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RFC 9690	RSA-KEM with CMS KEMRecipientInfo	February 2025
Housley & Turner	Standards Track	[Page]

1.Introduction

The RSA Key Encapsulation Mechanism (RSA-KEM) algorithm is a one-pass(store-and-forward) cryptographic mechanism for an originator to securelysend 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 keytransport mechanisms[RFC8017] with the goal of providing highersecurity assurance while also satisfying the KEM interface. TheRSA-KEM algorithm encrypts a random integer with the recipient'sRSA public key and derives a shared secret from the random integer. Theoriginator and recipient can derive a symmetric key from the sharedsecret. For example, a key-encryption key (KEK) can be derived from the sharedsecret to wrap a content-encryption key (CEK).¶

In the Cryptographic Message Syntax (CMS)[RFC5652] usingKEMRecipientInfo[RFC9629], the shared-secret valueis input to a key derivation function (KDF) to compute a key-encryption key andwrap a symmetric content-encryption key with the key-encryption key. Inthis way, the originator and the recipient end up with the samecontent-encryption key.¶

For completeness, a specification of the RSA-KEM algorithm is given inAppendix A of this document. ASN.1 syntax is given inAppendix B.¶

1.1.RSA-KEM Algorithm Rationale

The RSA-KEM algorithm provides higher security assurance than other variants of the RSA cryptosystem for two reasons. First, the input to the underlying RSA operation is a string-encoded 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 depends on the keying material. Additionally, the provable security assurances are not as strong.)¶

The approach is also architecturally convenient because thepublic-key operations are separate from the symmetric operations on thekeying material. Another benefit is that the length of the keying materialis determined by the symmetric algorithms, not the size of the RSA modulus.¶

1.2.RSA-KEM Algorithm Summary

All KEM algorithms provide three functions: KeyGen(), Encapsulate(),and Decapsulate().¶

The following summarizes these three functions for the RSA-KEM algorithm:¶

KeyGen() -> (pk, sk):

Generate the public key (pk) and a private key (sk) as described inSection 3 of [RFC8017].¶

Encapsulate(pk) -> (ct, SS):

Given the recipient's public key (pk), produce a ciphertext (ct) to be passed to the recipient and a shared secret (SS) for use by the originator as follows:¶

Generate a random integer z between 0 and n-1.¶
Encrypt the integer z with the recipient's RSA public key to obtain the ciphertext:¶
```
       ct = z^e mod n
```
¶
Derive a shared secret from the integer z using a Key Derivation Function (KDF):¶
```
       SS = KDF(Z, ssLen)
```
¶
The ciphertext and the shared secret are returned by the function. The originator sends the ciphertext to the recipient.¶

Decapsulate(sk, ct) -> SS:

Given the private key (sk) and the ciphertext (ct), produce the shared secret (SS) for the recipient as follows:¶

Decrypt the ciphertext with the recipient's RSA private key to obtain the random integer z:¶
```
       z = ct^d mod n
```
¶
Derive a shared secret from the integer z:¶
```
       SS = KDF(Z, ssLen)
```
¶
The shared secret is returned by the function.¶

1.3.CMS KEMRecipientInfo Processing Summary

To support the RSA-KEM algorithm, the CMS originatorMUST implement Encapsulate().¶

Given a content-encryption key CEK, the RSA-KEM algorithm processing by the originator to produce the values that are carried in the CMS KEMRecipientInfo can be summarized as follows:¶

Obtain the shared secret using the Encapsulate() function of the RSA-KEM algorithm and the recipient's RSA public key:¶
```
       (ct, SS) = Encapsulate(pk)
```
¶
Derive a key-encryption key KEK from the shared secret:¶
```
       KEK = KDF(SS, kekLength, otherInfo)
```
¶
Wrap the CEK with the KEK to obtain wrapped keying material WK:¶
```
       WK = WRAP(KEK, CEK)
```
¶
The originator sends the ciphertext and WK to the recipient in the CMS KEMRecipientInfo structure.¶

To support the RSA-KEM algorithm, the CMS recipientMUST implement Decapsulate().¶

The RSA-KEM algorithm recipient processing of the values obtained from the KEMRecipientInfo structure is summarized as follows:¶

