RFC 9690

Use of the RSA-KEM Algorithm in the Cryptographic Message Syntax (CMS)

📅 published February 2025, from ietf

RFC 9690: Use of the RSA-KEM Algorithm in the Cryptographic Message Syntax (CMS) 🎀

Request for Comments: 9690, which makes this the official spec, bestie 📜
Authors: R. Housley (Vigil Security) and S. Turner (sn3rd) 👑
Category: Standards Track 🌈
ISSN: 2070-1721
Date: February 2025 📅
Obsoletes: RFC 5990 💅

This one obsoletes RFC 5990, so the older version is officially replaced. Its IETF status is Standards Track, which means it's the real deal and not just an opinion piece 🧚

Abstract 🦋

Okay so the RSA Key Encapsulation Mechanism (RSA-KEM) is a one-pass (store-and-forward) crypto mechanism. Its whole job is letting an originator securely send keying material to a recipient using the recipient's RSA public key 🔐. It's specified in Clause 11.5 of ISO/IEC: 18033-2:2006.

This document explains how to use RSA-KEM two ways. The first is as a standalone KEM algorithm. The second is inside the Cryptographic Message Syntax (CMS) using KEMRecipientInfo, as specified in RFC 9629 ✨. And yes, it obsoletes RFC 5990, so that older version is out and this is the new source of truth 💖

Status of This Memo 🌸

This is an Internet Standards Track document.

This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Further information on Internet Standards is available in Section 2 of RFC 7841 🫶

Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at https://www.rfc-editor.org/info/rfc9690.

Copyright Notice 🍓

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 and restrictions with respect to this document. Code Components extracted from this document must include Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised BSD License. Read the fine print, babe 💅

Table of Contents 🧚

1.  Introduction
  1.1.  RSA-KEM Algorithm Rationale
  1.2.  RSA-KEM Algorithm Summary
  1.3.  CMS KEMRecipientInfo Processing Summary
  1.4.  Conventions and Definitions
  1.5.  ASN.1
  1.6.  Changes Since RFC 5990
2.  Use of the RSA-KEM Algorithm in CMS
  2.1.  Mandatory To Implement
  2.2.  RecipientInfo Conventions
  2.3.  Certificate Conventions
  2.4.  SMIMECapabilities Attribute Conventions
3.  Security Considerations
4.  IANA Considerations
5.  References
  5.1.  Normative References
  5.2.  Informative References
Appendix A.  RSA-KEM Algorithm
  A.1.  Originator's Operations: RSA-KEM Encapsulate()
  A.2.  Recipient's Operations: RSA-KEM Decapsulate()
Appendix B.  ASN.1 Syntax
  B.1.  Underlying Components
  B.2.  ASN.1 Module
Appendix C.  SMIMECapabilities Examples
Appendix D.  RSA-KEM CMS Enveloped-Data Example
  D.1.  Originator RSA-KEM Encapsulate() Processing
  D.2.  Originator CMS Processing
  D.3.  Recipient RSA-KEM Decapsulate() Processing
  D.4.  Recipient CMS Processing
Acknowledgements
Authors' Addresses

1. Introduction ✨

Okay so the RSA-KEM algorithm is a one-pass (store-and-forward) crypto mechanism. An originator uses it to securely send keying material to a recipient, and it only needs the recipient's RSA public key to do that 🔐. It's specified in Clause 11.5 of [ISO18033-2].

