Limited Additional Mechanisms for PKIX and SMIME              R. Housley
Internet-Draft                                            Vigil Security
Obsoletes: 5990 (if approved)                                  S. Turner
Intended status: Standards Track                                   sn3rd
Expires: 15 March 2024                                 12 September 2023


 Use of the RSA-KEM Algorithm in the Cryptographic Message Syntax (CMS)
                     draft-ietf-lamps-rfc5990bis-01

Abstract

   The RSA Key Encapsulation Mechanism (RSA-KEM) Algorithm is a one-pass
   (store-and-forward) cryptographic mechanism for an originator to
   securely 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.  This document specifies the conventions for
   using the RSA-KEM Algorithm with the Cryptographic Message Syntax
   (CMS) using KEMRecipientInfo as specified in draft-ietf-lamps-cms-
   kemri.

About This Document

   This note is to be removed before publishing as an RFC.

   Status information for this document may be found at
   https://datatracker.ietf.org/doc/draft-ietf-lamps-rfc5990bis/.

   Discussion of this document takes place on the Limited Additional
   Mechanisms for PKIX and SMIME Working Group mailing list
   (mailto:spasm@ietf.org), which is archived at
   https://mailarchive.ietf.org/arch/browse/spasm/.  Subscribe at
   https://www.ietf.org/mailman/listinfo/spasm/.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."



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   This Internet-Draft will expire on 15 March 2024.

Copyright Notice

   Copyright (c) 2023 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.
   Please review these documents carefully, as they describe your rights
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   provided without warranty as described in the Revised BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Conventions and Definitions . . . . . . . . . . . . . . .   4
     1.2.  ASN.1 . . . . . . . . . . . . . . . . . . . . . . . . . .   4
     1.3.  Changes Since RFC 5990  . . . . . . . . . . . . . . . . .   4
   2.  Use of the RSA-KEM Algorithm in CMS . . . . . . . . . . . . .   5
     2.1.  Underlying Components . . . . . . . . . . . . . . . . . .   6
     2.2.  RecipientInfo Conventions . . . . . . . . . . . . . . . .   6
     2.3.  Certificate Conventions . . . . . . . . . . . . . . . . .   7
     2.4.  SMIMECapabilities Attribute Conventions . . . . . . . . .   8
   3.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
   4.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  10
   5.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  10
     5.1.  Normative References  . . . . . . . . . . . . . . . . . .  10
     5.2.  Informative References  . . . . . . . . . . . . . . . . .  12
   Appendix A.  RSA-KEM Algorithm  . . . . . . . . . . . . . . . . .  13
     A.1.  Underlying Components . . . . . . . . . . . . . . . . . .  13
     A.2.  Originator's Operations . . . . . . . . . . . . . . . . .  14
     A.3.  Recipient's Operations  . . . . . . . . . . . . . . . . .  15
   Appendix B.  ASN.1 Syntax . . . . . . . . . . . . . . . . . . . .  16
     B.1.  Underlying Components . . . . . . . . . . . . . . . . . .  16
     B.2.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . .  17
   Appendix C.  SMIMECapabilities Examples . . . . . . . . . . . . .  22
   Appendix D.  RSA-KEM CMS Enveloped-Data Example . . . . . . . . .  23
     D.1.  Originator Processing . . . . . . . . . . . . . . . . . .  24
     D.2.  ContentInfo and EnvelopedData . . . . . . . . . . . . . .  26
     D.3.  Recipient Processing  . . . . . . . . . . . . . . . . . .  28
   Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . .  30
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  31





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1.  Introduction

   The RSA Key Encapsulation Mechanism (RSA-KEM) Algorithm is a one-pass
   (store-and-forward) cryptographic mechanism for an originator to
   securely send keying material to a recipient using the recipient's
   RSA public key.  The RSA-KEM Algorithm is specified in Clause 11.5 of
   [ISO18033-2].

   The RSA-KEM Algorithm takes a different approach than other RSA key
   transport mechanisms [RFC8017], with the goal of providing higher
   security assurance.  The RSA-KEM Algorithm encrypts a random integer
   with the recipient's RSA public key, derives a key-encryption key
   from the random integer, and wraps a symmetric content-encryption key
   with the key-encryption key.  In this way, the originator and the
   recipient end up with the same content-encryption key.  Given a
   content-encryption key CEK, RSA-KEM can be summarized as:

   1.  Generate a random integer z between 0 and n-1.

   2.  Encrypt the integer z with the recipient's RSA public key:

          c = z^e mod n

   3.  Derive a key-encryption key KEK from the integer z:

          KEK = KDF(z)

   4.  Wrap the CEK with the KEK to obtain wrapped keying material WK:

          WK = WRAP(KEK, CEK)

   5.  The originator sends c and WK to the recipient.



















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   This different approach provides higher security assurance for two
   reasons.  First, the input to the underlying RSA operation is
   effectively a random integer between 0 and n-1, where n is the RSA
   modulus, so it does not have any structure that could be exploited by
   an adversary.  Second, the input is independent of the keying
   material so the result of the RSA decryption operation is not
   directly available to an adversary.  As a result, the RSA-KEM
   Algorithm enjoys a "tight" security proof in the random oracle model.
   (In other padding schemes, such as PKCS #1 v1.5 [RFC8017], the input
   has structure and/or depends on the keying material, and the provable
   security assurances are not as strong.)  The approach is also
   architecturally convenient because the public-key operations are
   separate from the symmetric operations on the keying material.
   Another benefit is that the length of the keying material is bounded
   only by the symmetric key-wrapping algorithm, not the size of the RSA
   modulus.

   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.

1.1.  Conventions and Definitions

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

1.2.  ASN.1

   CMS values are generated using ASN.1 [X.680], which uses the Basic
   Encoding Rules (BER) and the Distinguished Encoding Rules (DER)
   [X.690].

1.3.  Changes Since RFC 5990

   RFC 5990 [RFC5990] specified the conventions for using the RSA-KEM
   Algorithm in CMS as a key transport algorithm.  That is, it used
   KeyTransRecipientInfo [RFC5652] for each recipient.  This approach
   resulted in a very complex parameter definition with the id-rsa-kem
   algorithm identifier.  Implementation experience with many different
   algorithms has shown that complex parameter structures cause
   interoperability issues.  Since the publication of RFC 5990, a new
   KEMRecipientInfo structure [I-D.ietf-lamps-cms-kemri] has been
   defined to support KEM algorithms, and this new structure avoids the
   complex parameters structure that was used in RFC 5990.  Likewise,
   when the id-rsa-kem algorithm identifier appears in the
   SubjectPublicKeyInfo field of a certificate, this document encourages



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   the omission of any parameters.  Also, to avoid visual confusion with
   id-kem-rsa, id-rsa-kem-spki is introduced as an alias for id-rsa-kem.

   RFC 5990 uses EK and the EncryptedKey, which the concatenation of C
   and WK (C || WK).  The use of EK is necessary to align with the
   KeyTransRecipientInfo structure.  In this document, C and WK are sent
   in separate fields of new KEMRecipientInfo structure.  In particular,
   C is carried in the kemct field, and WK is carried in the
   encryptedKey field.

   RFC 5990 supports the future definition of additional KEM algorithms
   that use RSA; this document supports only one, and it is identified
   by the id-kem-rsa object identifier.

   RFC 5990 includes support for Camellia and Triple-DES block ciphers;
   discussion of these block ciphers is removed from this document, but
   the algorithm identifiers remain in the ASN.1 Module Appendix B.2.

   RFC 5990 includes support for SHA-1 hash function; discussion of this
   hash function is removed from this document, but the algorithm
   identifier remains in the ASN.1 module Appendix B.2.

   RFC 5990 required support for the KDF3 [ANS-X9.44] key-derivation
   function; this document continues to require support for the KDF3
   key-derivation function, but it requires support for SHA-256 [SHS] as
   the hash function.

   RFC 5990 recommends support for alternatives to KDF3 and AES-Wrap-
   128; this document simply states that other key-derivation functions
   and key-encryption algorithms MAY be supported.

