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Security Limited Additional Mechanisms for PKIX and SMIME Key Encapsulation Mechanism (KEM) KEMRecipientInfo 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 as a standalone KEM algorithm and the conventions for using the RSA-KEM Algorithm with the Cryptographic Message Syntax (CMS) using KEMRecipientInfo as specified in RFC XXXX. This document obsoletes RFC 5990. RFC EDITOR: Please replace XXXX with the RFC number assigned to draft-ietf-lamps-cms-kemri. About This Document Status information for this document may be found at . Discussion of this document takes place on the Limited Additional Mechanisms for PKIX and SMIME Working Group mailing list (), which is archived at . Subscribe at .

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 . The RSA-KEM Algorithm takes a different approach than other RSA key transport mechanisms , with the goal of providing higher security assurance while also satisfying the KEM interface. The RSA-KEM Algorithm encrypts a random integer with the recipient's RSA public key, and derives a shared secret from the random integer. The originator and recipient can derive a symmetric key from the shared secret. For example, a key-encryption key can be derived from the shared secret to wrap a content-encryption key. In the Cryptographic Message Syntax (CMS) using KEMRecipientInfo , the shared secret value is input to a key-derivation function to compute a key-encryption key, and wrap a symmetric content-encryption key with the key-encryption key. In this way, the originator and the recipient end up with the same content-encryption key. 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.

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 , 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 determined by the symmetric algorithms, not the size of the RSA modulus.

RSA-KEM Algorithm Summary All KEM algorithms provide three functions: KeyGen(), Encapsulate(), and Decapsulate(). The following summarizes these three functions for RSA-KEM: KeyGen() -> (pk, sk):

• Generate the public key (pk) and a private key (sk) as described in .

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:

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

• 2. Encrypt the integer z with the recipient's RSA public key to obtain the ciphertext:

• 3. Derive a shared secret from the integer z using a Key Derivation Function (KDF):

• 4. 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:

• 1. Decrypt the ciphertext with the recipient's RSA private key to obtain the random integer z:

• 2. Derive a shared secret from the integer z:

3. The shared secret is returned by the function.

CMS KEMRecipientInfo Processing Summary To support the RSA-KEM algorithm, the CMS originator MUST 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:

• 1. Obtain the shared secret using the Encapsulate() function of the RSA-KEM algorithm and the recipient's RSA public key:

• 2. Derive a key-encryption key KEK from the shared secret:

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

• 4. The originator sends the ciphertext and WK to the recipient in the CMS KEMRecipientInfo structure.

To support the RSA-KEM algorithm, the CMS recipient MUST implement Decapsulate(). The RSA-KEM algorithm recipient processing of the values obtained from the KEMRecipientInfo structure can be summarized as:

• 1. Obtain the shared secret using the Decapsulate() function of the RSA-KEM algorithm and the recipient's RSA private key:

• 2. Derive a key-encryption key KEK from the shared secret:

• 3. Unwrap the WK with the KEK to obtain content-encryption key CEK:

Note that the KDF used to process the KEMRecipientInfo structure MAY be different from the KDF used to derive the shared secret in the RSA-KEM algorithm.

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 when, and only when, they appear in all capitals, as shown here.

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

Changes Since RFC 5990 RFC 5990 specified the conventions for using the RSA-KEM Algorithm in CMS as a key transport algorithm. That is, it used KeyTransRecipientInfo for each recipient. Since the publication of RFC 5990, a new KEMRecipientInfo structure has been defined to support KEM algorithms. When the id-rsa-kem algorithm identifier appears in the SubjectPublicKeyInfo field of a certificate, the complex parameter structure defined in RFC 5990 can be omitted; however, the parameters are allowed for backward 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 of the ciphertext C and the wrapped key WK, EK = (C || WK). The use of EK was necessary to align with the KeyTransRecipientInfo structure. In this document, the ciphertext and the wrapped key are sent in separate fields of the KEMRecipientInfo structure. In particular, the ciphertext is carried in the kemct field, and wrapped key is carried in the encryptedKey field. See for details about the computation of the ciphertext. RFC 5990 included 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 . RFC 5990 included 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 . RFC 5990 required support for the KDF3 key-derivation function ; this document continues to require support for the KDF3 key-derivation function, but it requires support for SHA-256 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 other key-encryption algorithms MAY be supported. RFC 5990 supported 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 included an ASN.1 module; this document provides an alternative ASN.1 module that follows the conventions established in , , and . The new ASN.1 module produces the same bits-on-the-wire as the one in RFC 5990.