RSA-KEM is giving "different approach" energy compared to other RSA key transport mechanisms [RFC8017] 🦋. The goal is higher security assurance while still fitting the KEM interface. It encrypts a random integer with the recipient's RSA public key and then derives a shared secret from that integer. From there, the originator and recipient can both derive a symmetric key from the shared secret. For example, a key-encryption key (KEK) can be derived from the shared secret to wrap a content-encryption key (CEK) 💜

In the Cryptographic Message Syntax (CMS) [RFC5652] using KEMRecipientInfo [RFC9629], the shared-secret value goes into a key derivation function (KDF). That gives you a key-encryption key, which then wraps a symmetric content-encryption key. The end result is that the originator and the recipient finish up with the same content-encryption key 🎀

For completeness, a specification of the RSA-KEM algorithm is given in Appendix A of this document. The ASN.1 syntax lives in Appendix B 🧚

1.1. RSA-KEM Algorithm Rationale 🌈

RSA-KEM gives higher security assurance than other variants of the RSA cryptosystem, and there are two reasons why 💅

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. Because of that, it has no structure an adversary could exploit. Second, the input is independent of the keying material, so the result of the RSA decryption operation isn't directly available to an adversary 🙈. As a result, the RSA-KEM algorithm gets 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. The provable security assurances are also 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 perk is that the length of the keying material is set by the symmetric algorithms, not by the size of the RSA modulus ⭐

1.2. RSA-KEM Algorithm Summary 🍓

Every KEM algorithm provides three functions: KeyGen(), Encapsulate(), and Decapsulate(). Here's how those three work for RSA-KEM 🎀

KeyGen() -> (pk, sk): Generate the public key (pk) and a private key (sk) as described in Section 3 of [RFC8017].

Encapsulate(pk) -> (ct, SS): Given the recipient's public key (pk), produce a ciphertext (ct) to pass to the recipient, plus a shared secret (SS) for the originator to use. Here's how it goes:

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. Here's the flow:

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 originator MUST implement Encapsulate().

Given a content-encryption key CEK, here's the RSA-KEM processing the originator does to produce the values carried in the CMS KEMRecipientInfo ✨

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 recipient MUST implement Decapsulate().

Now the recipient side. This is how RSA-KEM recipient processing works on the values pulled from the KEMRecipientInfo structure 🫶

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 structure MAY be different from the KDF used to derive the shared secret in the RSA-KEM algorithm 👑

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 Basic Encoding Rules (BER) and the Distinguished Encoding Rules (DER) [X.690] 🦋

1.6. Changes Since RFC 5990 🦋

okay bestie, so RFC 5990 [RFC5990] is the one that originally laid out how to use RSA-KEM in CMS as a key transport algorithm. 💅 It used KeyTransRecipientInfo [RFC5652] for every recipient. Then the KEMRecipientInfo structure [RFC9629] showed up to support KEM algorithms, and it's giving glow-up energy ✨. When the id-rsa-kem algorithm identifier appears in the SubjectPublicKeyInfo field of a certificate, the complex parameter structure from RFC 5990 can be left out. Parameters are still allowed for backward compatibility though 🫶. Also, so nobody mixes it up with id-kem-rsa, they added id-rsa-kem-spki as an alias for id-rsa-kem 🎀.

RFC 5990 used EK as the EncryptedKey, which was the concatenation of the ciphertext C and the wrapped key WK, so EK = (C || WK). That was needed to line up with KeyTransRecipientInfo, but this document is a different vibe 🌸. Now the ciphertext and the wrapped key get sent in separate fields of the KEMRecipientInfo structure. The ciphertext goes in the kemct field, and the wrapped key goes in the encryptedKey field. Check Appendix A for how the ciphertext is computed 🧚.

RFC 5990 also supported the Camellia and Triple-DES block ciphers. This document doesn't discuss them, but their algorithm identifiers are still in the ASN.1 module (see Appendix B.2) 🍓.

RFC 5990 supported the SHA-1 hash function too. This document doesn't discuss that one either, but its algorithm identifier is still in the ASN.1 module (see Appendix B.2) 🙈.

RFC 5990 required support for the KDF3 key derivation function [ANS-X9.44]. This document keeps that requirement, but now it also requires SHA-256 [SHS] as the hash function 🔥.

RFC 5990 recommended support for alternatives to KDF3 and AES-Wrap-128. This document just says that other key derivation functions and other key-encryption algorithms MAY be supported 🌈.

