719b78f12de08cf286e09]]></artwork>
]]></artwork>
<t>Alice encrypts the padded content using AES-128-CBC with the <t>Alice encrypts the padded content using AES-128-CBC with the
content-encryption key. The 16-octet IV used is:</t> content-encryption key. The 16-octet IV used is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
480ccafebabefacedbaddecaf8887781 480ccafebabefacedbaddecaf8887781]]></artwork>
]]></artwork>
<t>The padded content plaintext is:</t> <t>The padded content plaintext is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
48656c6c6f2c20776f726c6421030303 48656c6c6f2c20776f726c6421030303]]></artwork>
]]></artwork>
<t>The resulting ciphertext is:</t> <t>The resulting ciphertext is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
c6ca65db7bdd76b0f37e2fab6264b66d c6ca65db7bdd76b0f37e2fab6264b66d]]></artwork>
]]></artwork>
<t>Alice encodes the EnvelopedData (using KEMRecipientInfo) and <t>Alice encodes the EnvelopedData (using KEMRecipientInfo) and
ContentInfo, and then sends the result to Bob. The Base64-encoded ContentInfo, and then sends the result to Bob. The Base64-encoded
result is:</t> result is:</t>
<ul empty="true">
<li>
<artwork><![CDATA[ <artwork><![CDATA[
MIICXAYJKoZIhvcNAQcDoIICTTCCAkkCAQMxggIEpIICAAYLKoZIhvcNAQkQDQMw MIICXAYJKoZIhvcNAQcDoIICTTCCAkkCAQMxggIEpIICAAYLKoZIhvcNAQkQDQMw
ggHvAgEAgBSe62fJuVp01E0vFjlmgOgBtcuknDAJBgcogYxxAgIEBIIBgMBx/Cc6 ggHvAgEAgBSe62fJuVp01E0vFjlmgOgBtcuknDAJBgcogYxxAgIEBIIBgMBx/Cc6
+Oe9sVLga/czEDYQdBVKQ6vPPJPBNJnSBlNEPu2e9dPAaF5Kp2poVIFbuXaR/5+N +Oe9sVLga/czEDYQdBVKQ6vPPJPBNJnSBlNEPu2e9dPAaF5Kp2poVIFbuXaR/5+N
rBXup9dPRSvzUKZGFj1oKI6XjL96cwie5ScS+aT0ngas57vIWrFNTjNsl8VyiiZU rBXup9dPRSvzUKZGFj1oKI6XjL96cwie5ScS+aT0ngas57vIWrFNTjNsl8VyiiZU
E4x7JuiDXGsKn77SZJXE6t90Wikzvig/aoixZpX8BmZoc8+202cY7zN2zvwQDDlB E4x7JuiDXGsKn77SZJXE6t90Wikzvig/aoixZpX8BmZoc8+202cY7zN2zvwQDDlB
88SUlEB4MlgHpVkYa5XMq/NxTPr3n4O9MFN/3ZrtWkzcvYvQSG+u1z6dSGswh9bI 88SUlEB4MlgHpVkYa5XMq/NxTPr3n4O9MFN/3ZrtWkzcvYvQSG+u1z6dSGswh9bI
BlRrbiZxV1yYRh5EH2VUK9ld4m0PU6ZOeEjXMdlgjQU+jTRVRmAthiNv/jcEyYrV BlRrbiZxV1yYRh5EH2VUK9ld4m0PU6ZOeEjXMdlgjQU+jTRVRmAthiNv/jcEyYrV
kUTzCJ5ebVJ7VJe6EDx51i6A0CNUELBvcafZvRw4AA+RDWMS6i8go1V1Na0Bswk/ kUTzCJ5ebVJ7VJe6EDx51i6A0CNUELBvcafZvRw4AA+RDWMS6i8go1V1Na0Bswk/
tffuUHCA0Pd9SMnDs3lva33TeGCF+4lRI/BMofHBviLHR6jfrOMjcPsNVweD4n27 tffuUHCA0Pd9SMnDs3lva33TeGCF+4lRI/BMofHBviLHR6jfrOMjcPsNVweD4n27
fnT8qU7jlnb949ipVT2HgiRzbjfhkdq5U8fiKMB61coxIkIcFN69ByqatjAbBgor fnT8qU7jlnb949ipVT2HgiRzbjfhkdq5U8fiKMB61coxIkIcFN69ByqatjAbBgor
