💾 Archived View for radia.bortzmeyer.org › rfc-mirror › rfc5990.txt captured on 2024-07-09 at 04:06:05.
⬅️ Previous capture (2023-06-14)
-=-=-=-=-=-=-
Internet Engineering Task Force (IETF) J. Randall
Request for Comments: 5990 Randall Consulting
Category: Standards Track B. Kaliski
ISSN: 2070-1721 EMC
J. Brainard
RSA
S. Turner
IECA
September 2010
Use of the RSA-KEM Key Transport Algorithm
in the Cryptographic Message Syntax (CMS)
Abstract
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.
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 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc5990.
Randall, et al. Standards Track [Page 1]
RFC 5990 Use of RSA-KEM in CMS September 2010
Copyright Notice
Copyright (c) 2010 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://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 Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
Table of Contents
1. Introduction ....................................................3
1.1. Conventions Used in This Document ..........................4
2. Use in CMS ......................................................4
2.1. Underlying Components ......................................4
2.2. RecipientInfo Conventions ..................................5
2.3. Certificate Conventions ....................................5
2.4. SMIMECapabilities Attribute Conventions ....................6
3. Security Considerations .........................................7
4. IANA Considerations .............................................9
5. Acknowledgements ................................................9
6. References .....................................................10
6.1. Normative References ......................................10
6.2. Informative References ....................................11
Appendix A. RSA-KEM Key Transport Algorithm ......................12
A.1. Underlying Components ....................................12
A.2. Sender's Operations ......................................12
A.3. Recipient's Operations ...................................13
Appendix B. ASN.1 Syntax .........................................15
B.1. RSA-KEM Key Transport Algorithm ..........................16
B.2. Selected Underlying Components ...........................18
B.2.1. Key Derivation Functions ............................18
B.2.2. Symmetric Key-Wrapping Schemes ......................19
B.3. ASN.1 Module .............................................20
B.4. Examples .................................................25
Randall, et al. Standards Track [Page 2]
RFC 5990 Use of RSA-KEM in CMS September 2010
1. Introduction
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.
Most previous key transport algorithms based on the RSA public-key
cryptosystem (e.g., the popular PKCS #1 v1.5 algorithm [PKCS1]) have
the following general form:
1. Format or "pad" the keying data to obtain an integer m.
2. Encrypt the integer m with the recipient's RSA public key:
c = m^e mod n
3. Output c as the encrypted keying data.
The RSA-KEM Key Transport Algorithm takes a different approach that
provides higher security assurance, by encrypting a _random_ integer
with the recipient's public key, and using a symmetric key-wrapping
scheme to encrypt the keying data. It has the following form:
1. Generate a random integer z between 0 and n-1.
2. Encrypt the integer z with the recipient's RSA public key:
c = z^e mod n
3. Derive a key-encrypting key KEK from the integer z.
4. Wrap the keying data using KEK to obtain wrapped keying data WK.
5. Output c and WK as the encrypted keying data.
This different approach provides higher security assurance because
(a) the input to the underlying RSA operation is effectively a random
integer between 0 and n-1, where n is the RSA modulus, so it does not
have any structure that could be exploited by an adversary, and
(b) the input is independent of the keying data so the result of the
RSA decryption operation is not directly available to an adversary.
As a result, the 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 data, and
the provable security assurances are not as strong.) The approach is
also architecturally convenient because the public-key operations are
Randall, et al. Standards Track [Page 3]
RFC 5990 Use of RSA-KEM in CMS September 2010
separate from the symmetric operations on the keying data. Another
benefit is that the length of the keying data is bounded only by the
symmetric key-wrapping scheme, not the size of the RSA modulus.
The RSA-KEM Key Transport Algorithm in various forms is being adopted
in several draft standards as well as in American National Standard
(ANS) X9.44 [ANS-X9.44]. It has also been recommended by the New
European Schemes for Signatures, Integrity, and Encryption (NESSIE)
project [NESSIE]. Originally, [ANS-X9.44] specified a different
object identifier to identify the RSA-KEM Key Transport Algorithm.