RFC 5990 allowed for future definitions of additional KEM algorithms that use RSA. This document only supports one, and it's identified by the id-kem-rsa object identifier 👑.

RFC 5990 included an ASN.1 module. This document gives an alternative ASN.1 module that follows the conventions set 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 used 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 every case, the KEMRecipientInfo [RFC9629] is used with the RSA-KEM algorithm to securely transfer the content-encryption key from the originator to the recipient 💖.

2.1. 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 [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 other key-encryption algorithms 🌸.

2.2. RecipientInfo Conventions 🦋

When the RSA-KEM algorithm is used for a recipient, the RecipientInfo alternative for that recipient MUST be OtherRecipientInfo using the KEMRecipientInfo structure [RFC9629]. 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 function (KDF). The KDF used for the CMS RecipientInfo process MAY be different from 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. With the CMS enveloped-data content type [RFC5652], the keying material is a content-encryption key. With the CMS authenticated-data content type [RFC5652], the keying material is a message-authentication key. With the CMS authenticated-enveloped-data content type [RFC5083], the keying material is a content-authenticated-encryption key (CAEK) 🔐.

NOTE: For backward compatibility, implementations MAY also support the RSA-KEM Key Transport algorithm, identified by id-rsa-kem-spki, which uses KeyTransRecipientInfo as specified in [RFC5990] 🙈.

2.3. Certificate Conventions 🎀

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

A recipient who uses the RSA-KEM algorithm MAY identify the public key in a certificate with the same AlgorithmIdentifier as PKCS #1 v1.5, which is the rsaEncryption object identifier [RFC8017]. Using this object identifier does not indicate that the recipient will accept the RSA-KEM algorithm with that public key 🤷. The willingness to accept the RSA-KEM algorithm MAY be signaled with the SMIMECapabilities Attribute, as specified in Section 2.5.2 of [RFC8551], or with the SMIMECapabilities certificate extension, as specified in [RFC4262] 📣.

If the recipient only wants to use 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 for details 💜. Using id-rsa-kem-spki lets certificates that were issued to be compatible with the RSA-KEM Key Transport algorithm also be used with this specification ✨. When id-rsa-kem-spki appears in the SubjectPublicKeyInfo algorithm field of the certificate, the parameters field from the AlgorithmIdentifier SHOULD be absent. In other words, the AlgorithmIdentifier SHOULD 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] is 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 Section 2.4, 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 which AlgorithmIdentifier is 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 [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 carries 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

Other keyUsage extension values MUST NOT be present. That means a public key meant only for the RSA-KEM algorithm MUST NOT also be used for data encryption or for digital signatures 🚫. Good cryptographic practice uses a given RSA key pair in only one scheme. This avoids the risk that a vulnerability in one scheme compromises the security of the other, and it may be essential to keep provable security 🔒.

2.4. SMIMECapabilities Attribute Conventions 💅

Section 2.5.2 of [RFC8551] defines the SMIMECapabilities attribute, which announces a partial list of algorithms that an S/MIME implementation can support. When building a CMS signed-data content type [RFC5652], 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 Appendix B for the object identifier value and Appendix C for examples 🧁. When id-rsa-kem-spki appears in the capabilityID field and the parameters are present, the parameters field MUST use the GenericHybridParameters type:

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

The fields of the GenericHybridParameters type mean the following:

kem is an AlgorithmIdentifier. The algorithm field MUST be set to id-kem-rsa, and the parameters field MUST be RsaKemParameters. RsaKemParameters 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, the provided dem value MUST be used in the wrap field of KEMRecipientInfo ✨.

If the GenericHybridParameters are present, 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 💖.

3. Security Considerations ✨

okay bestie, this is the section where we talk about how to not get hacked 🫶💅 and it's lowkey the most important part of the whole doc, so pay attention!!