gQUQhkgJLAECMA0GCWCGSAFlAwQCAQUAAgEQMAsGCWCGSAFlAwQBBQQYKHguXT15 gQUQhkgJLAECMA0GCWCGSAFlAwQCAQUAAgEQMAsGCWCGSAFlAwQBBQQYKHguXT15
SnYWuGP7z8cZt48S3gjPKG4JMDwGCSqGSIb3DQEHATAdBglghkgBZQMEAQIEEEgM SnYWuGP7z8cZt48S3gjPKG4JMDwGCSqGSIb3DQEHATAdBglghkgBZQMEAQIEEEgM
yv66vvrO263eyviId4GAEMbKZdt73Xaw834vq2Jktm0= yv66vvrO263eyviId4GAEMbKZdt73Xaw834vq2Jktm0=]]></artwork>
]]></artwork>
</li>
</ul>
<t>This result decodes to:</t> <t>This result decodes to:</t>
<ul empty="true">
<li>
<artwork><![CDATA[ <artwork><![CDATA[
0 604: SEQUENCE { 0 604: SEQUENCE {
4 9: OBJECT IDENTIFIER envelopedData (1 2 840 113549 1 7 3) 4 9: OBJECT IDENTIFIER envelopedData (1 2 840 113549 1 7 3)
15 589: [0] { 15 589: [0] {
19 585: SEQUENCE { 19 585: SEQUENCE {
23 1: INTEGER 3 23 1: INTEGER 3
26 516: SET { 26 516: SET {
30 512: [4] { 30 512: [4] {
34 11: OBJECT IDENTIFIER 34 11: OBJECT IDENTIFIER
: KEMRecipientInfo (1 2 840 113549 1 9 16 13 3) : KEMRecipientInfo (1 2 840 113549 1 9 16 13 3)
skipping to change at line 1610 skipping to change at line 1337
559 29: SEQUENCE { 559 29: SEQUENCE {
561 9: OBJECT IDENTIFIER 561 9: OBJECT IDENTIFIER
: aes128-CBC (2 16 840 1 101 3 4 1 2) : aes128-CBC (2 16 840 1 101 3 4 1 2)
572 16: OCTET STRING 572 16: OCTET STRING
: 48 0C CA FE BA BE FA CE DB AD DE CA F8 88 77 81 : 48 0C CA FE BA BE FA CE DB AD DE CA F8 88 77 81
: } : }
590 16: [0] C6 CA 65 DB 7B DD 76 B0 F3 7E 2F AB 62 64 B6 6D 590 16: [0] C6 CA 65 DB 7B DD 76 B0 F3 7E 2F AB 62 64 B6 6D
: } : }
: } : }
: } : }
: } : }]]></artwork>
]]></artwork>
</li>
</ul>
</section> </section>
<section anchor="recipient-rsa-kem-decapsulate-processing"> <section anchor="recipient-rsa-kem-decapsulate-processing">
<name>Recipient RSA-KEM Decapsulate() Processing</name> <name>Recipient RSA-KEM Decapsulate() Processing</name>
<t>Bob's private key:</t> <t>Bob's private key:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIG5AIBAAKCAYEA3ocW14cxncPJ47fnEjBZAyfC2lqapL3ET4jvV6C7gGeVrRQx MIIG5AIBAAKCAYEA3ocW14cxncPJ47fnEjBZAyfC2lqapL3ET4jvV6C7gGeVrRQx
WPDwl+cFYBBR2ej3j3/0ecDmu+XuVi2+s5JHKeeza+itfuhsz3yifgeEpeK8T+Su WPDwl+cFYBBR2ej3j3/0ecDmu+XuVi2+s5JHKeeza+itfuhsz3yifgeEpeK8T+Su
sHhn20/NBLhYKbh3kiAcCgQ56dpDrDvDcLqqvS3jg/VO+OPnZbofoHOOevt8Q/ro sHhn20/NBLhYKbh3kiAcCgQ56dpDrDvDcLqqvS3jg/VO+OPnZbofoHOOevt8Q/ro
ahJe1PlIyQ4udWB8zZezJ4mLLfbOA9YVaYXx2AHHZJevo3nmRnlgJXo6mE00E/6q ahJe1PlIyQ4udWB8zZezJ4mLLfbOA9YVaYXx2AHHZJevo3nmRnlgJXo6mE00E/6q