   RFC 5990 includes an ASN.1 module; this document provides an
   alternative ASN.1 module that follows the conventions established in
   [RFC5911], [RFC5912], and [RFC6268].  The new ASN.1 module
   Appendix B.2 produces the same bits-on-the-wire as the one in RFC
   5990.

2.  Use of the RSA-KEM Algorithm in CMS

   The RSA-KEM Algorithm MAY be employed for one or more recipients in
   the CMS enveloped-data content type [RFC5652], the CMS authenticated-
   data content type [RFC5652], or the CMS authenticated-enveloped-data
   content type [RFC5083].  In each case, the KEMRecipientInfo
   [I-D.ietf-lamps-cms-kemri] is used with with the RSA-KEM Algorithm to
   securely transfer the content-encryption key from the originator to
   the recipient.





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2.1.  Underlying Components

   A CMS implementation that supports the RSA-KEM Algorithm MUST support
   at least the following underlying components:

   *  For the key-derivation function, an implementation MUST support
      KDF3 [ANS-X9.44] with SHA-256 [SHS].

   *  For key-wrapping, an implementation MUST support the AES-Wrap-128
      [RFC3394] key-encryption algorithm.

   An implementation MAY also support other key-derivation functions and
   key-encryption algorithms as well.

2.2.  RecipientInfo Conventions

   When the RSA-KEM Algorithm is employed for a recipient, the
   RecipientInfo alternative for that recipient MUST be
   OtherRecipientInfo using the KEMRecipientInfo structure
   [I-D.ietf-lamps-cms-kemri].  The fields of the KEMRecipientInfo MUST
   have the following values:

      version is the syntax version number; it MUST be 0.

      rid identifies the recipient's certificate or public key.

      kem identifies the KEM algorithm; it MUST contain id-kem-rsa.

      kemct is the ciphertext produced for this recipient; it contains C
      from steps 1 and 2 of Originator's Operations in Appendix A.

      kdf identifies the key-derivation algorithm.

      kekLength is the size of the key-encryption key in octets.

      ukm is an optional random input to the key-derivation function.

      wrap identifies a key-encryption algorithm used to encrypt the
      content-encryption key.

      encryptedKey is the result of encrypting the keying material with
      the key-encryption key.  When used with the CMS enveloped-data
      content type [RFC5652], the keying material is a content-
      encryption key.  When used with the CMS authenticated-data content
      type [RFC5652], the keying material is a message-authentication
      key.  When used with the CMS authenticated-enveloped-data content
      type [RFC5083], the keying material is a content-authenticated-
      encryption key.



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   NOTE: For backward compatibility, implementations MAY also support
   RSA-KEM Key Transport Algorithm, which uses KeyTransRecipientInfo as
   specified in [RFC5990].

2.3.  Certificate Conventions

   The conventions specified in this section augment RFC 5280 [RFC5280].

   A recipient who employs the RSA-KEM Algorithm MAY identify the public
   key in a certificate by the same AlgorithmIdentifier as for the PKCS
   #1 v1.5 algorithm, that is, using the rsaEncryption object identifier
   [RFC8017].  The fact that the recipient will accept RSA-KEM with this
   public key is not indicated by the use of this object identifier.
   The willingness to accept the RSA-KEM Algorithm MAY be signaled by
   the use of the appropriate SMIME Capabilities either in a message or
   in the certificate.

   If the recipient wishes only to employ the RSA-KEM Algorithm with a
   given public key, the recipient MUST identify the public key in the
   certificate using the id-rsa-kem-spki object identifier; see
   Appendix B.  When the id-rsa-kem-spki object identifier appears in
   the SubjectPublicKeyInfo algorithm field of the certificate, the
   parameters field from AlgorithmIdentifier SHOULD be absent.  That is,
   the AlgorithmIdentifier SHOULD be a SEQUENCE of one component, the
   id-rsa-kem-spki object identifier.

   When the AlgorithmIdentifier parameters are present, the
   GenericHybridParameters MUST be used.  As described in the next
   section, the GenericHybridParameters constrain the values that can be
   used with the RSA public key for the kdf, kekLength, and wrap fields
   of the KEMRecipientInfo structure.

   Regardless of the AlgorithmIdentifier used, the RSA public key MUST
   be carried in the subjectPublicKey BIT STRING within the
   SubjectPublicKeyInfo filed of the certificate using the RSAPublicKey
   type defined in [RFC8017].

   The intended application for the public key MAY be indicated in the
   key usage certificate extension as specified in Section 4.2.1.3 of
   [RFC5280].  If the 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 usage extension MUST
   contain the following value:

      keyEncipherment






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   The digitalSignatrure and dataEncipherment values SHOULD NOT be
   present.  That is, a public key intended to be employed only with the
   RSA-KEM Algorithm SHOULD NOT also be employed for data encryption or
   for digital signatures.  Good cryptographic practice employs a given
   RSA 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 to maintain provable security.

2.4.  SMIMECapabilities Attribute Conventions

   Section 2.5.2 of [RFC8551] defines the SMIMECapabilities signed
   attribute (defined as a SEQUENCE of SMIMECapability SEQUENCEs) to
   announce a partial list of algorithms that an S/MIME implementation
   can support.  When constructing a CMS signed-data content type
   [RFC5652], a compliant implementation MAY include the
   SMIMECapabilities signed attribute announcing that it supports the
   RSA-KEM Algorithm.

   The SMIMECapability SEQUENCE representing the RSA-KEM Algorithm MUST
   include the id-rsa-kem-spki object identifier in the capabilityID
   field; see Appendix B for the object identifier value, and see
   Appendix C for examples.  When the id-rsa-kem-spki object identifier
   appears in the capabilityID field and the parameters are present,
   then the parameters field MUST use the GenericHybridParameters type.

     GenericHybridParameters ::= SEQUENCE {
       kem  KeyEncapsulationMechanism,
       dem  DataEncapsulationMechanism }

   The fields of the GenericHybridParameters type have the following
   meanings:

      kem is an AlgorithmIdentifer; the algorithm field MUST be set to
      id-kem-rsa; the parameters field MUST be RsaKemParameters, which
      is a SEQUENCE of an AlgorithmIdentifier that identifies the
      supported key-derivation function and a positive INTEGER that
      identifies the length of the key-encryption key in octets.  If the
      GenericHybridParameters are present, then the provided kem value
      MUST be used as the key-derivation function in the kdf field of
      KEMRecipientInfo, and the provided key length MUST be used in the
      kekLength of KEMRecipientInfo.

      dem is an AlgorithmIdentifier; the algorithm field MUST be
      present, and it identifies the key-encryption algorithm;
      parameters are optional.  If the GenericHybridParameters are
      present, then the provided dem value MUST be used in the wrap
      field of KEMRecipientInfo.




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3.  Security Considerations

   The RSA-KEM Algorithm should be considered as a replacement for the
   widely implemented PKCS #1 v1.5 [RFC8017] for new applications that
   use CMS to avoid potential vulnerabilities to chosen-ciphertext
   attacks and gain a tighter security proof; however, the RSA-KEM
   Algorithm has the disadvantage of slightly longer encrypted keying
   material.

   The security of the RSA-KEM Algorithm can be shown to be tightly
   related to the difficulty of either solving the RSA problem or
   breaking the underlying symmetric key-encryption algorithm, if the
   underlying key-derivation function is modeled as a random oracle, and
   assuming that the symmetric key-encryption algorithm satisfies the
   properties of a data encapsulation mechanism [SHOUP].  While in
   practice a random-oracle result does not provide an actual security
   proof for any particular key-derivation function, the result does
   provide assurance that the general 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.

   The RSA key size and the underlying components need to be selected
   consistent with the desired security level.  Several security levels
   have been identified in the NIST SP 800-57 Part 1
   [NISTSP800-57pt1r5].  To achieve 128-bit security, the RSA key size
   SHOULD be at least 3072 bits, the key-derivation function SHOULD make
   use of SHA-256, and the symmetric key-encryption algorithm SHOULD be
   AES Key Wrap with a 128-bit key.