Obtain the shared secret using the Decapsulate() function of the RSA-KEM algorithm and the recipient's RSA private key:¶
```
       SS = Decapsulate(sk, ct)
```
¶
Derive a key-encryption key KEK from the shared secret:¶
```
       KEK = KDF(SS, kekLength, otherInfo)
```
¶
Unwrap the WK with the KEK to obtain the content-encryption key CEK:¶
```
       CEK = UNWRAP(KEK, WK)
```
¶

Note that the KDF used to process the KEMRecipientInfo structureMAY bedifferent from the KDF used to derive the shared secret in the RSA-KEMalgorithm.¶

1.4.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.¶

1.5.ASN.1

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

1.6.Changes Since RFC 5990

RFC 5990[RFC5990] specified the conventions for using the RSA-KEM algorithmin CMS as a key transport algorithm. That is, it used KeyTransRecipientInfo[RFC5652]for each recipient. Since the publication of RFC 5990, a new KEMRecipientInfostructure[RFC9629] has been defined to support KEMalgorithms. When the id-rsa-kem algorithm identifier appears in theSubjectPublicKeyInfo field of a certificate, the complex parameter structuredefined in RFC 5990 can be omitted; however, the parameters are allowed forbackward compatibility. Also, to avoid visual confusion with id‑kem‑rsa, id‑rsa‑kem‑spki is introduced as an alias for id-rsa-kem.¶

RFC 5990 used EK as the EncryptedKey, which is the concatenation ofthe ciphertext C and the wrapped key WK, EK = (C || WK). The use of EK wasnecessary to align with the KeyTransRecipientInfo structure. In thisdocument, the ciphertext and the wrapped key are sent in separate fields ofthe KEMRecipientInfo structure. In particular, the ciphertext is carried inthe kemct field, and the wrapped key is carried in the encryptedKeyfield. SeeAppendix A for details about the computation of the ciphertext.¶

RFC 5990 included support for Camellia and Triple-DES block ciphers;discussion of these block ciphers does not appear in this document, butthe algorithm identifiers remain in the ASN.1 module (seeAppendix B.2).¶

RFC 5990 included support for SHA-1 hash function; discussion of thishash function does not appear this document, but the algorithm identifierremains in the ASN.1 module (seeAppendix B.2).¶

RFC 5990 required support for the KDF3 key derivation function[ANS-X9.44]; 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 recommended support for alternatives to KDF3 and AES-Wrap-128;this document simply states that other key derivation functions and otherkey-encryption algorithmsMAY be supported.¶

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

RFC 5990 included an ASN.1 module; this document provides an alternativeASN.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 algorithmMAY be employed for one or more recipients in theCMS enveloped-data content type[RFC5652], the CMS authenticated-datacontent type[RFC5652], or the CMS authenticated-enveloped-datacontent type[RFC5083]. In each case, the KEMRecipientInfo[RFC9629] is used with the RSA-KEM algorithmto securely transfer the content-encryption key from the originator tothe recipient.¶

2.1.Mandatory To Implement

A CMS implementation that supports the RSA-KEM algorithmMUST support atleast the following underlying components:¶

For the key derivation function, an implementationMUST supportKDF3[ANS-X9.44] with SHA-256[SHS].¶
For key-wrapping, an implementationMUST support theAES-Wrap-128[RFC3394] key-encryption algorithm.¶

An implementationMAY also support other key derivation functions andother key-encryption algorithms.¶

2.2.RecipientInfo Conventions

When the RSA-KEM algorithm is employed for a recipient, theRecipientInfo alternative for that recipientMUST beOtherRecipientInfo using the KEMRecipientInfo structure[RFC9629]. The fields of theKEMRecipientInfoMUST have the following values:¶

version is the syntax version number; itMUST be 0.¶
rid identifies the recipient's certificate or public key.¶
kem identifies the KEM algorithm; itMUST contain id-kem-rsa.¶
kemct is the ciphertext produced for this recipient; it contains C from steps 1 and 2 of Originator's Operations inAppendix A.¶
kdf identifies the key derivation function (KDF). Note that the KDF used for CMS RecipientInfo processMAY be different than the KDF used within the RSA-KEM 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 keying material.¶
encryptedKey is the result of encrypting the keying material with thekey-encryption key. When used with the CMS enveloped-data contenttype[RFC5652], the keying material is a content-encryption key. Whenused with the CMS authenticated-data content type[RFC5652], thekeying material is a message-authentication key. When used with theCMS authenticated-enveloped-data content type[RFC5083], thekeying material is a content-authenticated-encryption key (CAEK).¶