khjDHKSMdl2WG6mO9TCDZc9qY3cAJDU6Ir0vSH7qUl8/vN13y4UOFkn8hM4kmZ6b khjDHKSMdl2WG6mO9TCDZc9qY3cAJDU6Ir0vSH7qUl8/vN13y4UOFkn8hM4kmZ6b
JqbZt5NbjHtY4uQ0VMW3RyESzhrO02mrp39auLNnH3EXdXaV1tk75H3qC7zJaeGW JqbZt5NbjHtY4uQ0VMW3RyESzhrO02mrp39auLNnH3EXdXaV1tk75H3qC7zJaeGW
MJyQfOE3YfEGRKn8fxubji716D8UecAxAzFyFL6m1JiOyV5acAiOpxN14qRYZdHn MJyQfOE3YfEGRKn8fxubji716D8UecAxAzFyFL6m1JiOyV5acAiOpxN14qRYZdHn
XOM9DqGIGpoeY1UuD4Mo05osOqOUpBJHA9fSwhSZG7VNf+vgNWTLNYSYLI04KiMd XOM9DqGIGpoeY1UuD4Mo05osOqOUpBJHA9fSwhSZG7VNf+vgNWTLNYSYLI04KiMd
skipping to change at line 1657 skipping to change at line 1383
B8oph/jD8O2YCk4YCTDOXPEi8Rjusxzro+whvRR+kG0gsGGcKSVNCPj1fNISEte4 B8oph/jD8O2YCk4YCTDOXPEi8Rjusxzro+whvRR+kG0gsGGcKSVNCPj1fNISEte4
gJId7O1mUAAzeDjn/VaS/PXQovEMolssPPKn9NocbKbpAoHBAJnFHJunl22W/lrr gJId7O1mUAAzeDjn/VaS/PXQovEMolssPPKn9NocbKbpAoHBAJnFHJunl22W/lrr
ppmPnIzjI30YVcYOA5vlqLKyGaAsnfYqP1WUNgfVhq2jRsrHx9cnHQI9Hu442PvI ppmPnIzjI30YVcYOA5vlqLKyGaAsnfYqP1WUNgfVhq2jRsrHx9cnHQI9Hu442PvI
x+c5H30YFJ4ipE3eRRRmAUi4ghY5WgD+1hw8fqyUW7E7l5LbSbGEUVXtrkU5G64T x+c5H30YFJ4ipE3eRRRmAUi4ghY5WgD+1hw8fqyUW7E7l5LbSbGEUVXtrkU5G64T
UR91LEyMF8OPATdiV/KD4PWYkgaqRm3tVEuCVACDTQkqNsOOi3YPQcm270w6gxfQ UR91LEyMF8OPATdiV/KD4PWYkgaqRm3tVEuCVACDTQkqNsOOi3YPQcm270w6gxfQ
SOEy/kdhCFexJFA8uZvmh6Cp2crczxyBilR/yCxqKOONqlFdOQKBwFbJk5eHPjJz SOEy/kdhCFexJFA8uZvmh6Cp2crczxyBilR/yCxqKOONqlFdOQKBwFbJk5eHPjJz
AYueKMQESPGYCrwIqxgZGCxaqeVArHvKsEDx5whI6JWoFYVkFA8F0MyhukoEb/2x AYueKMQESPGYCrwIqxgZGCxaqeVArHvKsEDx5whI6JWoFYVkFA8F0MyhukoEb/2x
2qB5T88Dg3EbqjTiLg3qxrWJ2OxtUo8pBP2I2wbl2NOwzcbrlYhzEZ8bJyxZu5i1 2qB5T88Dg3EbqjTiLg3qxrWJ2OxtUo8pBP2I2wbl2NOwzcbrlYhzEZ8bJyxZu5i1
sYILC8PJ4Qzw6jS4Qpm4y1WHz8e/ElW6VyfmljZYA7f9WMntdfeQVqCVzNTvKn6f sYILC8PJ4Qzw6jS4Qpm4y1WHz8e/ElW6VyfmljZYA7f9WMntdfeQVqCVzNTvKn6f
hg6GSpJTzp4LV3ougi9nQuWXZF2wInsXkLYpsiMbL6Fz34RwohJtYA== hg6GSpJTzp4LV3ougi9nQuWXZF2wInsXkLYpsiMbL6Fz34RwohJtYA==
-----END PRIVATE KEY----- -----END PRIVATE KEY-----]]></artwork>
]]></artwork>
<t>Bob checks that the length of the ciphertext is less than nLen bytes. </t> <t>Bob checks that the length of the ciphertext is less than nLen bytes. </t>
<t>Bob checks that the ciphertext is greater than zero and is less <t>Bob checks that the ciphertext is greater than zero and is less
than his RSA modulus.</t> than his RSA modulus.</t>
<t>Bob decrypts the ciphertext with his RSA private key to obtain <t>Bob decrypts the ciphertext with his RSA private key to obtain
the integer z:</t> the integer z:</t>
<artwork><![CDATA[ <artwork><![CDATA[