   Implementations MUST protect the RSA private key, the key-encryption
   key, the content-encryption key, the content-authenticated-encryption
   key.  Compromise of the RSA private key could result in the
   disclosure of all messages protected with that key.  Compromise of
   the key-encryption key, the content-encryption key, or content-
   authenticated-encryption key could result in disclosure of the
   associated encrypted content.

   Additional considerations related to key management may be found in
   [NISTSP800-57pt1r5].

   The security of the RSA-KEM Algorithm also depends on the strength of
   the random number generator, which SHOULD have a comparable security
   level.  For further discussion on random number generation, see
   [RFC4086].

   Implementations SHOULD NOT reveal information about intermediate
   values or calculations, whether by timing or other "side channels",
   otherwise an opponent may be able to determine information about the



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   keying data and/or the recipient's private key.  Although not all
   intermediate information may be useful to an opponent, it is
   preferable to conceal as much information as is practical, unless
   analysis specifically indicates that the information would not be
   useful to an opponent.

   Generally, good cryptographic practice employs a given RSA 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 to maintain provable security.  While RSA public keys have
   often been employed for multiple purposes such as key transport and
   digital signature without any known bad interactions, for increased
   security assurance, such combined use of an RSA key pair is NOT
   RECOMMENDED in the future (unless the different schemes are
   specifically designed to be used together).

   Accordingly, an RSA key pair used for the RSA-KEM Algorithm SHOULD
   NOT also be used for digital signatures.  Indeed, the Accredited
   Standards Committee X9 (ASC X9) requires such a separation between
   key pairs used for key establishment and key pairs used for digital
   signature [ANS-X9.44].  Continuing this principle of key separation,
   a key pair used for the RSA-KEM Algorithm SHOULD NOT be used with
   other key establishment schemes, or for data encryption, or with more
   than one set of underlying algorithm components.

   Parties MAY gain assurance that implementations are correct through
   formal implementation validation, such as the NIST Cryptographic
   Module Validation Program (CMVP) [CMVP].

4.  IANA Considerations

   For the ASN.1 Module in Appendix B.2, IANA is requested to assign an
   object identifier (OID) for the module identifier.  The OID for the
   module should be 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 should be set to "id-mod-cms-rsa-kem-2023".

5.  References

5.1.  Normative References

   [I-D.ietf-lamps-cms-kemri]
              Housley, R., Gray, J., and T. Okubo, "Using Key
              Encapsulation Mechanism (KEM) Algorithms in the
              Cryptographic Message Syntax (CMS)", Work in Progress,
              Internet-Draft, draft-ietf-lamps-cms-kemri-04, 9 August
              2023, <https://datatracker.ietf.org/doc/html/draft-ietf-
              lamps-cms-kemri-04>.



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   [ISO18033-2]
              ISO/IEC JTC 1/SC 27, "Information technology -- Security
              techniques -- Encryption algorithms -- Part 2: Asymmetric
              ciphers", ISO/IEC 18033-2:2006, 2006,
              <https://www.iso.org/standard/37971.html>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC5083]  Housley, R., "Cryptographic Message Syntax (CMS)
              Authenticated-Enveloped-Data Content Type", RFC 5083,
              DOI 10.17487/RFC5083, November 2007,
              <https://www.rfc-editor.org/info/rfc5083>.

   [RFC5280]  Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
              Housley, R., and W. Polk, "Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,
              <https://www.rfc-editor.org/info/rfc5280>.

   [RFC5652]  Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
              RFC 5652, DOI 10.17487/RFC5652, September 2009,
              <https://www.rfc-editor.org/info/rfc5652>.

   [RFC5911]  Hoffman, P. and J. Schaad, "New ASN.1 Modules for
              Cryptographic Message Syntax (CMS) and S/MIME", RFC 5911,
              DOI 10.17487/RFC5911, June 2010,
              <https://www.rfc-editor.org/info/rfc5911>.

   [RFC5912]  Hoffman, P. and J. Schaad, "New ASN.1 Modules for the
              Public Key Infrastructure Using X.509 (PKIX)", RFC 5912,
              DOI 10.17487/RFC5912, June 2010,
              <https://www.rfc-editor.org/info/rfc5912>.

   [RFC6268]  Schaad, J. and S. Turner, "Additional New ASN.1 Modules
              for the Cryptographic Message Syntax (CMS) and the Public
              Key Infrastructure Using X.509 (PKIX)", RFC 6268,
              DOI 10.17487/RFC6268, July 2011,
              <https://www.rfc-editor.org/info/rfc6268>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.






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   [RFC8551]  Schaad, J., Ramsdell, B., and S. Turner, "Secure/
              Multipurpose Internet Mail Extensions (S/MIME) Version 4.0
              Message Specification", RFC 8551, DOI 10.17487/RFC8551,
              April 2019, <https://www.rfc-editor.org/info/rfc8551>.

   [SHS]      National Institute of Standards and Technology, "Secure
              Hash Standard", DOI 10.6028/nist.fips.180-4, July 2015,
              <https://doi.org/10.6028/nist.fips.180-4>.

   [X.680]    ITU-T, "Information technology -- Abstract Syntax Notation
              One (ASN.1): Specification of basic notation", ITU-T
              Recommendation X.680, ISO/IEC 8824-1:2021, February 2021,
              <https://www.itu.int/rec/T-REC-X.680>.

   [X.690]    ITU-T, "Information technology -- ASN.1 encoding rules:
              Specification of Basic Encoding Rules (BER), Canonical
              Encoding Rules (CER) and Distinguished Encoding Rules
              (DER)", ITU-T Recommendation X.690, ISO/IEC 8825-1:2021,
              February 2021, <https://www.itu.int/rec/T-REC-X.680>.

5.2.  Informative References

   [ANS-X9.44]
              American National Standards Institute, "Public Key
              Cryptography for the Financial Services Industry -- Key
              Establishment Using Integer Factorization Cryptography",
              American National Standard X9.44, 2007.

   [CMVP]     National Institute of Standards and Technology,
              "Cryptographic Module Validation Program", 2016,
              <https://csrc.nist.gov/projects/cryptographic-module-
              validation-program>.

   [NISTSP800-57pt1r5]
              Barker, E. and National Institute of Standards and
              Technology, "Recommendation for key management:",
              DOI 10.6028/nist.sp.800-57pt1r5, May 2020,
              <https://doi.org/10.6028/nist.sp.800-57pt1r5>.

   [RFC3394]  Schaad, J. and R. Housley, "Advanced Encryption Standard
              (AES) Key Wrap Algorithm", RFC 3394, DOI 10.17487/RFC3394,
              September 2002, <https://www.rfc-editor.org/info/rfc3394>.

   [RFC4086]  Eastlake 3rd, D., Schiller, J., and S. Crocker,
              "Randomness Requirements for Security", BCP 106, RFC 4086,
              DOI 10.17487/RFC4086, June 2005,
              <https://www.rfc-editor.org/info/rfc4086>.




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   [RFC5990]  Randall, J., Kaliski, B., Brainard, J., and S. Turner,
              "Use of the RSA-KEM Key Transport Algorithm in the
              Cryptographic Message Syntax (CMS)", RFC 5990,
              DOI 10.17487/RFC5990, September 2010,
              <https://www.rfc-editor.org/info/rfc5990>.

   [RFC6194]  Polk, T., Chen, L., Turner, S., and P. Hoffman, "Security
              Considerations for the SHA-0 and SHA-1 Message-Digest
              Algorithms", RFC 6194, DOI 10.17487/RFC6194, March 2011,
              <https://www.rfc-editor.org/info/rfc6194>.

   [RFC8017]  Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch,
              "PKCS #1: RSA Cryptography Specifications Version 2.2",
              RFC 8017, DOI 10.17487/RFC8017, November 2016,
              <https://www.rfc-editor.org/info/rfc8017>.

   [SHOUP]    Shoup, V., "A Proposal for an ISO Standard for Public Key
              Encryption", Cryptology ePrint Archive Paper 2001/112,
              2001, <https://eprint.iacr.org/2001/112>.

Appendix A.  RSA-KEM Algorithm

   The RSA-KEM Algorithm is a one-pass (store-and-forward) cryptographic
   mechanism for an originator to securely send keying material to a
   recipient using the recipient's RSA public key.