NOTE: For backward compatibility, implementationsMAY also supportthe RSA-KEM Key Transport algorithm, identified by id-rsa-kem-spki, which usesKeyTransRecipientInfo 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 algorithmMAY identify the public key in a certificate by the same AlgorithmIdentifier as for PKCS #1 v1.5, that is, using the rsaEncryption object identifier[RFC8017]. The fact that the recipient will accept the RSA-KEM algorithm with this public key is not indicated by the use of this object identifier. The willingness to accept the RSA-KEM algorithmMAY be signaled by the use of the SMIMECapabilities Attribute as specified inSection 2.5.2 of [RFC8551] or the SMIMECapabilities certificate extension as specified in[RFC4262].¶

If the recipient wishes only to employ the RSA-KEM algorithm with a given public key, the recipientMUST identify the public key in the certificate using the id-rsa-kem-spki object identifier; seeAppendix B. The use of the id-rsa-kem-spki object identifier allows certificates that were issued to be compatible with the RSA-KEM Key Transport algorithm to also be used with this specification. When the id-rsa-kem-spki object identifier appears in the SubjectPublicKeyInfo algorithm field of the certificate, the parameters field from AlgorithmIdentifierSHOULD be absent. That is, the AlgorithmIdentifierSHOULD be a SEQUENCE of one component, the id-rsa-kem-spki object identifier. With absent parameters, the KDF3 key derivation function[ANS-X9.44] with SHA-256[SHS] are used to derive the shared secret.¶

When the AlgorithmIdentifier parameters are present, theGenericHybridParametersMUST be used. Within the kem element, the algorithmidentifierMUST be set to id-kem-rsa, and RsaKemParametersMUST be included.As described inSection 2.4, the GenericHybridParameters constrain the valuesthat can be used with the RSA public key for the kdf, kekLength, and wrapfields of the KEMRecipientInfo structure.¶

Regardless of the AlgorithmIdentifier used, the RSA public keyMUST becarried in the subjectPublicKey BIT STRING within the SubjectPublicKeyInfofield of the certificate using the RSAPublicKey type defined in[RFC8017].¶

The intended application for the public keyMAY be indicated in the key usagecertificate extension as specified inSection 4.2.1.3 of [RFC5280]. If thekeyUsage extension is present in a certificate that conveys an RSA public keywith the id-rsa-kem-spki object identifier as discussed above, then the keyusage extensionMUST contain only the following value:¶

keyEncipherment¶

Other keyUsage extension valuesMUST NOT bepresent. That is, a public key intended to be employed only with theRSA-KEM algorithmMUST NOT also be employed for data encryption orfor digital signatures. Good cryptographic practice employs a given RSAkey pair in only one scheme. This practice avoids the risk that vulnerabilityin one scheme may compromise the security of the other and may be essentialto maintain provable security.¶

2.4.SMIMECapabilities Attribute Conventions

Section 2.5.2 of [RFC8551] defines the SMIMECapabilities attribute toannounce a partial list of algorithms that an S/MIME implementation cansupport. When constructing a CMS signed-data content type[RFC5652],a compliant implementationMAY include the SMIMECapabilities attributethat announces support for the RSA-KEM algorithm.¶

The SMIMECapability SEQUENCE representing the RSA-KEM algorithmMUSTinclude the id-rsa-kem-spki object identifier in the capabilityID field;seeAppendix B for the object identifier value andAppendix Cfor examples. When the id-rsa-kem-spki object identifier appears in thecapabilityID field and the parameters are present, then the parametersfieldMUST 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 fieldMUST be set to id-kem-rsa,and the parameters fieldMUST be RsaKemParameters, which is a SEQUENCE of anAlgorithmIdentifier that identifies the supported key derivation functionand a positive INTEGER that identifies the length of the key-encryptionkey in octets.¶
dem is an AlgorithmIdentifier. The algorithm fieldMUST be present, and itidentifies the key-encryption algorithm. The parameters are optional. If theGenericHybridParameters are present, then the provided dem valueMUST beused in the wrap field of KEMRecipientInfo.¶