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 , the CMS authenticated-data content type , or the CMS authenticated-enveloped-data content type . In each case, the KEMRecipientInfo is used with the RSA-KEM Algorithm to securely transfer the content-encryption key from the originator to the recipient.

Mandatory To Implement 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 with SHA-256 .
• For key-wrapping, an implementation MUST support the AES-Wrap-128 key-encryption algorithm.

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

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 . 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 .

• kdf identifies the key-derivation function (KDF). Note that the KDF used for CMS RecipientInfo process MAY 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 the key-encryption key. When used with the CMS enveloped-data content type , the keying material is a content-encryption key. When used with the CMS authenticated-data content type , the keying material is a message-authentication key. When used with the CMS authenticated-enveloped-data content type , the keying material is a content-authenticated-encryption key.

NOTE: For backward compatibility, implementations MAY also support RSA-KEM Key Transport Algorithm, identified by id-rsa-kem-spki, which uses KeyTransRecipientInfo as specified in .

Certificate Conventions The conventions specified in this section augment RFC 5280 . 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 . 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 SMIMECapabilities Attribute as specified in or the SMIMECapabilities certificate extension as specified in . 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 . The use of the id-rsa-kem-spki object identifier allows certificates that were issued to be compatible with RSA-KEM Key Transport to also be used with this specification. 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. With absent parameters, the KDF3 key-derivation function with SHA-256 are used to derive the shared secret. When the AlgorithmIdentifier parameters are present, the GenericHybridParameters MUST be used. Within the kem element, the algorithm identifier MUST be set to id-kem-rsa, and RsaKemParameters MUST be included. As described in , 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 field of the certificate using the RSAPublicKey type defined in . The intended application for the public key MAY be indicated in the key usage certificate extension as specified in . 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 only the following value:

• keyEncipherment

The digitalSignature 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.

SMIMECapabilities Attribute Conventions defines the SMIMECapabilities attribute to announce a partial list of algorithms that an S/MIME implementation can support. When constructing a CMS signed-data content type , a compliant implementation MAY include the SMIMECapabilities attribute that announces support for 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 for the object identifier value, and see 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. The fields of the GenericHybridParameters type have the following meanings:

• kem is an AlgorithmIdentifer. The algorithm field MUST be set to id-kem-rsa, and 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.

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

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.