   With this type of algorithm, an originator encrypts the keying
   material using the recipient's public key, and then sends the
   resulting encrypted keying material to the recipient.  The recipient
   decrypts the encrypted keying material using the recipient's private
   key to recover the keying material.

A.1.  Underlying Components

   The RSA-KEM Algorithm has the following underlying components:

   *  KDF, a key-derivation function, which derives key-encryption key
      of a specified length from a shared secret value;

   *  Wrap, a symmetric key-encryption algorithm, which encrypts keying
      material using key-encryption key that was produced by the KDF.

   The kekLen value denotes the length in bytes of the key-encryption
   key for the underlying symmetric key-encryption algorithm.







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   The length of the keying material MUST be among the lengths supported
   by the underlying symmetric key-encryption algorithm.  For example,
   the AES-Wrap key-encryption algorithm requires the kekLen to be 16,
   24, or 32 octets.  Usage and formatting of the keying material is
   outside the scope of the RSA-KEM Algorithm.

   Many key-derivation functions support the inclusion of other
   information in addition to the shared secret value in the input to
   the function.  Also, with some symmetric key-encryption algorithms,
   it is possible to associate a label with the keying material.  Such
   uses are outside the scope of this document, as they are not directly
   supported by CMS.

A.2.  Originator's Operations

   Let (n,e) be the recipient's RSA public key; see [RFC8017] for
   details.

   Let K be the keying material to be securely transferred from the
   originator to the recipient.

   Let nLen denote the length in bytes of the modulus n, i.e., the least
   integer such that 2^(8*nLen) > n.

   The originator performs the following operations:

   1.  Generate a random integer z between 0 and n-1 (see note), and
       convert z to a byte string Z of length nLen, most significant
       byte first:

           z = RandomInteger (0, n-1)

           Z = IntegerToString (z, nLen)

   2.  Encrypt the random integer z using the recipient's RSA public key
       (n,e), and convert the resulting integer c to a ciphertext C, a
       byte string of length nLen:

           c = z^e mod n

           C = IntegerToString (c, nLen)

   3.  Derive a symmetric key-encryption key KEK of length kekLen bytes
       from the byte string Z using the underlying key-derivation
       function:

           KEK = KDF (Z, kekLen)




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   4.  Wrap the keying material K with the symmetric key-encryption key
       KEK using the key-encryption algorithm to obtain wrapped keying
       material WK:

           WK = Wrap (KEK, K)

   5.  Send the ciphertext C and the wrapped keying material WK to the
       recipient.

   NOTE: The random integer z MUST be generated independently at random
   for different encryption operations, whether for the same or
   different recipients.

A.3.  Recipient's Operations

   Let (n,d) be the recipient's RSA private key; see [RFC8017] for
   details, but other private key formats are allowed.

   Let WK be the encrypted keying material.

   Let C be the ciphertext.

   Let nLen denote the length in bytes of the modulus n.

   The recipient performs the following operations:

   1.  If the length of the encrypted keying material is less than nLen
       bytes, output "decryption error", and stop.

   2.  Convert the ciphertext C to an integer c, most significant byte
       first.  Decrypt the integer c using the recipient's private key
       (n,d) to recover an integer z (see NOTE below):

           c = StringToInteger (C)

           z = c^d mod n

       If the integer c is not between 0 and n-1, output "decryption
       error", and stop.

   3.  Convert the integer z to a byte string Z of length nLen, most
       significant byte first (see NOTE below):

           Z = IntegerToString (z, nLen)

   4.  Derive a symmetric key-encryption key KEK of length kekLen bytes
       from the byte string Z using the key-derivation function (see
       NOTE below):



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           KEK = KDF (Z, kekLen)

   5.  Unwrap the wrapped keying material WK with the symmetric key-
       encryption key KEK using the underlying key-encryption algorithm
       to recover the keying material K:

           K = Unwrap (KEK, WK)

       If the unwrapping operation outputs an error, output "decryption
       error", and stop.

   6.  Output the keying material K.

   NOTE: Implementations SHOULD NOT reveal information about the integer
   z, the string Z, or about the calculation of the exponentiation in
   Step 2, the conversion in Step 3, or the key derivation in Step 4,
   whether by timing or other "side channels".  The observable behavior
   of the implementation SHOULD be the same at these steps for all
   ciphertexts C that are in range.  For example, IntegerToString
   conversion should take the same amount of time regardless of the
   actual value of the integer z.  The integer z, the string Z, and
   other intermediate results MUST be securely deleted when they are no
   longer needed.

Appendix B.  ASN.1 Syntax

   The ASN.1 syntax for identifying the RSA-KEM Algorithm is an
   extension of the syntax for the "generic hybrid cipher" in ANS X9.44
   [ANS-X9.44].

   The ASN.1 Module is unchanged from RFC 5990.  The id-rsa-kem-spki
   object identifier is used in a backward compatible manner in
   certificates [RFC5280] and SMIMECapabilities [RFC8551].  Of course,
   the use of the id-kem-rsa object identifier in the new
   KEMRecipientInfo structure [I-D.ietf-lamps-cms-kemri] was not yet
   defined at the time that RFC 5990 was written.

B.1.  Underlying Components

   Implementations that conform to this specification MUST support the
   KDF3 [ANS-X9.44] key-derivation function using SHA-256 [SHS].

   The object identifier for KDF3 is:

      id-kdf-kdf3 OBJECT IDENTIFIER ::= { x9-44-components kdf3(2) }






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   The KDF3 parameters identify the underlying hash function.  For
   alignment with the ANS X9.44, the hash function MUST be an ASC
   X9-approved hash function.  While the SHA-1 hash algorithm is
   included in the ASN.1 definitions, SHA-1 MUST NOT be used.  SHA-1 is
   considered to be obsolete; see [RFC6194].  SHA-1 remains in the ASN.1
   module for compatibility with RFC 5990.  In addition, other hash
   functions MAY be used with CMS.

      kda-kdf3 KEY-DERIVATION ::= {
         IDENTIFIER id-kdf-kdf3
         PARAMS TYPE KDF3-HashFunction ARE required
         -- No S/MIME caps defined -- }

      KDF3-HashFunction ::=
         AlgorithmIdentifier { DIGEST-ALGORITHM, {KDF3-HashFunctions} }

      KDF3-HashFunctions DIGEST-ALGORITHM ::= { X9-HashFunctions, ... }

      X9-HashFunctions DIGEST-ALGORITHM ::= {
         mda-sha1 | mda-sha224 | mda-sha256 | mda-sha384 |
         mda-sha512, ... }

   Implementations that conform to this specification MUST support the
   AES Key Wrap [RFC3394] key-encryption algorithm with a 128-bit 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
   identifiers imported from [RFC5912], and none of these algorithm
   identifiers have associated parameters:

      kwa-aes128-wrap KEY-WRAP ::= {
          IDENTIFIER id-aes128-wrap
          PARAMS ARE absent
          SMIME-CAPS { IDENTIFIED BY id-aes128-wrap } }

      kwa-aes192-wrap KEY-WRAP ::= {
          IDENTIFIER id-aes192-wrap
          PARAMS ARE absent
          SMIME-CAPS { IDENTIFIED BY id-aes192-wrap } }

      kwa-aes256-wrap KEY-WRAP ::= {
          IDENTIFIER id-aes256-wrap
          PARAMS ARE absent
          SMIME-CAPS { IDENTIFIED BY id-aes256-wrap } }

B.2.  ASN.1 Module

   RFC EDITOR: Please replace TBD2 with the value assigned by IANA
   during the publication of [I-D.ietf-lamps-cms-kemri].