If the GenericHybridParameters are present, then the provided kem valueMUSTbe used as the key derivation function in the kdf field of KEMRecipientInfoand the provided key lengthMUST be used in the kekLength of KEMRecipientInfo.¶

3.Security Considerations

The RSA-KEM algorithm should be considered as a replacement for the key transport portion of thewidely implemented PKCS #1 v1.5[RFC8017] for new applicationsthat use CMS to avoid potential vulnerabilities to chosen-ciphertextattacks and gain a tighter security proof. However, the RSA-KEM algorithmhas the disadvantage of slightly longer encrypted keying material. WithPKCS #1 v1.5, the originator encrypts the key-encryption key directly withthe recipient's RSA public key. With the RSA-KEM algorithm, the key-encryption keyis encrypted separately.¶

The security of the RSA-KEM algorithm can be shown to be tightly relatedto the difficulty of either solving the RSA problem or breaking the underlyingsymmetric key-encryption algorithm if the underlying key derivation functionis modeled as a random oracle, assuming that the symmetric key-encryptionalgorithm satisfies the properties of a data encapsulation mechanism[SHOUP]. While in practice a random-oracle result does not providean actual security proof for any particular key derivation function, theresult does provide assurance that the general construction is reasonable; akey derivation function would need to be particularly weak to lead to anattack that is not possible in the random-oracle model.¶

The RSA key size and the underlying components need to be selectedconsistent with the desired security level. Several security levelshave been identified in the NIST SP 800-57 Part 1[NISTSP800-57pt1r5]. For example, one wayto achieve 128-bit security, the RSA key size would be at least 3072 bits,the key derivation function would be SHA-256, and the symmetrickey-encryption algorithm would be AES Key Wrap with a 128-bit key.¶

ImplementationsMUST protect the RSA private key, the key-encryption key,the content-encryption key, message-authentication key, and thecontent-authenticated-encryption key. Disclosure of the RSA private keycould result in the compromise of all messages protected with that key.Disclosure of the key-encryption key, the content-encryption key, or thecontent-authenticated-encryption key could result in compromise of theassociated encrypted content. Disclosure of the key-encryption key, themessage-authentication key, or the content-authenticated-encryption keycould allow modification of the associated authenticated content.¶

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

The security of the RSA-KEM algorithm depends on a quality random numbergenerator. For further discussion on random number generation,see[RFC4086].¶

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)is directly encrypted with the recipient's RSA public key. TheIntegerToString(z, nLen) encoding produces a string that is the full length ofthe RSA modulus. In addition, the random value is passed through a KDF to reduce possible harm from a poorly implemented random numbersource or a maliciously chosen random value (z). ImplementationsMUST NOTuse z directly for any purpose.¶

As long as a fresh random integer z is chosen as part of each invocationof the Encapsulate() function, the RSA-KEM algorithm does not degrade as the number ofciphertexts increases. Since RSA encryption provides a bijective map,a collision in the KDF is the only way that the RSA-KEM algorithm can produce more thanone ciphertext that encapsulates the same shared secret.¶

The RSA-KEM algorithm provides a fixed-length ciphertext. The recipientMUSTcheck that the received byte string is the expected length and the lengthcorresponds to an integer in the expected range prior to attempting decryptionwith their RSA private key as described in Steps 1 and 2 ofAppendix A.2.¶

ImplementationsSHOULD NOT reveal information about intermediatevalues or calculations, whether by timing or other "side channels";otherwise, an opponent may be able to determine information aboutthe keying data and/or the recipient's private key. Although not allintermediate information may be useful to an opponent, it ispreferable to conceal as much information as is practical, unlessanalysis specifically indicates that the information would not beuseful to an opponent.¶