So the RSA-KEM algorithm should be considered as a replacement for the key transport part of the widely used PKCS #1 v1.5 [RFC8017] 🔥 for new apps that use CMS, because PKCS #1 v1.5 has potential vulnerabilities to chosen-ciphertext attacks 💀 and RSA-KEM gives you a tighter security proof 👑. The tradeoff? RSA-KEM has slightly longer encrypted keying material 🙈. With PKCS #1 v1.5, the originator encrypts the key-encryption key straight up with the recipient's RSA public key. With RSA-KEM, the key-encryption key gets encrypted separately 🎀.

The security of RSA-KEM can be shown to be tightly related to how hard it is to either solve the RSA problem or break the underlying symmetric key-encryption algorithm, if the key derivation function is modeled as a random oracle and the symmetric key-encryption algorithm has the properties of a data encapsulation mechanism [SHOUP] 🧚. Okay so, in practice a random-oracle result doesn't give you an actual security proof for any specific key derivation function 😭, but it does tell you the general construction is reasonable 🦋. A key derivation function would have to be seriously weak to lead to an attack that isn't possible in the random-oracle model 💅.

The RSA key size and the underlying components need to match the security level you want 🌈. NIST SP 800-57 Part 1 [NISTSP800-57pt1r5] lists several security levels 💜. For example, to get 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, the message-authentication key, and the content-authenticated-encryption key 🔥🔥. Like, seriously. If the RSA private key leaks, every message protected with that key is cooked 💀. If the key-encryption key, content-encryption key, or content-authenticated-encryption key leaks, the encrypted content tied to it can be compromised 😭. And if the key-encryption key, message-authentication key, or content-authenticated-encryption key leaks, somebody could modify the authenticated content 🙈.

More key management stuff can be found in [NISTSP800-57pt1r5] 🧚.

The security of RSA-KEM depends on a quality random number generator 🎲✨. For more on random number generation, check [RFC4086] 🌸.

RSA-KEM doesn't use an explicit padding scheme 🦋. Instead, an encoded random value (z), somewhere between zero and the RSA modulus minus one (n-1), gets encrypted directly with the recipient's RSA public key 💖. The IntegerToString(z, nLen) encoding makes a string that's the full length of the RSA modulus 👑. On top of that, the random value goes through a KDF so a badly implemented random number source, or a maliciously chosen random value (z), can't do as much harm 🛡️. Implementations MUST NOT use z directly for any purpose 🚫💅.

As long as you pick a fresh random integer z for every invocation of the Encapsulate() function, RSA-KEM doesn't get weaker as the number of ciphertexts goes up 📈✨. RSA encryption gives you a bijective map, so a collision in the KDF is the only way RSA-KEM can produce more than one ciphertext that encapsulates the same shared secret 🔥.

RSA-KEM gives you a fixed-length ciphertext 🎀. The recipient MUST check that the received byte string is the expected length, and that the length corresponds to an integer in the expected range, before trying to decrypt with their RSA private key, as described in Steps 1 and 2 of Appendix A.2 🙌.

Implementations SHOULD NOT reveal information about intermediate values or calculations, whether through timing or other "side channels" 👀. Otherwise, an opponent might figure out stuff about the keying data and/or the recipient's private key 😱. Not all intermediate info is useful to an opponent, but it's still better to hide as much as is practical, unless analysis specifically shows the info wouldn't help an opponent 🫶.

Generally, good crypto practice uses a given RSA key pair in only one scheme 💅. This avoids the risk that a vulnerability in one scheme compromises the other, and it may be essential for provable security 🔒. RSA public keys have often been used for multiple things, like key transport and digital signatures, with no known bad interactions 🤷‍♀️. Still, using one RSA key pair for combined purposes is NOT RECOMMENDED in the future (unless the different schemes are specifically designed to work together) 🚫.

So, an RSA key pair used for RSA-KEM SHOULD NOT also be used for digital signatures 💖. Even the Accredited Standards Committee X9 (ASC X9) requires separate key pairs for key establishment and digital signatures [ANS-X9.44] 👑. Continuing with that key separation energy, a key pair used for RSA-KEM SHOULD NOT be used with other key establishment schemes, for data encryption, or with more than one set of underlying algorithm components 🧚✨.