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   <CODE BEGINS>
   CMS-RSA-KEM-2023
      { 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) }

   DEFINITIONS ::= BEGIN

   -- EXPORTS ALL

   IMPORTS

     KEM-ALGORITHM
       FROM KEMAlgorithmInformation-2023  -- [I-D.ietf-lamps-cms-kemri]
          { iso(1) identified-organization(3) dod(6) internet(1)
            security(5) mechanisms(5) pkix(7) id-mod(0)
            id-mod-kemAlgorithmInformation-2023(TBD3) }

     AlgorithmIdentifier{}, PUBLIC-KEY, DIGEST-ALGORITHM,
     KEY-DERIVATION, KEY-WRAP
       FROM AlgorithmInformation-2009  -- [RFC5912]
         { iso(1) identified-organization(3) dod(6) internet(1)
           security(5) mechanisms(5) pkix(7) id-mod(0)
           id-mod-algorithmInformation-02(58) }

     kwa-aes128-wrap, kwa-aes192-wrap, kwa-aes256-wrap
       FROM CMSAesRsaesOaep-2009  -- [RFC5911]
         { iso(1) member-body(2) us(840) rsadsi(113549)
           pkcs(1) pkcs-9(9) smime(16) modules(0)
           id-mod-cms-aes-02(38) }

     kwa-3DESWrap
       FROM CryptographicMessageSyntaxAlgorithms-2009  -- [RFC5911]
         { iso(1) member-body(2) us(840) rsadsi(113549)
           pkcs(1) pkcs-9(9) smime(16) modules(0)
           id-mod-cmsalg-2001-02(37) }

     id-camellia128-wrap, id-camellia192-wrap, id-camellia256-wrap
       FROM CamelliaEncryptionAlgorithmInCMS  -- [RFC3657]
         { iso(1) member-body(2) us(840) rsadsi(113549)
           pkcs(1) pkcs9(9) smime(16) modules(0)
           id-mod-cms-camellia(23) }

     mda-sha1, pk-rsa, RSAPublicKey
       FROM PKIXAlgs-2009  -- [RFC5912]
         { iso(1) identified-organization(3) dod(6) internet(1)
           security(5) mechanisms(5) pkix(7) id-mod(0)
           id-mod-pkix1-algorithms2008-02(56) }




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     mda-sha224, mda-sha256, mda-sha384, mda-sha512
       FROM PKIX1-PSS-OAEP-Algorithms-2009  -- [RFC5912]
         { iso(1) identified-organization(3) dod(6) internet(1)
           security(5) mechanisms(5) pkix(7) id-mod(0)
           id-mod-pkix1-rsa-pkalgs-02(54) } ;


   -- Useful types and definitions

   OID ::= OBJECT IDENTIFIER  -- alias

   NullParms ::= NULL

   -- ISO/IEC 18033-2 arc

   is18033-2 OID ::= { iso(1) standard(0) is18033(18033) part2(2) }

   -- NIST algorithm arc

   nistAlgorithm OID ::= { joint-iso-itu-t(2) country(16) us(840)
      organization(1) gov(101) csor(3) nistAlgorithm(4) }

   -- PKCS #1 arc

   pkcs-1 OID ::= { iso(1) member-body(2) us(840) rsadsi(113549)
      pkcs(1) pkcs-1(1) }

   -- X9.44 arc

   x9-44 OID ::= { iso(1) identified-organization(3) tc68(133)
      country(16) x9(840) x9Standards(9) x9-44(44) }

   x9-44-components OID ::= { x9-44 components(1) }

   -- RSA-KEM Algorithm

   id-rsa-kem OID ::= { iso(1) member-body(2) us(840) rsadsi(113549)
      pkcs(1) pkcs-9(9) smime(16) alg(3) 14 }

   id-rsa-kem-spki OID ::= id-rsa-kem

   GenericHybridParameters ::= SEQUENCE {
      kem  KeyEncapsulationMechanism,
      dem  DataEncapsulationMechanism }

   KeyEncapsulationMechanism ::=
      AlgorithmIdentifier { KEM-ALGORITHM, {KEMAlgorithms} }




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   KEMAlgorithms KEM-ALGORITHM ::= { kema-kem-rsa | kema-rsa-kem, ... }

   kema-rsa-kem KEM-ALGORITHM ::= {
      IDENTIFIER id-rsa-kem-spki
      PARAMS TYPE GenericHybridParameters ARE optional
      PUBLIC-KEYS { pk-rsa | pk-rsa-kem }
      UKM ARE optional
      SMIME-CAPS { TYPE GenericHybridParameters
         IDENTIFIED BY id-rsa-kem-spki } }

   kema-kem-rsa KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-rsa
      PARAMS TYPE RsaKemParameters ARE optional
      PUBLIC-KEYS { pk-rsa | pk-rsa-kem }
      UKM ARE optional
      SMIME-CAPS { TYPE GenericHybridParameters
         IDENTIFIED BY id-rsa-kem-spki } }

   id-kem-rsa OID ::= { is18033-2 key-encapsulation-mechanism(2)
      rsa(4) }

   RsaKemParameters ::= SEQUENCE {
      keyDerivationFunction  KeyDerivationFunction,
      keyLength              KeyLength }

   pk-rsa-kem PUBLIC-KEY ::= {
     IDENTIFIER id-rsa-kem-spki
     KEY RSAPublicKey
     PARAMS TYPE GenericHybridParameters ARE preferredAbsent
     -- Private key format is not specified here --
     CERT-KEY-USAGE {keyEncipherment} }

   KeyDerivationFunction ::=
      AlgorithmIdentifier { KEY-DERIVATION, {KDFAlgorithms} }

   KDFAlgorithms KEY-DERIVATION ::= { kda-kdf2 | kda-kdf3, ... }

   KeyLength ::= INTEGER (1..MAX)

   DataEncapsulationMechanism ::=
      AlgorithmIdentifier { KEY-WRAP, {DEMAlgorithms} }

   DEMAlgorithms KEY-WRAP ::= {
      X9-SymmetricKeyWrappingSchemes |
      Camellia-KeyWrappingSchemes, ... }

   X9-SymmetricKeyWrappingSchemes KEY-WRAP ::= {
      kwa-aes128-wrap | kwa-aes192-wrap | kwa-aes256-wrap |



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      kwa-3DESWrap, ... }

   X9-SymmetricKeyWrappingScheme ::=
      AlgorithmIdentifier { KEY-WRAP, {X9-SymmetricKeyWrappingSchemes} }

   Camellia-KeyWrappingSchemes KEY-WRAP ::= {
      kwa-camellia128-wrap | kwa-camellia192-wrap |
      kwa-camellia256-wrap, ... }

   Camellia-KeyWrappingScheme ::=
      AlgorithmIdentifier { KEY-WRAP, {Camellia-KeyWrappingSchemes} }

   kwa-camellia128-wrap KEY-WRAP ::= {
      IDENTIFIER id-camellia128-wrap
      PARAMS ARE absent
      SMIME-CAPS { IDENTIFIED BY id-camellia128-wrap } }

   kwa-camellia192-wrap KEY-WRAP ::= {
      IDENTIFIER id-camellia192-wrap
      PARAMS ARE absent
      SMIME-CAPS { IDENTIFIED BY id-camellia192-wrap } }

   kwa-camellia256-wrap KEY-WRAP ::= {
      IDENTIFIER id-camellia256-wrap
      PARAMS ARE absent
      SMIME-CAPS { IDENTIFIED BY id-camellia256-wrap } }

   -- Key Derivation Functions

   id-kdf-kdf2 OID ::= { x9-44-components kdf2(1) }

   kda-kdf2 KEY-DERIVATION ::= {
      IDENTIFIER id-kdf-kdf2
      PARAMS TYPE KDF2-HashFunction ARE required
      -- No S/MIME caps defined -- }

   KDF2-HashFunction ::=
      AlgorithmIdentifier { DIGEST-ALGORITHM, {KDF2-HashFunctions} }

   KDF2-HashFunctions DIGEST-ALGORITHM ::= { X9-HashFunctions, ... }

   id-kdf-kdf3 OID ::= { x9-44-components kdf3(2) }

   kda-kdf3 KEY-DERIVATION ::= {
      IDENTIFIER id-kdf-kdf3
      PARAMS TYPE KDF3-HashFunction ARE required
      -- No S/MIME caps defined -- }




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   KDF3-HashFunction ::=
      AlgorithmIdentifier { DIGEST-ALGORITHM, {KDF3-HashFunctions} }