[ANS-X9.44] used id-ac-generic-hybrid, while this document uses
id-rsa-kem. These OIDs are used in the KeyTransportInfo field to
indicate the key encryption algorithm, in certificates to allow
recipients to restrict their public keys for use with RSA-KEM only,
and in SMIME Capability attributes to allow recipients to advertise
their support for RSA-KEM. Legacy implementations that wish to
interoperate with [ANS-X9.44] should consult that specification for
more information on id-ac-generic-hybrid.
For completeness, a specification of the algorithm is given in
Appendix A of this document; ASN.1 syntax is given in Appendix B.
NOTE: The term "KEM" stands for "key encapsulation mechanism" and
refers to the first three steps of the process above. The
formalization of key transport algorithms (or more generally,
asymmetric encryption schemes) in terms of key encapsulation
mechanisms is described further in research by Victor Shoup
leading to the development of the ISO/IEC 18033-2 standard
[SHOUP].
1.1. Conventions Used in This Document
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [STDWORDS].
2. Use in CMS
The RSA-KEM Key Transport Algorithm MAY be employed for one or more
recipients in the CMS enveloped-data content type (Section 6 of
[CMS]), where the keying data processed by the algorithm is the CMS
content-encryption key.
2.1. Underlying Components
A CMS implementation that supports the RSA-KEM Key Transport
Algorithm MUST support at least the following underlying components:
Randall, et al. Standards Track [Page 4]
RFC 5990 Use of RSA-KEM in CMS September 2010
o For the key derivation function, KDF3 (see [ANS-X9.44]) based on
SHA-256 (see [FIPS-180-3]). KDF3 is an instantiation of the
Concatenation Key Derivation Function defined in [NIST-SP800-56A].
o For the key-wrapping scheme, AES-Wrap-128, i.e., the AES Key Wrap
with a 128-bit key-encrypting key (see [AES-WRAP]).
An implementation SHOULD also support KDF2 (see [ANS-X9.44]) based on
SHA-1 (this function is also specified as the key derivation function
in [ANS-X9.63]). The Camellia key wrap algorithm (see [CAMELLIA])
SHOULD be supported if Camellia is supported as a content-encryption
cipher. The Triple-DES Key Wrap (see [3DES-WRAP]) SHOULD also be
supported if Triple-DES is supported as a content-encryption cipher.
It MAY support other underlying components. When AES or Camellia is
used, the data block size is 128 bits and the key size can be 128,
192, or 256 bits, while Triple-DES requires a data block size of
64 bits and a key size of 112 or 168 bits.
2.2. RecipientInfo Conventions
When the RSA-KEM Key Transport Algorithm is employed for a recipient,
the RecipientInfo alternative for that recipient MUST be
KeyTransRecipientInfo. The algorithm-specific fields of the
KeyTransRecipientInfo value MUST have the following values:
o keyEncryptionAlgorithm.algorithm MUST be id-rsa-kem (see
Appendix B);
o keyEncryptionAlgorithm.parameters MUST be a value of type
GenericHybridParameters, identifying the RSA-KEM key encapsulation
mechanism (see Appendix B);
o encryptedKey MUST be the encrypted keying data output by the
algorithm, where the keying data is the content-encryption key
(see Appendix A).
2.3. Certificate Conventions
The conventions specified in this section augment RFC 5280 [PROFILE].
A recipient who employs the RSA-KEM Key Transport Algorithm MAY
identify the public key in a certificate by the same
AlgorithmIdentifier as for the PKCS #1 v1.5 algorithm, i.e., using
the rsaEncryption object identifier [PKCS1]. The fact that the user
will accept RSA-KEM with this public key is not indicated by the use
Randall, et al. Standards Track [Page 5]
RFC 5990 Use of RSA-KEM in CMS September 2010
of this identifier. This MAY be signaled by the use of the
appropriate SMIME Capabilities either in a message or in the
certificate.