Generally, good cryptographic practice employs a given RSA key pairin only one scheme. This practice avoids the risk that vulnerabilityin one scheme may compromise the security of the other, and may beessential to maintain provable security. RSA public keys have oftenbeen employed for multiple purposes such as key transport and digitalsignature without any known bad interactions; however, such combined useof an RSA key pair isNOT RECOMMENDED in the future (unless the differentschemes are specifically designed to be used together).¶

Accordingly, an RSA key pair used for the RSA-KEM algorithmSHOULD NOTalso be used for digital signatures. Indeed, the Accredited StandardsCommittee X9 (ASC X9) requires such a separation between key pairs usedfor key establishment and key pairs used for digital signature[ANS-X9.44]. Continuing this principle of key separation, a key pairused for the RSA-KEM algorithmSHOULD NOT be used with other keyestablishment schemes, or for data encryption, or with morethan one set of underlying algorithm components.¶

It is acceptable to use the same RSA key pair for the RSA-KEM Key Transport algorithm as specified in[RFC5990] and this specification. This is acceptable because the operations involving the RSA public key and the RSA private key are identical in the two specifications.¶

Parties can gain assurance that implementations are correct throughformal implementation validation, such as the NIST CryptographicModule Validation Program (CMVP)[CMVP].¶

5.References

5.1.Normative References

[ANS-X9.44]: American National Standards Institute,"Public Key Cryptography for the Financial Services Industry -- Key Establishment Using Integer Factorization Cryptography",ANSI X9.44-2007 (R2017),2007,<https://webstore.ansi.org/standards/ascx9/ansix9442007r2017>.
[ISO18033-2]: ISO/IEC,"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>.
[RFC3394]: Schaad, J. andR. Housley,"Advanced Encryption Standard (AES) Key Wrap Algorithm",RFC 3394,DOI 10.17487/RFC3394,September 2002,<https://www.rfc-editor.org/info/rfc3394>.
[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., andW. 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. andJ. 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. andJ. 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. andS. 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>.
[RFC8017]: Moriarty, K., Ed.,Kaliski, B.,Jonsson, J., andA. Rusch,"PKCS #1: RSA Cryptography Specifications Version 2.2",RFC 8017,DOI 10.17487/RFC8017,November 2016,<https://www.rfc-editor.org/info/rfc8017>.
[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>.
[RFC8551]: Schaad, J.,Ramsdell, B., andS. 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>.
[RFC9629]: Housley, R.,Gray, J., andT. Okubo,"Using Key Encapsulation Mechanism (KEM) Algorithms in the Cryptographic Message Syntax (CMS)",RFC 9629,DOI 10.17487/RFC9629,August 2024,<https://www.rfc-editor.org/info/rfc9629>.
[SHS]: National Institute of Standards and Technology,"Secure Hash Standard",NIST FIPS PUB 180-4,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.690>.

5.2.Informative References

[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.,"Recommendation for Key Management: Part 1 - General",NIST SP 800-57, Part 1, Revision 5,DOI 10.6028/nist.sp.800-57pt1r5,May 2020,<https://doi.org/10.6028/nist.sp.800-57pt1r5>.
[RFC4086]: Eastlake 3rd, D.,Schiller, J., andS. Crocker,"Randomness Requirements for Security",BCP 106,RFC 4086,DOI 10.17487/RFC4086,June 2005,<https://www.rfc-editor.org/info/rfc4086>.
[RFC4262]: Santesson, S.,"X.509 Certificate Extension for Secure/Multipurpose Internet Mail Extensions (S/MIME) Capabilities",RFC 4262,DOI 10.17487/RFC4262,December 2005,<https://www.rfc-editor.org/info/rfc4262>.
[RFC5990]: Randall, J.,Kaliski, B.,Brainard, J., andS. 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., andP. 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>.
[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) cryptographicmechanism for an originator to securely send keying material to a recipientusing the recipient's RSA public key.¶

With the RSA-KEM algorithm, an originator encrypts a random integer (z) withthe recipient's RSA public key to produce a ciphertext (ct), and the originatorderives a shared secret (SS) from the random integer (z). The originator thensends the ciphertext (ct) to the recipient. The recipient decrypts theciphertext (ct) using their private key to recover the random integer (z),and the recipient derives a shared secret (SS) from the random integer (z). Inthis way, the originator and recipient obtain the same shared secret (SS).¶