9c126102a5c1c0354672a3c2f19fc9ddea988f815e1da812c7bd4f8eb082bdd1 9c126102a5c1c0354672a3c2f19fc9ddea988f815e1da812c7bd4f8eb082bdd1
4f85a7f7c2f1af11d5333e0d6bcb375bf855f208da72ba27e6fb0655f2825aa6 4f85a7f7c2f1af11d5333e0d6bcb375bf855f208da72ba27e6fb0655f2825aa6
2b93b1f9bbd3491fed58f0380fa0de36430e3a144d569600bd362609be5b9481 2b93b1f9bbd3491fed58f0380fa0de36430e3a144d569600bd362609be5b9481
0875990b614e406fa6dff500043cbca95968faba61f795096a7fb3687a51078c 0875990b614e406fa6dff500043cbca95968faba61f795096a7fb3687a51078c
4ca2cb663366b0bea0cd9cccac72a25f3f4ed03deb68b4453bba44b943f4367b 4ca2cb663366b0bea0cd9cccac72a25f3f4ed03deb68b4453bba44b943f4367b
67d6cd10c8ace53f545aac50968fc3c6ecc80f3224b64e37038504e2d2c0e2b2 67d6cd10c8ace53f545aac50968fc3c6ecc80f3224b64e37038504e2d2c0e2b2
9d45e46c62826d96331360e4c17ea3ef89a9efc5fac99eda830e81450b6534dc 9d45e46c62826d96331360e4c17ea3ef89a9efc5fac99eda830e81450b6534dc
0bdf042b8f3b706649c631fe51fc2445cc8d447203ec2f41f79cdfea16de1ce6 0bdf042b8f3b706649c631fe51fc2445cc8d447203ec2f41f79cdfea16de1ce6
abdfdc1e2ef2e5d5d8a65e645f397240ef5a26f5e4ff715de782e30ecf477293 abdfdc1e2ef2e5d5d8a65e645f397240ef5a26f5e4ff715de782e30ecf477293
e89e13171405909a8e04dd31d21d0c57935fc1ceea8e1033e31e1bc8c56da0f3 e89e13171405909a8e04dd31d21d0c57935fc1ceea8e1033e31e1bc8c56da0f3
d79510f3f380ff58e5a61d361f2f18e99fbae5663172e8cd1f21deaddc5bbbea d79510f3f380ff58e5a61d361f2f18e99fbae5663172e8cd1f21deaddc5bbbea
060d55f1842b93d1a9c888d0bf85d0af9947fe51acf940c7e7577eb79cabecb3 060d55f1842b93d1a9c888d0bf85d0af9947fe51acf940c7e7577eb79cabecb3]]></artwork>
]]></artwork>
<t>Bob checks that the integer z is greater than zero and is less <t>Bob checks that the integer z is greater than zero and is less
than his RSA modulus.</t> than his RSA modulus.</t>
<t>Bob derives the shared secret (SS) using KDF3 with SHA-256:</t> <t>Bob derives the shared secret (SS) using KDF3 with SHA-256:</t>
<artwork><![CDATA[ <artwork><![CDATA[
3cf82ec41b54ed4d37402bbd8f805a52 3cf82ec41b54ed4d37402bbd8f805a52]]></artwork>
]]></artwork>
</section> </section>
<section anchor="recipient-cms-processing"> <section anchor="recipient-cms-processing">
<name>Recipient CMS Processing</name> <name>Recipient CMS Processing</name>
<t>Bob encodes the CMSORIforKEMOtherInfo structure with the algorithm <t>Bob encodes the CMSORIforKEMOtherInfo structure with the algorithm
identifier for AES-128-KEYWRAP and a key length of 16 octets. identifier for AES-128-KEYWRAP and a key length of 16 octets.