If the recipient wishes only to employ the RSA-KEM Key Transport
Algorithm with a given public key, the recipient MUST identify the
public key in the certificate using the id-rsa-kem object identifier
(see Appendix B). When the id-rsa-kem algorithm identifier appears
in the SubjectPublicKeyInfo algorithm field, the encoding SHALL omit
the parameters field from AlgorithmIdentifier. That is, the
AlgorithmIdentifier SHALL be a SEQUENCE of one component, the object
identifier id-rsa-kem.
Regardless of the AlgorithmIdentifier used, the RSA public key is
encoded in the same manner in the subject public key information.
The RSA public key MUST be encoded using the type RSAPublicKey type:
RSAPublicKey ::= SEQUENCE {
modulus INTEGER, -- n
publicExponent INTEGER -- e
}
Here, the modulus is the modulus n, and publicExponent is the public
exponent e. The Distinguished Encoding Rules (DER)-encoded
RSAPublicKey is carried in the subjectPublicKey BIT STRING within the
subject public key information.
The intended application for the key MAY be indicated in the key
usage certificate extension (see [PROFILE], Section 4.2.1.3). If the
keyUsage extension is present in a certificate that conveys an RSA
public key with the id-rsa-kem object identifier as discussed above,
then the key usage extension MUST contain the following value:
keyEncipherment
dataEncipherment SHOULD NOT be present. That is, a key intended to
be employed only with the RSA-KEM Key Transport Algorithm SHOULD NOT
also be employed for data encryption or for authentication such as in
signatures. Good cryptographic practice employs a given RSA key pair
in only one scheme. This practice avoids the risk that vulnerability
in one scheme may compromise the security of the other, and may be
essential to maintain provable security.
2.4. SMIMECapabilities Attribute Conventions
RFC 3851 [MSG], Section 2.5.2 defines the SMIMECapabilities signed
attribute (defined as a SEQUENCE of SMIMECapability SEQUENCEs) to be
used to specify a partial list of algorithms that the software
Randall, et al. Standards Track [Page 6]
RFC 5990 Use of RSA-KEM in CMS September 2010
announcing the SMIMECapabilities can support. When constructing a
signedData object, compliant software MAY include the
SMIMECapabilities signed attribute announcing that it supports the
RSA-KEM Key Transport Algorithm.
The SMIMECapability SEQUENCE representing the RSA-KEM Key Transport
Algorithm MUST include the id-rsa-kem object identifier (see
Appendix B) in the capabilityID field and MUST include a
GenericHybridParameters value in the parameters field identifying the
components with which the algorithm is to be employed.
The DER encoding of a SMIMECapability SEQUENCE is the same as the DER
encoding of an AlgorithmIdentifier. Example DER encodings for
typical sets of components are given in Appendix B.4.
3. Security Considerations
The RSA-KEM Key Transport Algorithm should be considered for new CMS-
based applications as a replacement for the widely implemented RSA
encryption algorithm specified originally in PKCS #1 v1.5 (see
[PKCS1] and Section 4.2.1 of [CMSALGS]), which is vulnerable to
chosen-ciphertext attacks. The RSA Encryption Scheme - Optimal
Asymmetric Encryption Padding (RSAES-OAEP) Key Transport Algorithm
has also been proposed as a replacement (see [PKCS1] and [CMS-OAEP]).
RSA-KEM has the advantage over RSAES-OAEP of a tighter security
proof, but the disadvantage of slightly longer encrypted keying data.
The security of the RSA-KEM Key Transport Algorithm described in this
document can be shown to be tightly related to the difficulty of
either solving the RSA problem or breaking the underlying symmetric
key-wrapping scheme, if the underlying key derivation function is
modeled as a random oracle, and assuming that the symmetric key-
wrapping scheme satisfies the properties of a data encapsulation
mechanism [SHOUP]. While in practice a random-oracle result does not
provide an actual security proof for any particular key derivation
function, the result does provide assurance that the general
construction is reasonable; a key derivation function would need to
be particularly weak to lead to an attack that is not possible in the
random oracle model.