The RSA-KEM algorithm depends on a key derivation function (KDF), which isused to derive the shared secret (SS). Many key derivation functions supportthe inclusion of other information in addition to the shared secret (SS) inthe input to the function; however, no other information is included as aninput to the KDF by the RSA-KEM algorithm.¶

A.1.Originator's Operations: RSA-KEM Encapsulate()

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

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

The originator performs the following operations:¶

Generate a random integer z between 0 and n-1 (see NOTE below), and convert z to a byte string Z of length nLen, most significant byte first:¶
```
     z = RandomInteger (0, n-1)     Z = IntegerToString (z, nLen)
```
¶
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     ct = IntegerToString (c, nLen)
```
¶
Derive a symmetric shared secret SS of length ssLen bytes (whichMUST be the length of the key-encryption key) from thebyte string Z using the underlying key derivation function:¶
```
     SS = KDF (Z, ssLen)
```
¶
Output the shared secret SS and the ciphertext ct. Send theciphertext ct to the recipient.¶

NOTE: The random integer zMUST be generated independently at randomfor different encryption operations, whether for the same or differentrecipients.¶

A.2.Recipient's Operations: RSA-KEM Decapsulate()

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

Let ct be the ciphertext received from the originator.¶

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

The recipient performs the following operations:¶

If the length of the encrypted keying material is less than nLenbytes, output "decryption error", and stop.¶
Convert the ciphertext ct to an integer c, most significant bytefirst (see NOTE below):¶
```
     c = StringToInteger (ct)
```
¶
If the integer c is not between 0 and n-1, output "decryption error", and stop.¶
Decrypt the integer c using the recipient's private key (n,d) to recover an integer z (see NOTE below):¶
```
     z = c^d mod n
```
¶
Convert the integer z to a byte string Z of length nLen, mostsignificant byte first (see NOTE below):¶
```
     Z = IntegerToString (z, nLen)
```
¶
Derive a shared secret SS of length ssLen bytes from the bytestring Z using the key derivation function (see NOTE below):¶
```
     SS = KDF (Z, ssLen)
```
¶
Output the shared secret SS.¶

NOTE: ImplementationsSHOULD NOT reveal information about theinteger z, the string Z, or about the calculation of theexponentiation in Step 2, the conversion in Step 3, or the keyderivation in Step 4, whether by timing or other "side channels".The observable behavior of the implementationSHOULD be the same atthese steps for all ciphertexts C that are in range. For example,IntegerToString conversion should take the same amount of timeregardless of the actual value of the integer z. The integer z, thestring Z, and other intermediate resultsMUST be securely deletedwhen they are no longer needed.¶

Appendix B.ASN.1 Syntax

The ASN.1 syntax for identifying the RSA-KEM algorithmis an extension of the syntax for the "generic hybrid cipher" inANS X9.44[ANS-X9.44].¶

The ASN.1 Module is unchanged from RFC 5990. The id-rsa-kem-spkiobject identifier is used in a backward compatible mannerin certificates[RFC5280] and SMIMECapabilities[RFC8551].Of course, the use of the id-kem-rsa object identifier in thenew KEMRecipientInfo structure[RFC9629]was not yet defined at the time that RFC 5990 was written.¶

B.1.Underlying Components

Implementations that conform to this specificationMUST supportthe KDF3[ANS-X9.44] key derivation function using SHA-256[SHS].¶

KDF2[ANS-X9.44] and KDF3 are both key derivation functions based ona hash function. The only difference between KDF2 and KDF3 is the orderof the components to be hashed.¶