Security Considerations The RSA-KEM Algorithm should be considered as a replacement for the key transport portion of the widely implemented PKCS #1 v1.5 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. With PKCS #1 v1.5, the originator encrypts the key-encryption key directly with the recipient's RSA public key. With the RSA-KEM, the key-encryption key is encrypted separately. 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 . 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 . For example, one way to achieve 128-bit security, the RSA key size would be at least 3072 bits, the key-derivation function would be SHA-256, and the symmetric key-encryption algorithm would be AES Key Wrap with a 128-bit key. Implementations MUST protect the RSA private key, the key-encryption key, the content-encryption key, message-authentication key, and the content-authenticated-encryption key. Disclosure of the RSA private key could result in the compromise of all messages protected with that key. Disclosure of the key-encryption key, the content-encryption key, or the content-authenticated-encryption key could result in compromise of the associated encrypted content. Disclosure of the key-encryption key, the message-authentication key, or the content-authenticated-encryption key could allow modification of the associated authenticated content. Additional considerations related to key management may be found in . The security of the RSA-KEM Algorithm depends on a quality random number generator. For further discussion on random number generation, see . 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. The IntegerToString(z, nLen) encoding produces a string that is the full length of the RSA modulus. In addition, the random value is passed through a key-derivation function (KDF) to reduce possible harm from a poorly implemented random number source or a maliciously chosen random value (z). Implementations MUST NOT use z directly for any purpose. As long as a fresh random integer z is chosen as part of each invocation of the Encapsulate() function, RSA-KEM does not degrade as the number of ciphertexts increases. Since RSA encryption provides a bijective map, a collision in the KDF is the only way that RSA-KEM can produce more than one ciphertext that encapsulates the same shared secret. The RSA-KEM Algorithm provides a fixed-length ciphertext. The recipient MUST check that the received byte string is the expected length and the length corresponds to an integer in the expected range prior to attempting decryption with their RSA private key as described in Steps 1 and 2 of . 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 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. RSA public keys have often been employed for multiple purposes such as key transport and digital signature without any known bad interactions; however, 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 . 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. It is acceptable to use the same RSA key pair for RSA-KEM Key Transport as specified in 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 through formal implementation validation, such as the NIST Cryptographic Module Validation Program (CMVP) .

IANA Considerations For the ASN.1 Module in , 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".