The RSA key size and the underlying components should be selected
consistent with the desired symmetric security level for an
application. Several security levels have been identified in the
NIST FIPS PUB 800-57 [NIST-GUIDELINE]. For brevity, the first three
levels are mentioned here:
Randall, et al. Standards Track [Page 7]
RFC 5990 Use of RSA-KEM in CMS September 2010
o 80-bit security. The RSA key size SHOULD be at least 1024 bits,
the hash function underlying the KDF SHOULD be SHA-1 or above, and
the symmetric key-wrapping scheme SHOULD be AES Key Wrap, Triple-
DES Key Wrap, or Camellia Key Wrap.
o 112-bit security. The RSA key size SHOULD be at least 2048 bits,
the hash function underlying the KDF SHOULD be SHA-224 or above,
and the symmetric key-wrapping scheme SHOULD be AES Key Wrap,
Triple-DES Key Wrap, or Camellia Key Wrap.
o 128-bit security. The RSA key size SHOULD be at least 3072 bits,
the hash function underlying the KDF SHOULD be SHA-256 or above,
and the symmetric key-wrapping scheme SHOULD be AES Key Wrap or
Camellia Key Wrap.
Note that the AES Key Wrap or Camellia Key Wrap MAY be used at all
three of these levels; the use of AES or Camellia does not require a
128-bit security level for other components.
Implementations MUST protect the RSA private key and the content-
encryption key. Compromise of the RSA private key may result in the
disclosure of all messages protected with that key. Compromise of
the content-encryption key may result in disclosure of the associated
encrypted content.
Additional considerations related to key management may be found in
[NIST-GUIDELINE].
The security of the algorithm also depends on the strength of the
random number generator, which SHOULD have a comparable security
level. For further discussion on random number generation, please
see [RANDOM].
Implementations SHOULD NOT reveal information about intermediate
values or calculations, whether by timing or other "side channels",
or 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.
Generally, good cryptographic practice employs a given RSA key pair
in only one scheme. This practice avoids the risk that vulnerability
in one scheme may compromise the security of the other, and may be
essential to maintain provable security. While RSA public keys have
often been employed for multiple purposes such as key transport and
digital signature without any known bad interactions, for increased
Randall, et al. Standards Track [Page 8]
RFC 5990 Use of RSA-KEM in CMS September 2010
security assurance, such combined use of an RSA key pair is NOT
RECOMMENDED in the future (unless the different schemes are
specifically designed to be used together).
Accordingly, an RSA key pair used for the RSA-KEM Key Transport
Algorithm SHOULD NOT also be used for digital signatures. (Indeed,
the Accredited Standards Committee X9 (ASC X9) requires such a
separation between key establishment key pairs and digital signature
key pairs.) Continuing this principle of key separation, a key pair
used for the RSA-KEM Key Transport Algorithm SHOULD NOT be used with
other key establishment schemes, or for data encryption, or with more
than one set of underlying algorithm components.
Parties MAY formalize the assurance that one another's
implementations are correct through implementation validation, e.g.,
NIST's Cryptographic Module Validation Program (CMVP).
4. IANA Considerations
Within the CMS, algorithms are identified by object identifiers
(OIDs). With one exception, all of the OIDs used in this document
were assigned in other IETF documents, in ISO/IEC standards
documents, by the National Institute of Standards and Technology
(NIST), and in Public-Key Cryptography Standards (PKCS) documents.
The two exceptions are the ASN.1 module's identifier (see Appendix
B.3) and id-rsa-kem that are both assigned in this document. The
module object identifiers are defined in an arc delegated by the
former company RSA Data Security Inc. to the S/MIME Working Group.