   KDF2 calculates T as:   T = T || Hash (Z || D || otherInfo)   KDF3 calculates T as:   T = T || Hash (D || Z || otherInfo)

The object identifier for KDF3 is:¶

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

The KDF3 parameters identify the underlying hash function. Foralignment with ANS X9.44, the hash functionMUST be an ASC X9-approvedhash function. While the SHA-1 hash algorithm is included in theASN.1 definitions, SHA-1MUST NOT be used. SHA-1 is consideredto be obsolete; see[RFC6194]. SHA-1 remains in the ASN.1 module forcompatibility with RFC 5990. In addition, other hash functionsMAY beused 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 specificationMUST supportthe AES Key Wrap[RFC3394] key-encryption algorithm with a 128-bitkey. There are three object identifiers for the AES Key Wrap, one foreach permitted size of the key-encryption key. There are three objectidentifiers imported from[RFC5912], and none of these algorithmidentifiers 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

<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(79) }   DEFINITIONS EXPLICIT TAGS ::= BEGIN-- EXPORTS ALLIMPORTS  KEM-ALGORITHM    FROM KEMAlgorithmInformation-2023  -- [RFC9629]       { iso(1) identified-organization(3) dod(6) internet(1)         security(5) mechanisms(5) pkix(7) id-mod(0)         id-mod-kemAlgorithmInformation-2023(109) }  AlgorithmIdentifier{}, PUBLIC-KEY, DIGEST-ALGORITHM,  KEY-DERIVATION, KEY-WRAP, SMIME-CAPS    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) }  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 definitionsOID ::= OBJECT IDENTIFIER  -- aliasNullParms ::= NULL-- ISO/IEC 18033-2 arcis18033-2 OID ::= { iso(1) standard(0) is18033(18033) part2(2) }-- NIST algorithm arcnistAlgorithm OID ::= { joint-iso-itu-t(2) country(16) us(840)   organization(1) gov(101) csor(3) nistAlgorithm(4) }-- PKCS #1 arcpkcs-1 OID ::= { iso(1) member-body(2) us(840) rsadsi(113549)   pkcs(1) pkcs-1(1) }-- X9.44 arcx9-44 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 algorithmid-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-kemGenericHybridParameters ::= SEQUENCE {   kem  KeyEncapsulationMechanism,   dem  DataEncapsulationMechanism }KeyEncapsulationMechanism ::=   AlgorithmIdentifier { KEM-ALGORITHM, {KEMAlgorithms} }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 |   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 Functionsid-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 -- }KDF3-HashFunction ::=   AlgorithmIdentifier { DIGEST-ALGORITHM, {KDF3-HashFunctions} }KDF3-HashFunctions DIGEST-ALGORITHM ::= { X9-HashFunctions, ... }-- Hash FunctionsX9-HashFunctions DIGEST-ALGORITHM ::= {   mda-sha1 | mda-sha224 | mda-sha256 | mda-sha384 |   mda-sha512, ... }-- Updates for the SMIME-CAPS Set from RFC 5911SMimeCapsSet SMIME-CAPS ::= {   kema-kem-rsa.&smimeCaps |   kwa-aes128-wrap |   kwa-aes192-wrap |   kwa-aes256-wrap |   kwa-camellia128-wrap.&smimeCaps |   kwa-camellia192-wrap.&smimeCaps |   kwa-camellia256-wrap.&smimeCaps,   ... }END<CODE ENDS>

Appendix D.RSA-KEM CMS Enveloped-Data Example

This example shows the establishment of an AES-128 content-encryptionkey using:¶

RSA-KEM with a 3072-bit key and KDF3 with SHA-256;¶
KEMRecipientInfo key derivation using KDF3 with SHA-256; and¶
KEMRecipientInfo Key Wrap using AES-128-KEYWRAP.¶

In real-world use, the originator would encrypt the content-encryptionkey in a manner that would allow decryption with their own private keyas well as the recipient's private key. This is omitted in an attemptto simplify the example.¶

D.1.Originator RSA-KEM Encapsulate() Processing