It's fine to use the same RSA key pair for the RSA-KEM Key Transport algorithm specified in [RFC5990] and this spec 🎀. That's because the operations involving the RSA public key and the RSA private key are identical in the two specs 💜.

Parties can get assurance that implementations are correct through formal implementation validation, like the NIST Cryptographic Module Validation Program (CMVP) [CMVP] 🌈🔥.

4. IANA Considerations 🌸

For the ASN.1 Module in Appendix B.2, IANA has assigned an object identifier (OID) for the module identifier 🦋. The OID for the module was 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 was set to "id-mod-cms-rsa-kem-2023" 💖.

IANA updated the id-alg-rsa-kem entry in the "SMI Security for S/MIME Algorithms (1.2.840.113549.1.9.16.3)" repository to refer to this document 👑. IANA also added this note to the registry:

Value 14, "id-alg-rsa-kem," is also referred to as "id-rsa-kem-spki." 🧚

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. 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>. 🎀

[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>. 🌸

[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>. 💖

[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., 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>. 🌈

[RFC9629] Housley, R., Gray, J., and T. 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 📚

Okay, now the extra reading list, bestie 🤓 These are the ones that give context but aren't required to implement the spec.

[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., and S. 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., 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.

[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 ✨

RSA-KEM is a one-pass (store-and-forward) cryptographic mechanism 🔐 It lets an originator securely send keying material to a recipient using the recipient's RSA public key. Super clean.

Here's the flow. The originator encrypts a random integer (z) with the recipient's RSA public key to get a ciphertext (ct), and the originator also derives a shared secret (SS) from that random integer (z). Then the originator sends ct over to the recipient. The recipient decrypts ct with their private key to recover z, and then derives the same shared secret (SS) from z. So both sides end up with the same SS 💖

The RSA-KEM algorithm depends on a key derivation function (KDF), and that KDF is what turns things into the shared secret (SS). Lots of KDFs can take extra info alongside the shared secret in their input. RSA-KEM doesn't do that, though. It doesn't feed any other information into the KDF 🫶

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

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

Let nLen be the length in bytes of the modulus n. That's the least integer where 2^(8*nLen) > n.

Here's what the originator does:

Generate a random integer z between 0 and n-1 (see NOTE below), and convert z into 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), then convert the resulting integer c into a ciphertext C, which is 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 (which MUST be the length of the key-encryption key) from the byte string Z, using the underlying key derivation function:

SS = KDF (Z, ssLen)

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. ⚠️

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

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

Let ct be the ciphertext received from the originator.

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

Here's what the recipient does:

If the length of the encrypted keying material is less than nLen bytes, output "decryption error", and stop.
Convert the ciphertext ct into an integer c, most significant byte first (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 into a byte string Z of length nLen, most significant byte first (see NOTE below):

Z = IntegerToString (z, nLen)

Derive a shared secret SS of length ssLen bytes from the byte string Z, using the key derivation function (see NOTE below):

SS = KDF (Z, ssLen)

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. 🙈🔥

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 [RFC9629] wasn't defined yet when RFC 5990 was written, so that part is new 🦋

B.1. Underlying Components

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

KDF2 [ANS-X9.44] 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 that get 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. For alignment with 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 stays 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. Three of these object identifiers are 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 💖

Okay bestie, this is the big ASN.1 module 🧚 It's named CMS-RSA-KEM-2023 and lives at its own OID, { 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) }. It imports types from a bunch of other modules (RFC 9629, RFC 5912, RFC 5911, and RFC 3657), then defines the RSA-KEM stuff, the KDF2 and KDF3 key derivation functions, the hash functions, and an updated SMimeCapsSet. Copy it exactly, because one stray space and the whole thing is cooked 💀

<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 ALL

IMPORTS

  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 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} }

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 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 -- }