When the S/MIME Working Group closes, this arc and its registration
procedures will be transferred to IANA.
5. Acknowledgements
This document is one part of a strategy to align algorithm standards
produced by ASC X9, ISO/IEC JTC1 SC27, NIST, and the IETF. We would
like to thank the members of the ASC X9F1 working group for their
contributions to drafts of ANS X9.44, which led to this
specification.
Our thanks to Russ Housley as well for his guidance and
encouragement. We also appreciate the helpful direction we've
received from Blake Ramsdell and Jim Schaad in bringing this document
to fruition. A special thanks to Magnus Nystrom for his assistance
on Appendix B. Thanks also to Bob Griffin and John Linn for both
editorial direction and procedural guidance.
Randall, et al. Standards Track [Page 9]
RFC 5990 Use of RSA-KEM in CMS September 2010
6. References
6.1. Normative References
[3DES-WRAP] Housley, R., "Triple-DES and RC2 Key Wrapping",
RFC 3217, December 2001.
[AES-WRAP] Schaad, J. and R. Housley, "Advanced Encryption
Standard (AES) Key Wrap Algorithm", RFC 3394,
September 2002.
[ANS-X9.44] ASC X9F1 Working Group. American National Standard
X9.44: Public Key Cryptography for the Financial
Services Industry -- Key Establishment Using
Integer Factorization Cryptography. 2007.
[ANS-X9.63] American National Standard X9.63-2002: Public Key
Cryptography for the Financial Services Industry:
Key Agreement and Key Transport Using Elliptic
Curve Cryptography.
[CAMELLIA] Moriai, S. and A. Kato, "Use of the Camellia
Encryption Algorithm in Cryptographic Message
Syntax (CMS)", RFC 3657, January 2004.
[CMS] Housley, R., "Cryptographic Message Syntax (CMS)",
RFC 5652, September 2009.
[CMSALGS] Housley, R., "Cryptographic Message Syntax (CMS)
Algorithms", RFC 3370, August 2002.
[FIPS-180-3] National Institute of Standards and Technology
(NIST). FIPS 180-3: Secure Hash Standard. October
2008.
[MSG] Ramsdell, B. and S. Turner, "Secure/Multipurpose
Internet Mail Extensions (S/MIME) Version 3.2
Message Specification", RFC 5751, January 2010.
[PROFILE] 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, May 2008.
[STDWORDS] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
Randall, et al. Standards Track [Page 10]
RFC 5990 Use of RSA-KEM in CMS September 2010
6.2. Informative References
[AES-WRAP-PAD] Housley, R. and M. Dworkin, "Advanced Encryption
Standard (AES) Key Wrap with Padding Algorithm",
RFC 5649, September 2009.
[CMS-OAEP] Housley, R., "Use of the RSAES-OAEP Key Transport
Algorithm in Cryptographic Message Syntax (CMS)",
RFC 3560, July 2003.
[NESSIE] NESSIE Consortium. Portfolio of Recommended
Cryptographic Primitives. February 2003.
http://www.cryptonessie.org/.
[NIST-GUIDELINE] National Institute of Standards and Technology.
Special Publication 800-57: Recommendation for Key
Management - Part 1: General (Revised). March
2007.
http://csrc.nist.gov/publications/index.html.
[NIST-SP800-56A] National Institute of Standards and Technology.
Special Publication 800-56A: Recommendation for
Pair-Wise Key Establishment Schemes Using Discrete
Logarithm Cryptography (Revised). March 2007.
http://csrc.nist.gov/publications/index.html.
[PKCS1] Jonsson, J. and B. Kaliski, "Public-Key
Cryptography Standards (PKCS) #1: RSA Cryptography
Specifications Version 2.1", RFC 3447, February
2003.
[RANDOM] Eastlake 3rd, D., Schiller, J., and S. Crocker,
"Randomness Requirements for Security", BCP 106,
RFC 4086, June 2005.