The DER encoding of CMSORIforKEMOtherInfo is not repeated here.</t> The DER encoding of CMSORIforKEMOtherInfo is not repeated here.</t>
<t>Bob derives the key-encryption key from shared secret and the <t>Bob derives the key-encryption key from shared secret and the
CMSORIforKEMOtherInfo structure with KDF3 and SHA-256, the KEK is:</t> CMSORIforKEMOtherInfo structure with KDF3 and SHA-256, the KEK is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
e6dc9d62ff2b469bef604c617b018718 e6dc9d62ff2b469bef604c617b018718]]></artwork>
]]></artwork>
<t>Bob uses AES-KEY-WRAP to decrypt the content-encryption key <t>Bob uses AES-KEY-WRAP to decrypt the content-encryption key
with the key-encryption key; the content-encryption key is:</t> with the key-encryption key. The content-encryption key is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
77f2a84640304be7bd42670a84a1258b 77f2a84640304be7bd42670a84a1258b]]></artwork>
]]></artwork>
<t>Bob decrypts the content using AES-128-CBC with the content- <t>Bob decrypts the content using AES-128-CBC with the content-
encryption key. The 16-octet IV used is:</t> encryption key. The 16-octet IV used is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
480ccafebabefacedbaddecaf8887781 480ccafebabefacedbaddecaf8887781]]></artwork>
]]></artwork>
<t>The received ciphertext content is:</t> <t>The received ciphertext content is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
c6ca65db7bdd76b0f37e2fab6264b66d c6ca65db7bdd76b0f37e2fab6264b66d]]></artwork>
]]></artwork>
<t>The resulting padded plaintext content is:</t> <t>The resulting padded plaintext content is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
48656c6c6f2c20776f726c6421030303 48656c6c6f2c20776f726c6421030303]]></artwork>
]]></artwork>
<t>After stripping the AES-CBC padding, the plaintext content is:</t> <t>After stripping the AES-CBC padding, the plaintext content is:</t>
<artwork><![CDATA[ <artwork><![CDATA[
Hello, world! Hello, world!]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
<section numbered="false" anchor="acknowledgements"> <section numbered="false" anchor="acknowledgements">
<name>Acknowledgements</name> <name>Acknowledgements</name>
<t>We thank James Randall, Burt Kaliski, and John Brainard as the <t>We thank <contact fullname="James Randall"/>, <contact fullname="Burt
original authors of <xref target="RFC5990"/>; this document is based on their wo Kaliski"/>, and <contact fullname="John Brainard"/> as the original
rk.</t> authors of <xref target="RFC5990"/>; this document is based on their
work.</t>
<t>We thank the members of the ASC X9F1 working group for their <t>We thank the members of the ASC X9F1 working group for their
contributions to drafts of ANS X9.44, which led to <xref target="RFC5990"/>.</t> contributions to drafts of ANS X9.44, which led to <xref
<t>We thank Blake Ramsdell, Jim Schaad, Magnus Nystrom, Bob Griffin, target="RFC5990"/>.</t>
and John Linn for helping bring <xref target="RFC5990"/> to fruition.</t> <t>We thank <contact fullname="Blake Ramsdell"/>, <contact fullname="Jim
<t>We thank Schaad"/>, <contact fullname="Magnus Nystrom"/>, <contact fullname="Bob
Burt Kaliski, Griffin"/>, and <contact fullname="John Linn"/> for helping bring <xref
Alex Railean, target="RFC5990"/> to fruition.</t>
Joe Mandel, <t>We thank <contact fullname="Burt Kaliski"/>, <contact fullname="Alex
Mike Ounsworth, Railean"/>, <contact fullname="Joe Mandel"/>, <contact fullname="Mike
Peter Campbell, Ounsworth"/>, <contact fullname="Peter Campbell"/>, <contact
Daniel Van Geest, and David Ireland fullname="Daniel Van Geest"/>, and <contact fullname="David Ireland"/>
for careful review and thoughtful comments that greatly improved this document.< for careful review and thoughtful comments that greatly improved this
/t> document.</t>
</section> </section>
</back> </back>
<!-- ##markdown-source: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<!-- [rfced] We note that the following terms appear inconsistently
throughout the document. If there are no objections, we will use the
form on the right.
PKCS #1 v1.5 vs. PKCS #1 v1.5 algorithm
RSA-KEM vs. RSA-KEM algorithm vs. RSA-KEM Algorithm
-->
</rfc> </rfc>
 End of changes. 192 change blocks. 
1274 lines changed or deleted 473 lines changed or added

This html diff was produced by rfcdiff 1.48.