References Normative References Vigil Security, LLC Entrust DigiCert, Inc. The Cryptographic Message Syntax (CMS) supports key transport and key agreement algorithms. In recent years, cryptographers have been specifying Key Encapsulation Mechanism (KEM) algorithms, including quantum-secure KEM algorithms. This document defines conventions for the use of KEM algorithms by the originator and recipients to encrypt and decrypt CMS content. This document updates RFC 5652. This document describes an additional content type for the Cryptographic Message Syntax (CMS). The authenticated-enveloped-data content type is intended for use with authenticated encryption modes. All of the various key management techniques that are supported in the CMS enveloped-data content type are also supported by the CMS authenticated-enveloped-data content type. [STANDARDS-TRACK] This memo profiles the X.509 v3 certificate and X.509 v2 certificate revocation list (CRL) for use in the Internet. An overview of this approach and model is provided as an introduction. The X.509 v3 certificate format is described in detail, with additional information regarding the format and semantics of Internet name forms. Standard certificate extensions are described and two Internet-specific extensions are defined. A set of required certificate extensions is specified. The X.509 v2 CRL format is described in detail along with standard and Internet-specific extensions. An algorithm for X.509 certification path validation is described. An ASN.1 module and examples are provided in the appendices. [STANDARDS-TRACK] This document describes the Cryptographic Message Syntax (CMS). This syntax is used to digitally sign, digest, authenticate, or encrypt arbitrary message content. [STANDARDS-TRACK] The Cryptographic Message Syntax (CMS) format, and many associated formats, are expressed using ASN.1. The current ASN.1 modules conform to the 1988 version of ASN.1. This document updates those ASN.1 modules to conform to the 2002 version of ASN.1. There are no bits-on-the-wire changes to any of the formats; this is simply a change to the syntax. This document is not an Internet Standards Track specification; it is published for informational purposes. The Public Key Infrastructure using X.509 (PKIX) certificate format, and many associated formats, are expressed using ASN.1. The current ASN.1 modules conform to the 1988 version of ASN.1. This document updates those ASN.1 modules to conform to the 2002 version of ASN.1. There are no bits-on-the-wire changes to any of the formats; this is simply a change to the syntax. This document is not an Internet Standards Track specification; it is published for informational purposes. The Cryptographic Message Syntax (CMS) format, and many associated formats, are expressed using ASN.1. The current ASN.1 modules conform to the 1988 version of ASN.1. This document updates some auxiliary ASN.1 modules to conform to the 2008 version of ASN.1; the 1988 ASN.1 modules remain the normative version. There are no bits- on-the-wire changes to any of the formats; this is simply a change to the syntax. This document is not an Internet Standards Track specification; it is published for informational purposes. This document provides recommendations for the implementation of public-key cryptography based on the RSA algorithm, covering cryptographic primitives, encryption schemes, signature schemes with appendix, and ASN.1 syntax for representing keys and for identifying the schemes. This document represents a republication of PKCS #1 v2.2 from RSA Laboratories' Public-Key Cryptography Standards (PKCS) series. By publishing this RFC, change control is transferred to the IETF. This document also obsoletes RFC 3447. This document defines Secure/Multipurpose Internet Mail Extensions (S/MIME) version 4.0. S/MIME provides a consistent way to send and receive secure MIME data. Digital signatures provide authentication, message integrity, and non-repudiation with proof of origin. Encryption provides data confidentiality. Compression can be used to reduce data size. This document obsoletes RFC 5751. National Institute of Standards and Technology ITU-T ITU-T American National Standards Institute ISO/IEC JTC 1/SC 27 In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. Informative References Security systems are built on strong cryptographic algorithms that foil pattern analysis attempts. However, the security of these systems is dependent on generating secret quantities for passwords, cryptographic keys, and similar quantities. The use of pseudo-random processes to generate secret quantities can result in pseudo-security. A sophisticated attacker may find it easier to reproduce the environment that produced the secret quantities and to search the resulting small set of possibilities than to locate the quantities in the whole of the potential number space. Choosing random quantities to foil a resourceful and motivated adversary is surprisingly difficult. This document points out many pitfalls in using poor entropy sources or traditional pseudo-random number generation techniques for generating such quantities. It recommends the use of truly random hardware techniques and shows that the existing hardware on many systems can be used for this purpose. It provides suggestions to ameliorate the problem when a hardware solution is not available, and it gives examples of how large such quantities need to be for some applications. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. This document defines a certificate extension for inclusion of Secure/Multipurpose Internet Mail Extensions (S/MIME) Capabilities in X.509 public key certificates, as defined by RFC 3280. This certificate extension provides an optional method to indicate the cryptographic capabilities of an entity as a complement to the S/MIME Capabilities signed attribute in S/MIME messages according to RFC 3851. [STANDARDS-TRACK] The RSA-KEM Key Transport Algorithm is a one-pass (store-and-forward) mechanism for transporting keying data to a recipient using the recipient's RSA public key. ("KEM" stands for "key encapsulation mechanism".) This document specifies the conventions for using the RSA-KEM Key Transport Algorithm with the Cryptographic Message Syntax (CMS). The ASN.1 syntax is aligned with an expected forthcoming change to American National Standard (ANS) X9.44. This document includes security considerations for the SHA-0 and SHA-1 message digest algorithm. This document is not an Internet Standards Track specification; it is published for informational purposes. National Institute of Standards and Technology National Institute of Standards and Technology

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 the RSA-KEM Algorithm, an originator encrypts a random integer (z) with the recipient's RSA public key to produce a ciphertext (ct), and the originator derives a shared secret (SS) from the random integer (z). The originator then sends the ciphertext (ct) to the recipient. The recipient decrypts the ciphertext (ct) using their private key to recover the random integer (z), and the recipient derives a shared secret (SS) from the random integer(z). In this way, originator and recipient obtain the same shared secret (SS). The RSA-KEM Algorithm depends on a key-derivation function (KDF), which is used to derive the shared secret (SS). Many key-derivation functions support the inclusion of other information in addition to the shared secret (SS) in the input to the function; however, no other information is included as an input to the KDF by the RSA-KEM Algorithm.

Originator's Operations: RSA-KEM Encapsulate() Let (n,e) be the recipient's RSA public key; see for details. 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:
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:
3. Derive a symmetric shared secret SS of length ssLen bytes from the byte string Z using the underlying key-derivation function:
4. Output the shared secret SS and the ciphertext ct. Send the ciphertext ct 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.