[SHOUP] Shoup, V. A Proposal for an ISO Standard for
Public Key Encryption. Version 2.1, December 20,
2001. http://eprint.iacr.org/2001/112.
Randall, et al. Standards Track [Page 11]
RFC 5990 Use of RSA-KEM in CMS September 2010
Appendix A. RSA-KEM Key Transport Algorithm
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.
With this type of algorithm, a sender encrypts the keying data using
the recipient's public key to obtain encrypted keying data. The
recipient decrypts the encrypted keying data using the recipient's
private key to recover the keying data.
A.1. Underlying Components
The algorithm has the following underlying components:
o KDF, a key derivation function, which derives keying data of a
specified length from a shared secret value;
o Wrap, a symmetric key-wrapping scheme, which encrypts keying Data
using a key-encrypting key.
In the following, kekLen denotes the length in bytes of the key-
encrypting key for the underlying symmetric key-wrapping scheme.
In this scheme, the length of the keying data to be transported MUST
be among the lengths supported by the underlying symmetric key-
wrapping scheme. (Both the AES and Camellia Key Wraps, for instance,
require the length of the keying data to be a multiple of 8 bytes,
and at least 16 bytes.) Usage and formatting of the keying data
(e.g., parity adjustment for Triple-DES keys) is outside the scope of
this algorithm. With some key derivation functions, it is possible
to include other information besides the shared secret value in the
input to the function. Also, with some symmetric key-wrapping
schemes, it is possible to associate a label with the keying data.
Such uses are outside the scope of this document, as they are not
directly supported by CMS.
A.2. Sender's Operations
Let (n,e) be the recipient's RSA public key (see [PKCS1] for
details), and let K be the keying data to be transported.
Let nLen denote the length in bytes of the modulus n, i.e., the least
integer such that 2^{8*nLen} > n.
Randall, et al. Standards Track [Page 12]
RFC 5990 Use of RSA-KEM in CMS September 2010
The sender performs the following operations:
1. Generate a random integer z between 0 and n-1 (see note), and
convert z to a byte string Z of length nLen, most significant byte
first:
z = RandomInteger (0, n-1)
Z = IntegerToString (z, nLen)
2. Encrypt the random integer z using the recipient's public key
(n,e), and convert the resulting integer c to a ciphertext C, a
byte string of length nLen:
c = z^e mod n
C = IntegerToString (c, nLen)
3. Derive a key-encrypting key KEK of length kekLen bytes from the
byte string Z using the underlying key derivation function:
KEK = KDF (Z, kekLen)
4. Wrap the keying data K with the key-encrypting key KEK using the
underlying key-wrapping scheme to obtain wrapped keying data WK:
WK = Wrap (KEK, K)
5. Concatenate the ciphertext C and the wrapped keying data WK to
obtain the encrypted keying data EK:
EK = C || WK
6. Output the encrypted keying data EK.
NOTE: The random integer z MUST be generated independently at random
for different encryption operations, whether for the same or
different recipients.
A.3. Recipient's Operations
Let (n,d) be the recipient's RSA private key (see [PKCS1]; other
private key formats are allowed), and let EK be the encrypted keying
data.
Let nLen denote the length in bytes of the modulus n.
Randall, et al. Standards Track [Page 13]
RFC 5990 Use of RSA-KEM in CMS September 2010
The recipient performs the following operations:
1. Separate the encrypted keying data EK into a ciphertext C of
length nLen bytes and wrapped keying data WK:
C || WK = EK
If the length of the encrypted keying data is less than nLen
bytes, output "decryption error", and stop.
2. Convert the ciphertext C to an integer c, most significant byte
first. Decrypt the integer c using the recipient's private key
(n,d) to recover an integer z (see note):
c = StringToInteger (C)
z = c^d mod n
If the integer c is not between 0 and n-1, output "decryption
error", and stop.