   KDF3-HashFunctions DIGEST-ALGORITHM ::= { X9-HashFunctions, ... }

   -- Hash Functions

   X9-HashFunctions DIGEST-ALGORITHM ::= {
      mda-sha1 | mda-sha224 | mda-sha256 | mda-sha384 |
      mda-sha512, ... }

   END
   <CODE ENDS>

Appendix C.  SMIMECapabilities Examples

   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-encryption algorithm 128-bit key-encryption key, the
   SMIMECapabilities will include the following entry:

   SEQUENCE {
      id-rsa-kem-spki,                           -- RSA-KEM Algorithm
      SEQUENCE {                           -- GenericHybridParameters
         SEQUENCE {                    -- key encapsulation mechanism
            id-kem-rsa,                                    -- RSA-KEM
            SEQUENCE {                            -- RsaKemParameters
               SEQUENCE {                  -- key derivation function
                  id-kdf-kdf3,                                -- KDF3
                  SEQUENCE {                     -- KDF3-HashFunction
                     id-sha256  -- SHA-256; no parameters (preferred)
                  },
               16                              -- KEK length in bytes
               },
         SEQUENCE {                   -- data encapsulation mechanism
            id-aes128-Wrap             -- AES-128 Wrap; no parameters
         }
      }
   }

   This SMIMECapability value has the following DER encoding (in
   hexadecimal):









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   30 47
     06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e          -- id-rsa-kem-spki
     30 38
        30 29
           06 07 28 81 8c 71 02 02 04                -- id-kem-rsa
           30 1e
              30 19
                 06 0a 2b 81 05 10 86 48 09 2c 01 02 -- id-kdf-kdf3
                 30 0b
                    06 09 60 86 48 01 65 03 04 02 01 -- id-sha256
                    02 01 10                         -- 16 bytes
         30 0b
            06 09 60 86 48 01 65 03 04 01 05         -- id-aes128-Wrap

   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-encryption algorithm 192-bit key-encryption key, the
   SMIMECapabilities will include the following SMIMECapability value
   (in hexadecimal):

     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
     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 01 19

   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-encryption algorithm 256-bit key-encryption key, the
   SMIMECapabilities will include the following SMIMECapability value
   (in hexadecimal):

     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
     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 01 2d

Appendix D.  RSA-KEM CMS Enveloped-Data Example

   This example shows the establishment of an AES-128 content-encryption
   key using:

   *  RSA-KEM with a 3072-bit key;

   *  key derivation using KDF2 with SHA-256; and

   *  key wrap using AES-128-KEYWRAP.



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   In real-world use, the originator would encrypt the content-
   encryption 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 to simplify the example.

D.1.  Originator Processing

   Alice obtains Bob's public key:

      -----BEGIN PUBLIC KEY-----
      MIIBojANBgkqhkiG9w0BAQEFAAOCAY8AMIIBigKCAYEA3ocW14cxncPJ47fnEjBZ
      AyfC2lqapL3ET4jvV6C7gGeVrRQxWPDwl+cFYBBR2ej3j3/0ecDmu+XuVi2+s5JH
      Keeza+itfuhsz3yifgeEpeK8T+SusHhn20/NBLhYKbh3kiAcCgQ56dpDrDvDcLqq
      vS3jg/VO+OPnZbofoHOOevt8Q/roahJe1PlIyQ4udWB8zZezJ4mLLfbOA9YVaYXx
      2AHHZJevo3nmRnlgJXo6mE00E/6qkhjDHKSMdl2WG6mO9TCDZc9qY3cAJDU6Ir0v
      SH7qUl8/vN13y4UOFkn8hM4kmZ6bJqbZt5NbjHtY4uQ0VMW3RyESzhrO02mrp39a
      uLNnH3EXdXaV1tk75H3qC7zJaeGWMJyQfOE3YfEGRKn8fxubji716D8UecAxAzFy
      FL6m1JiOyV5acAiOpxN14qRYZdHnXOM9DqGIGpoeY1UuD4Mo05osOqOUpBJHA9fS
      whSZG7VNf+vgNWTLNYSYLI04KiMdulnvU6ds+QPz+KKtAgMBAAE=
      -----END PUBLIC KEY-----

   Bob's RSA public key has the following key identifier:

      9eeb67c9b95a74d44d2f16396680e801b5cba49c

   Alice randomly generates integer z between 0 and n-1:

      9c126102a5c1c0354672a3c2f19fc9ddea988f815e1da812c7bd4f8eb082bdd1
      4f85a7f7c2f1af11d5333e0d6bcb375bf855f208da72ba27e6fb0655f2825aa6
      2b93b1f9bbd3491fed58f0380fa0de36430e3a144d569600bd362609be5b9481
      0875990b614e406fa6dff500043cbca95968faba61f795096a7fb3687a51078c
      4ca2cb663366b0bea0cd9cccac72a25f3f4ed03deb68b4453bba44b943f4367b
      67d6cd10c8ace53f545aac50968fc3c6ecc80f3224b64e37038504e2d2c0e2b2
      9d45e46c62826d96331360e4c17ea3ef89a9efc5fac99eda830e81450b6534dc
      0bdf042b8f3b706649c631fe51fc2445cc8d447203ec2f41f79cdfea16de1ce6
      abdfdc1e2ef2e5d5d8a65e645f397240ef5a26f5e4ff715de782e30ecf477293
      e89e13171405909a8e04dd31d21d0c57935fc1ceea8e1033e31e1bc8c56da0f3
      d79510f3f380ff58e5a61d361f2f18e99fbae5663172e8cd1f21deaddc5bbbea
      060d55f1842b93d1a9c888d0bf85d0af9947fe51acf940c7e7577eb79cabecb3

   Alice encrypts integer z using the Bob's RSA public key, the result
   is called c:









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      c071fc273af8e7bdb152e06bf73310361074154a43abcf3c93c13499d2065344
      3eed9ef5d3c0685e4aa76a6854815bb97691ff9f8dac15eea7d74f452bf350a6
      46163d68288e978cbf7a73089ee52712f9a4f49e06ace7bbc85ab14d4e336c97
      c5728a2654138c7b26e8835c6b0a9fbed26495c4eadf745a2933be283f6a88b1
      6695fc06666873cfb6d36718ef3376cefc100c3941f3c494944078325807a559
      186b95ccabf3714cfaf79f83bd30537fdd9aed5a4cdcbd8bd0486faed73e9d48
      6b3087d6c806546b6e2671575c98461e441f65542bd95de26d0f53a64e7848d7
      31d9608d053e8d345546602d86236ffe3704c98ad59144f3089e5e6d527b5497
      ba103c79d62e80d0235410b06f71a7d9bd1c38000f910d6312ea2f20a3557535
      ad01b3093fb5f7ee507080d0f77d48c9c3b3796f6b7dd3786085fb895123f04c
      a1f1c1be22c747a8dface32370fb0d570783e27dbb7e74fca94ee39676fde3d8
      a9553d878224736e37e191dab953c7e228c07ad5ca3122421c14debd072a9ab6

   Alice encodes the CMSORIforKEMOtherInfo structure with the algorithm
   identifier for AES-128-KEYWRAP and a key length of 16 octets.  The
   DER encoding of CMSORIforKEMOtherInfo produces 18 octets:

      3010300b0609608648016503040105020110

   The CMSORIforKEMOtherInfo structure contains:

        0  16: SEQUENCE {
        2  11:  SEQUENCE {
        4   9:   OBJECT IDENTIFIER aes128-wrap (2 16 840 1 101 3 4 1 5)
             :    }
       15   1:  INTEGER 16
             :   }

   Alice derives the key-encryption key from integer z and the
   CMSORIforKEMOtherInfo structure with KDF2 and SHA-256, the KEK is:

      4a95fe82f8d6ba56c83b4d51ef7dc06b

   Alice randomly generates a 128-bit content-encryption key:

      77f2a84640304be7bd42670a84a1258b

   Alice uses AES-128-KEYWRAP to encrypt the 128-bit content-encryption
   key with the derived key-encryption key:

      904dbeb0271fc02082fe6d358c03352ae4ae6b540b782423

   Alice encrypts the padded content using AES-128-CBC with the content-
   encryption key.  The 16-octet IV used is:

      480ccafebabefacedbaddecaf8887781

   The padded content plaintext is:



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      48656c6c6f2c20776f726c6421030303

   The resulting ciphertext is:

      c6ca65db7bdd76b0f37e2fab6264b66d

D.2.  ContentInfo and EnvelopedData

   Alice encodes the EnvelopedData (using KEMRecipientInfo) and
   ContentInfo, and then sends the result to Bob.  The Base64-encoded:
   result is:

     MIICXAYJKoZIhvcNAQcDoIICTTCCAkkCAQMxggIEpIICAAYLKoZIhvcNAQkQDQMwggH
     vAgEAgBSe62fJuVp01E0vFjlmgOgBtcuknDAJBgcogYxxAgIEBIIBgMBx/Cc6+Oe9sV
     Lga/czEDYQdBVKQ6vPPJPBNJnSBlNEPu2e9dPAaF5Kp2poVIFbuXaR/5+NrBXup9dPR
     SvzUKZGFj1oKI6XjL96cwie5ScS+aT0ngas57vIWrFNTjNsl8VyiiZUE4x7JuiDXGsK
     n77SZJXE6t90Wikzvig/aoixZpX8BmZoc8+202cY7zN2zvwQDDlB88SUlEB4MlgHpVk
     Ya5XMq/NxTPr3n4O9MFN/3ZrtWkzcvYvQSG+u1z6dSGswh9bIBlRrbiZxV1yYRh5EH2
     VUK9ld4m0PU6ZOeEjXMdlgjQU+jTRVRmAthiNv/jcEyYrVkUTzCJ5ebVJ7VJe6EDx51
     i6A0CNUELBvcafZvRw4AA+RDWMS6i8go1V1Na0Bswk/tffuUHCA0Pd9SMnDs3lva33T
     eGCF+4lRI/BMofHBviLHR6jfrOMjcPsNVweD4n27fnT8qU7jlnb949ipVT2HgiRzbjf
     hkdq5U8fiKMB61coxIkIcFN69ByqatjAbBgorgQUQhkgJLAEBMA0GCWCGSAFlAwQCAQ
     UAAgEQMAsGCWCGSAFlAwQBBQQYkE2+sCcfwCCC/m01jAM1KuSua1QLeCQjMDwGCSqGS
     Ib3DQEHATAdBglghkgBZQMEAQIEEEgMyv66vvrO263eyviId4GAEMbKZdt73Xaw834v
     q2Jktm0=

   This result decodes to:

        0 604: SEQUENCE {
        4   9:  OBJECT IDENTIFIER envelopedData (1 2 840 113549 1 7 3)
       15 589:  [0] {
       19 585:   SEQUENCE {
       23   1:    INTEGER 3
       26 516:    SET {
       30 512:     [4] {
       34  11:      OBJECT IDENTIFIER
             :       KEMRecipientInfo (1 2 840 113549 1 9 16 13 3)
       47 495:      SEQUENCE {
       51   1:       INTEGER 0
       54  20:       [0]
             :       9E EB 67 C9 B9 5A 74 D4 4D 2F 16 39 66 80 E8 01
             :       B5 CB A4 9C
       76   9:       SEQUENCE {
       78   7:        OBJECT IDENTIFIER kemRSA (1 0 18033 2 2 4)
             :         }
       87 384:       OCTET STRING
             :       C0 71 FC 27 3A F8 E7 BD B1 52 E0 6B F7 33 10 36
             :       10 74 15 4A 43 AB CF 3C 93 C1 34 99 D2 06 53 44



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             :       3E ED 9E F5 D3 C0 68 5E 4A A7 6A 68 54 81 5B B9
             :       76 91 FF 9F 8D AC 15 EE A7 D7 4F 45 2B F3 50 A6
             :       46 16 3D 68 28 8E 97 8C BF 7A 73 08 9E E5 27 12
             :       F9 A4 F4 9E 06 AC E7 BB C8 5A B1 4D 4E 33 6C 97
             :       C5 72 8A 26 54 13 8C 7B 26 E8 83 5C 6B 0A 9F BE
             :       D2 64 95 C4 EA DF 74 5A 29 33 BE 28 3F 6A 88 B1
             :       66 95 FC 06 66 68 73 CF B6 D3 67 18 EF 33 76 CE
             :       FC 10 0C 39 41 F3 C4 94 94 40 78 32 58 07 A5 59
             :       18 6B 95 CC AB F3 71 4C FA F7 9F 83 BD 30 53 7F
             :       DD 9A ED 5A 4C DC BD 8B D0 48 6F AE D7 3E 9D 48
             :       6B 30 87 D6 C8 06 54 6B 6E 26 71 57 5C 98 46 1E
             :       44 1F 65 54 2B D9 5D E2 6D 0F 53 A6 4E 78 48 D7
             :       31 D9 60 8D 05 3E 8D 34 55 46 60 2D 86 23 6F FE
             :       37 04 C9 8A D5 91 44 F3 08 9E 5E 6D 52 7B 54 97
             :       BA 10 3C 79 D6 2E 80 D0 23 54 10 B0 6F 71 A7 D9
             :       BD 1C 38 00 0F 91 0D 63 12 EA 2F 20 A3 55 75 35
             :       AD 01 B3 09 3F B5 F7 EE 50 70 80 D0 F7 7D 48 C9
             :       C3 B3 79 6F 6B 7D D3 78 60 85 FB 89 51 23 F0 4C
             :       A1 F1 C1 BE 22 C7 47 A8 DF AC E3 23 70 FB 0D 57
             :       07 83 E2 7D BB 7E 74 FC A9 4E E3 96 76 FD E3 D8
             :       A9 55 3D 87 82 24 73 6E 37 E1 91 DA B9 53 C7 E2
             :       28 C0 7A D5 CA 31 22 42 1C 14 DE BD 07 2A 9A B6
      475  27:       SEQUENCE {
      477  10:        OBJECT IDENTIFIER
             :         kdf2 (1 3 133 16 840 9 44 1 1)
      489  13:        SEQUENCE {
      491   9:         OBJECT IDENTIFIER
             :          sha-256 (2 16 840 1 101 3 4 2 1)
      502   0:         NULL
             :          }
             :         }
      504   1:       INTEGER 16
      507  11:       SEQUENCE {
      509   9:        OBJECT IDENTIFIER
             :         aes128-wrap (2 16 840 1 101 3 4 1 5)
             :         }
      520  24:       OCTET STRING
             :       90 4D BE B0 27 1F C0 20 82 FE 6D 35 8C 03 35 2A
             :       E4 AE 6B 54 0B 78 24 23
             :        }
             :       }
             :      }
      546  60:    SEQUENCE {
      548   9:     OBJECT IDENTIFIER data (1 2 840 113549 1 7 1)
      559  29:     SEQUENCE {
      561   9:      OBJECT IDENTIFIER
             :       aes128-CBC (2 16 840 1 101 3 4 1 2)
      572  16:      OCTET STRING



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             :      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
             :      }
             :     }
             :    }
             :   }

D.3.  Recipient Processing

   Bob's private key:








