Recipient's Operations: RSA-KEM Decapsulate() Let (n,d) be the recipient's RSA private key; see 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:

1. If the length of the encrypted keying material is less than nLen bytes, output "decryption error", and stop.
2. Convert the ciphertext ct to an integer c, most significant byte first (see NOTE below): If the integer c is not between 0 and n-1, output "decryption error", and stop.
3. Decrypt the integer c using the recipient's private key (n,d) to recover an integer z (see NOTE below):
4. Convert the integer z to a byte string Z of length nLen, most significant byte first (see NOTE below):
5. Derive a shared secret SS of length ssLen bytes from the byte string Z using the key-derivation function (see NOTE below):
6. Output the shared secret SS.

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.

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 . 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 and SMIMECapabilities . Of course, the use of the id-kem-rsa object identifier in the new KEMRecipientInfo structure was not yet defined at the time that RFC 5990 was written.

Underlying Components Implementations that conform to this specification MUST support the KDF3 key-derivation function using SHA-256 . KDF2 and KDF3 are both key-derivation functions based on a hash function. The only difference between KDF2 and KDF3 is the order of the components to be hashed. The object identifier for KDF3 is: 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 . SHA-1 remains in the ASN.1 module for compatibility with RFC 5990. In addition, other hash functions MAY be used with CMS. Implementations that conform to this specification MUST support the AES Key Wrap 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 , and none of these algorithm identifiers have associated parameters:

ASN.1 Module RFC EDITOR: Please replace TBD2 with the value assigned by IANA during the publication of .

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

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 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-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.

Originator RSA-KEM Encapsulate() Processing Alice obtains Bob's public key: Bob's RSA public key has the following key identifier: Alice randomly generates integer z between 0 and n-1: Alice encrypts integer z using the Bob's RSA public key, the result is called ct: Alice derives the shared secret (SS) using KDF3 with SHA-256:

Originator CMS Processing 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: The CMSORIforKEMOtherInfo structure contains:

Alice derives the key-encryption key from shared secret produced by RSA-KEM Encapsulate() and the CMSORIforKEMOtherInfo structure with KDF3 and SHA-256, the KEK is: Alice randomly generates a 128-bit content-encryption key: Alice uses AES-128-KEYWRAP to encrypt the 128-bit content-encryption key with the derived key-encryption key: Alice encrypts the padded content using AES-128-CBC with the content-encryption key. The 16-octet IV used is: The padded content plaintext is: The resulting ciphertext is: Alice encodes the EnvelopedData (using KEMRecipientInfo) and ContentInfo, and then sends the result to Bob. The Base64-encoded result is:

This result decodes to:

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 less than his RSA modulus. Bob decrypts the ciphertext with his RSA private key to obtain the integer z: Bob checks that the integer z is greater than zero and is less than his RSA modulus. Bob derives the shared secret (SS) using KDF3 with SHA-256:

Recipient CMS Processing 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 shared secret and the CMSORIforKEMOtherInfo structure with KDF3 and SHA-256, the KEK is: Bob uses AES-KEY-WRAP to decrypt the content-encryption key with the key-encryption key; the content-encryption key is: Bob decrypts the content using AES-128-CBC with the content- encryption key. The 16-octet IV used is: The received ciphertext content is: The resulting padded plaintext content is: After stripping the AES-CBC padding, the plaintext content is:

Acknowledgements We thank James Randall, Burt Kaliski, and John Brainard as the original authors of ; this document is based on their work. We thank the members of the ASC X9F1 working group for their contributions to drafts of ANS X9.44, which led to . We thank Blake Ramsdell, Jim Schaad, Magnus Nystrom, Bob Griffin, and John Linn for helping bring to fruition. We thank Burt Kaliski, Alex Railean, Joe Mandel, Mike Ounsworth, Peter Campbell, and Daniel Van Geest for careful review and thoughtful comments that greatly improved this document.