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, ... }

-- Updates for the SMIME-CAPS Set from RFC 5911

SMimeCapsSet 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 C. SMIMECapabilities Examples ✨

Time for the examples! 🎀 To say "yep, I do RSA-KEM with KDF3 + SHA-256, and AES Key Wrap with a 128-bit key-encryption key," your SMIMECapabilities will include this 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):

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

🦋 Next up: same RSA-KEM plus KDF3, but now with SHA-384 and an AES Key Wrap with a 192-bit key-encryption key. The SMIMECapabilities will include this 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

💅 And last one: RSA-KEM plus KDF3 with SHA-512 and an AES Key Wrap with a 256-bit key-encryption key. The SMIMECapabilities will include this 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 is giving "establish an AES-128 content-encryption key," and it uses:

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.

ngl, in the real world the originator would also encrypt the content-encryption key so they can decrypt it with their own private key as well as the recipient's 🙈 That part is left out here just to keep the example simple. 🫶

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

okay so this is where Alice gets Bob's public key and starts the RSA-KEM Encapsulate() magic 🔥 it's literally the first step of the whole thing, so let's go!! 💖

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 🎲 no pressure, just a big random number:
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Alice encrypts integer z using the Bob's RSA public key. The result is called ct 🔐 this is giving secret-keeper energy:
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Alice derives the shared secret (SS) using KDF3 with SHA-256 ✨ and the result is:

3cf82ec41b54ed4d37402bbd8f805a52

D.2. Originator CMS Processing 💅

now we're getting into the CMS side of things, bestie 🎀 Alice encodes the CMSORIforKEMOtherInfo structure using the algorithm identifier for AES-128-KEYWRAP and a key length of 16 octets. The DER encoding of CMSORIforKEMOtherInfo comes out to 18 octets, so ate 🙌

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 the shared secret produced by RSA-KEM Encapsulate() and the CMSORIforKEMOtherInfo structure, using 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-encryption key with the derived key-encryption key 🫶 the wrapped result is:

28782e5d3d794a7616b863fbcfc719b78f12de08cf286e09

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:

48656c6c6f2c20776f726c6421030303

The resulting ciphertext is:

c6ca65db7bdd76b0f37e2fab6264b66d

Alice encodes the EnvelopedData (using KEMRecipientInfo) and ContentInfo, and then sends the result to Bob 📬 the Base64-encoded result 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 B6
475  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 16
507  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 🔐

okay so now it's Bob's turn 🦋 he's the recipient and he's got his own private key, which is giving main character energy. Here's the key he's working with:

First up, Bob checks that the length of the ciphertext is less than nLen bytes. 🧐

Then he checks that the ciphertext is greater than zero and is less than his RSA modulus. 💅

Next, Bob decrypts the ciphertext with his RSA private key to get the integer z ✨ (this is the moment, bestie):
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Then Bob checks that the integer z is greater than zero and is less than his RSA modulus. 🔍

Finally, Bob derives the shared secret (SS) using KDF3 with SHA-256 🔥:

3cf82ec41b54ed4d37402bbd8f805a52

D.4. Recipient CMS Processing 🎀

Time for the CMS side of things! 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 isn't repeated here, so no need to panic 🙈

Next, Bob derives the key-encryption key from the shared secret and the CMSORIforKEMOtherInfo structure with KDF3 and SHA-256. The KEK is:

e6dc9d62ff2b469bef604c617b018718

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

77f2a84640304be7bd42670a84a1258b

Now 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!

Bestie, that's the whole thing decrypted 🥹✨ Bob gets his message back, and it says "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 💜

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 🍓

We thank Burt Kaliski, Alex Railean, Joe Mandel, Mike Ounsworth, Peter Campbell, Daniel Van Geest, and David Ireland for careful review and thoughtful comments that greatly improved this document 👑

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

📦 where this page comes from

ietf: rfc9690 2025-02
💖 girlified by claude-haiku-5-5 on 2026-10-19: a language model's rewrite of the original, under its terms