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      -----BEGIN PRIVATE KEY-----
      MIIG5AIBAAKCAYEA3ocW14cxncPJ47fnEjBZAyfC2lqapL3ET4jvV6C7gGeVrRQx
      WPDwl+cFYBBR2ej3j3/0ecDmu+XuVi2+s5JHKeeza+itfuhsz3yifgeEpeK8T+Su
      sHhn20/NBLhYKbh3kiAcCgQ56dpDrDvDcLqqvS3jg/VO+OPnZbofoHOOevt8Q/ro
      ahJe1PlIyQ4udWB8zZezJ4mLLfbOA9YVaYXx2AHHZJevo3nmRnlgJXo6mE00E/6q
      khjDHKSMdl2WG6mO9TCDZc9qY3cAJDU6Ir0vSH7qUl8/vN13y4UOFkn8hM4kmZ6b
      JqbZt5NbjHtY4uQ0VMW3RyESzhrO02mrp39auLNnH3EXdXaV1tk75H3qC7zJaeGW
      MJyQfOE3YfEGRKn8fxubji716D8UecAxAzFyFL6m1JiOyV5acAiOpxN14qRYZdHn
      XOM9DqGIGpoeY1UuD4Mo05osOqOUpBJHA9fSwhSZG7VNf+vgNWTLNYSYLI04KiMd
      ulnvU6ds+QPz+KKtAgMBAAECggGATFfkSkUjjJCjLvDk4aScpSx6+Rakf2hrdS3x
      jwqhyUfAXgTTeUQQBs1HVtHCgxQd+qlXYn3/qu8TeZVwG4NPztyi/Z5yB1wOGJEV
      3k8N/ytul6pJFFn6p48VM01bUdTrkMJbXERe6g/rr6dBQeeItCaOK7N5SIJH3Oqh
      9xYuB5tH4rquCdYLmt17Tx8CaVqU9qPY3vOdQEOwIjjMV8uQUR8rHSO9KkSj8AGs
      Lq9kcuPpvgJc2oqMRcNePS2WVh8xPFktRLLRazgLP8STHAtjT6SlJ2UzkUqfDHGK
      q/BoXxBDu6L1VDwdnIS5HXtL54ElcXWsoOyKF8/ilmhRUIUWRZFmlS1ok8IC5IgX
      UdL9rJVZFTRLyAwmcCEvRM1asbBrhyEyshSOuN5nHJi2WVJ+wSHijeKl1qeLlpMk
      HrdIYBq4Nz7/zXmiQphpAy+yQeanhP8O4O6C8e7RwKdpxe44su4Z8fEgA5yQx0u7
      8yR1EhGKydX5bhBLR5Cm1VM7rT2BAoHBAP/+e5gZLNf/ECtEBZjeiJ0VshszOoUq
      haUQPA+9Bx9pytsoKm5oQhB7QDaxAvrn8/FUW2aAkaXsaj9F+/q30AYSQtExai9J
      fdKKook3oimN8/yNRsKmhfjGOj8hd4+GjX0qoMSBCEVdT+bAjjry8wgQrqReuZnu
      oXU85dmb3jvv0uIczIKvTIeyjXE5afjQIJLmZFXsBm09BG87Ia5EFUKly96BOMJh
      /QWEzuYYXDqOFfzQtkAefXNFW21Kz4Hw2QKBwQDeiGh4lxCGTjECvG7fauMGlu+q
      DSdYyMHif6t6mx57eS16EjvOrlXKItYhIyzW8Kw0rf/CSB2j8ig1GkMLTOgrGIJ1
      0322o50FOr5oOmZPueeR4pOyAP0fgQ8DD1L3JBpY68/8MhYbsizVrR+Ar4jM0f96
      W2bF5Xj3h+fQTDMkx6VrCCQ6miRmBUzH+ZPs5n/lYOzAYrqiKOanaiHy4mjRvlsy
      mjZ6z5CG8sISqcLQ/k3Qli5pOY/v0rdBjgwAW/UCgcEAqGVYGjKdXCzuDvf9EpV4
      mpTWB6yIV2ckaPOn/tZi5BgsmEPwvZYZt0vMbu28Px7sSpkqUuBKbzJ4pcy8uC3I
      SuYiTAhMiHS4rxIBX3BYXSuDD2RD4vG1+XM0h6jVRHXHh0nOXdVfgnmigPGz3jVJ
      B8oph/jD8O2YCk4YCTDOXPEi8Rjusxzro+whvRR+kG0gsGGcKSVNCPj1fNISEte4
      gJId7O1mUAAzeDjn/VaS/PXQovEMolssPPKn9NocbKbpAoHBAJnFHJunl22W/lrr
      ppmPnIzjI30YVcYOA5vlqLKyGaAsnfYqP1WUNgfVhq2jRsrHx9cnHQI9Hu442PvI
      x+c5H30YFJ4ipE3eRRRmAUi4ghY5WgD+1hw8fqyUW7E7l5LbSbGEUVXtrkU5G64T
      UR91LEyMF8OPATdiV/KD4PWYkgaqRm3tVEuCVACDTQkqNsOOi3YPQcm270w6gxfQ
      SOEy/kdhCFexJFA8uZvmh6Cp2crczxyBilR/yCxqKOONqlFdOQKBwFbJk5eHPjJz
      AYueKMQESPGYCrwIqxgZGCxaqeVArHvKsEDx5whI6JWoFYVkFA8F0MyhukoEb/2x
      2qB5T88Dg3EbqjTiLg3qxrWJ2OxtUo8pBP2I2wbl2NOwzcbrlYhzEZ8bJyxZu5i1
      sYILC8PJ4Qzw6jS4Qpm4y1WHz8e/ElW6VyfmljZYA7f9WMntdfeQVqCVzNTvKn6f
      hg6GSpJTzp4LV3ougi9nQuWXZF2wInsXkLYpsiMbL6Fz34RwohJtYA==
      -----END PRIVATE KEY-----

   Bob decrypts the integer z with his RSA private key:










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      9c126102a5c1c0354672a3c2f19fc9ddea988f815e1da812c7bd4f8eb082bdd1
      4f85a7f7c2f1af11d5333e0d6bcb375bf855f208da72ba27e6fb0655f2825aa6
      2b93b1f9bbd3491fed58f0380fa0de36430e3a144d569600bd362609be5b9481
      0875990b614e406fa6dff500043cbca95968faba61f795096a7fb3687a51078c
      4ca2cb663366b0bea0cd9cccac72a25f3f4ed03deb68b4453bba44b943f4367b
      67d6cd10c8ace53f545aac50968fc3c6ecc80f3224b64e37038504e2d2c0e2b2
      9d45e46c62826d96331360e4c17ea3ef89a9efc5fac99eda830e81450b6534dc
      0bdf042b8f3b706649c631fe51fc2445cc8d447203ec2f41f79cdfea16de1ce6
      abdfdc1e2ef2e5d5d8a65e645f397240ef5a26f5e4ff715de782e30ecf477293
      e89e13171405909a8e04dd31d21d0c57935fc1ceea8e1033e31e1bc8c56da0f3
      d79510f3f380ff58e5a61d361f2f18e99fbae5663172e8cd1f21deaddc5bbbea
      060d55f1842b93d1a9c888d0bf85d0af9947fe51acf940c7e7577eb79cabecb3

   Bob encodes the CMSORIforKEMOtherInfo structure with the algorithm
   identifier for AES-128-KEYWRAP and a key length of 16 octets.  The
   DER encoding of CMSORIforKEMOtherInfo is not repeated here.

   Bob derives the key-encryption key from integer z and the
   CMSORIforKEMOtherInfo structure with KDF2 and SHA-256, the KEK is:

      4a95fe82f8d6ba56c83b4d51ef7dc06b

   Bob uses AES-KEY-WRAP to decrypt the content-encryption key with the
   key-encryption key; the content-encryption key is:

      77f2a84640304be7bd42670a84a1258b

   Bob decrypts the content using AES-128-CBC with the content-
   encryption key.  The 16-octet IV used is:

      480ccafebabefacedbaddecaf8887781

   The received ciphertext content is:

      c6ca65db7bdd76b0f37e2fab6264b66d

   The resulting padded plaintext content is:

      48656c6c6f2c20776f726c6421030303

   After stripping the padding, the plaintext content is:

      Hello, world!

Acknowledgements

   We thank James Randall, Burt Kaliski, and John Brainard as the
   original authors of [RFC5990]; this document is based on their work.



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   We thank the members of the ASC X9F1 working group for their
   contributions to drafts of ANS X9.44, which led to [RFC5990].

   We thank Blake Ramsdell, Jim Schaad, Magnus Nystrom, Bob Griffin, and
   John Linn for helping bring [RFC5990] to fruition.

Authors' Addresses

   Russ Housley
   Vigil Security, LLC
   516 Dranesville Road
   Herndon, VA,  20170
   United States of America

   Email: housley@vigilsec.com


   Sean Turner
   sn3rd

   Email: sean@sn3rd.com






























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