3. Convert the integer z to a byte string Z of length nLen, most
significant byte first (see note):
Z = IntegerToString (z, nLen)
4. Derive a key-encrypting key KEK of length kekLen bytes from the
byte string Z using the underlying key derivation function (see
note):
KEK = KDF (Z, kekLen)
5. Unwrap the wrapped keying data WK with the key-encrypting key KEK
using the underlying key-wrapping scheme to recover the keying
data K:
K = Unwrap (KEK, WK)
If the unwrapping operation outputs an error, output "decryption
error", and stop.
6. Output the keying data K.
NOTE: Implementations SHOULD NOT reveal information about the
integer z and the string Z, nor 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
Randall, et al. Standards Track [Page 14]
RFC 5990 Use of RSA-KEM in CMS September 2010
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 Key Transport Algorithm
is an extension of the syntax for the "generic hybrid cipher" in
ANS X9.44 [ANS-X9.44]. The syntax for the scheme is given in
Appendix B.1. The syntax for selected underlying components
including those mentioned above is given in Appendix B.2.
The following object identifier prefixes are used in the definitions
below:
is18033-2 OID ::= { iso(1) standard(0) is18033(18033) part2(2) }
nistAlgorithm OID ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
gov(101) csor(3) nistAlgorithm(4)
}
pkcs-1 OID ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1)
}
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) }
NullParms is a more descriptive synonym for NULL when an algorithm
identifier has null parameters:
NullParms ::= NULL
The material in this Appendix is based on ANS X9.44.
Randall, et al. Standards Track [Page 15]
RFC 5990 Use of RSA-KEM in CMS September 2010
B.1. RSA-KEM Key Transport Algorithm
The object identifier for the RSA-KEM Key Transport Algorithm is
id-rsa-kem, which is defined in this document as:
id-rsa-kem OID ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
pkcs-9(9) smime(16) alg(3) 14
}
When id-rsa-kem is used in an AlgorithmIdentifier, the parameters
MUST employ the GenericHybridParameters syntax. The parameters MUST
be absent when used in the SubjectPublicKeyInfo field. The syntax
for GenericHybridParameters is as follows:
GenericHybridParameters ::= {
kem KeyEncapsulationMechanism,
dem DataEncapsulationMechanism
}
The fields of type GenericHybridParameters have the following
meanings:
o kem identifies the underlying key encapsulation mechanism,
which in this case is also denoted as RSA-KEM.
The object identifier for RSA-KEM (as a key encapsulation
mechanism) is id-kem-rsa as:
id-kem-rsa OID ::= {
is18033-2 key-encapsulation-mechanism(2) rsa(4)
}
The associated parameters for id-kem-rsa have type
RsaKemParameters:
RsaKemParameters ::= {
keyDerivationFunction KeyDerivationFunction,
keyLength KeyLength
}
Randall, et al. Standards Track [Page 16]
RFC 5990 Use of RSA-KEM in CMS September 2010
The fields of type RsaKemParameters have the following
meanings:
* keyDerivationFunction identifies the underlying key
derivation function. For alignment with ANS X9.44, it MUST
be KDF2 or KDF3. However, other key derivation functions
MAY be used with CMS. Please see Appendix B.2.1 for the
syntax for KDF2 and KDF3.
KeyDerivationFunction ::=
AlgorithmIdentifier {{KDFAlgorithms}}
KDFAlgorithms ALGORITHM ::= {
kdf2 | kdf3,
... -- implementations may define other methods
}
* keyLength is the length in bytes of the key-encrypting key,
which depends on the underlying symmetric key-wrapping
scheme.
KeyLength ::= INTEGER (1..MAX)
o dem identifies the underlying data encapsulation mechanism.
For alignment with ANS X9.44, it MUST be an X9-approved
symmetric key-wrapping scheme. However, other symmetric key-
wrapping schemes MAY be used with CMS. Please see Appendix
B.2.2 for the syntax for the AES, Triple-DES, and Camellia Key
Wraps.