Alice obtains Bob's 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 iscalled ct:¶

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

Alice derives the shared secret (SS) using KDF3 with SHA-256:¶

   3cf82ec41b54ed4d37402bbd8f805a52

D.2.Originator CMS Processing

Alice encodes the CMSORIforKEMOtherInfo structure with the algorithmidentifier 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 shared secret producedby RSA-KEM Encapsulate() and the CMSORIforKEMOtherInfo structurewith KDF3 and SHA-256. The KEK is:¶

   e6dc9d62ff2b469bef604c617b018718

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

   77f2a84640304be7bd42670a84a1258b

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

   28782e5d3d794a7616b863fbcfc719b78f12de08cf286e09

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

   480ccafebabefacedbaddecaf8887781

The padded content plaintext is:¶

   48656c6c6f2c20776f726c6421030303

The resulting ciphertext is:¶

   c6ca65db7bdd76b0f37e2fab6264b66d

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

   MIICXAYJKoZIhvcNAQcDoIICTTCCAkkCAQMxggIEpIICAAYLKoZIhvcNAQkQDQMw   ggHvAgEAgBSe62fJuVp01E0vFjlmgOgBtcuknDAJBgcogYxxAgIEBIIBgMBx/Cc6   +Oe9sVLga/czEDYQdBVKQ6vPPJPBNJnSBlNEPu2e9dPAaF5Kp2poVIFbuXaR/5+N   rBXup9dPRSvzUKZGFj1oKI6XjL96cwie5ScS+aT0ngas57vIWrFNTjNsl8VyiiZU   E4x7JuiDXGsKn77SZJXE6t90Wikzvig/aoixZpX8BmZoc8+202cY7zN2zvwQDDlB   88SUlEB4MlgHpVkYa5XMq/NxTPr3n4O9MFN/3ZrtWkzcvYvQSG+u1z6dSGswh9bI   BlRrbiZxV1yYRh5EH2VUK9ld4m0PU6ZOeEjXMdlgjQU+jTRVRmAthiNv/jcEyYrV   kUTzCJ5ebVJ7VJe6EDx51i6A0CNUELBvcafZvRw4AA+RDWMS6i8go1V1Na0Bswk/   tffuUHCA0Pd9SMnDs3lva33TeGCF+4lRI/BMofHBviLHR6jfrOMjcPsNVweD4n27   fnT8qU7jlnb949ipVT2HgiRzbjfhkdq5U8fiKMB61coxIkIcFN69ByqatjAbBgor   gQUQhkgJLAECMA0GCWCGSAFlAwQCAQUAAgEQMAsGCWCGSAFlAwQBBQQYKHguXT15   SnYWuGP7z8cZt48S3gjPKG4JMDwGCSqGSIb3DQEHATAdBglghkgBZQMEAQIEEEgM   yv66vvrO263eyviId4GAEMbKZdt73Xaw834vq2Jktm0=

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       :       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 B6475  27:       SEQUENCE {477  10:        OBJECT IDENTIFIER       :         kdf3 (1 3 133 16 840 9 44 1 2)489  13:        SEQUENCE {491   9:         OBJECT IDENTIFIER       :          sha-256 (2 16 840 1 101 3 4 2 1)502   0:         NULL       :          }       :         }504   1:       INTEGER 16507  11:       SEQUENCE {509   9:        OBJECT IDENTIFIER       :         aes128-wrap (2 16 840 1 101 3 4 1 5)       :         }520  24:       OCTET STRING       :       28 78 2E 5D 3D 79 4A 76 16 B8 63 FB CF C7 19 B7       :       8F 12 DE 08 CF 28 6E 09       :        }       :       }       :      }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       :      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 RSA-KEM Decapsulate() Processing

Bob's private key:¶

Bob checks that the length of the ciphertext is less than nLen bytes.¶

Bob checks that the ciphertext is greater than zero and is lessthan his RSA modulus.¶

Bob decrypts the ciphertext with his RSA private key to obtainthe integer z:¶

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

Bob checks that the integer z is greater than zero and is lessthan his RSA modulus.¶

Bob derives the shared secret (SS) using KDF3 with SHA-256:¶

   3cf82ec41b54ed4d37402bbd8f805a52

D.4.Recipient CMS Processing

Bob encodes the CMSORIforKEMOtherInfo structure with the algorithmidentifier 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 shared secret and theCMSORIforKEMOtherInfo structure with KDF3 and SHA-256, the KEK is:¶

   e6dc9d62ff2b469bef604c617b018718

Bob uses AES-KEY-WRAP to decrypt the content-encryption keywith 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 AES-CBC padding, the plaintext content is:¶

   Hello, world!