DataEncapsulationMechanism ::=
AlgorithmIdentifier {{DEMAlgorithms}}
DEMAlgorithms ALGORITHM ::= {
X9-SymmetricKeyWrappingSchemes,
Camellia-KeyWrappingSchemes,
... -- implementations may define other methods
}
X9-SymmetricKeyWrappingSchemes ALGORITHM ::= {
aes128-Wrap | aes192-Wrap | aes256-Wrap | tdes-Wrap,
... -- allows for future expansion
}
Camellia-KeyWrappingSchemes ALGORITHM ::= {
Camellia128-Wrap | Camellia192-Wrap | Camellia256-Wrap
}
Randall, et al. Standards Track [Page 17]
RFC 5990 Use of RSA-KEM in CMS September 2010
B.2. Selected Underlying Components
B.2.1. Key Derivation Functions
The object identifier for KDF2 (see [ANS-X9.44]) is:
id-kdf-kdf2 OID ::= { x9-44-components kdf2(1) }
The associated parameters identify the underlying hash function. For
alignment with ANS X9.44, the hash function MUST be an ASC
X9-approved hash function. However, other hash functions MAY be used
with CMS.
kdf2 ALGORITHM ::= { OID id-kdf-kdf2 PARMS KDF2-HashFunction }
KDF2-HashFunction ::= AlgorithmIdentifier {{KDF2-HashFunctions}}
KDF2-HashFunctions ALGORITHM ::= {
X9-HashFunctions,
... -- implementations may define other methods
}
X9-HashFunctions ALGORITHM ::= {
sha1 | sha224 | sha256 | sha384 | sha512,
... -- allows for future expansion
}
The object identifier for SHA-1 is:
id-sha1 OID ::= {
iso(1) identified-organization(3) oiw(14) secsig(3)
algorithms(2) sha1(26)
}
The object identifiers for SHA-224, SHA-256, SHA-384, and SHA-512 are
id-sha224 OID ::= { nistAlgorithm hashAlgs(2) sha224(4) }
id-sha256 OID ::= { nistAlgorithm hashAlgs(2) sha256(1) }
id-sha384 OID ::= { nistAlgorithm hashAlgs(2) sha384(2) }
id-sha512 OID ::= { nistAlgorithm hashAlgs(2) sha512(3) }
There has been some confusion over whether the various SHA object
identifiers have a NULL parameter, or no associated parameters. As
also discussed in [PKCS1], implementations SHOULD generate algorithm
identifiers without parameters and MUST accept algorithm identifiers
either without parameters, or with NULL parameters.
Randall, et al. Standards Track [Page 18]
RFC 5990 Use of RSA-KEM in CMS September 2010
sha1 ALGORITHM ::= { OID id-sha1 } -- NULLParms MUST be
sha224 ALGORITHM ::= { OID id-sha224 } -- accepted for these
sha256 ALGORITHM ::= { OID id-sha256 } -- OIDs
sha384 ALGORITHM ::= { OID id-sha384 } -- ""
sha512 ALGORITHM ::= { OID id-sha512 } -- ""
The object identifier for KDF3 (see [ANS-X9.44]) is:
id-kdf-kdf3 OID ::= { x9-44-components kdf3(2) }
The associated parameters identify the underlying hash function. For
alignment with the draft ANS X9.44, the hash function MUST be an ASC
X9-approved hash function. However, other hash functions MAY be used
with CMS.
kdf3 ALGORITHM ::= { OID id-kdf-kdf3 PARMS KDF3-HashFunction }
KDF3-HashFunction ::= AlgorithmIdentifier { KDF3-HashFunctions }
KDF3-HashFunctions ALGORITHM ::= {
X9-HashFunctions,
... -- implementations may define other methods
}
B.2.2. Symmetric Key-Wrapping Schemes
The object identifiers for the AES Key Wrap depend on the size of the
key-encrypting key. There are three object identifiers (see
[AES-WRAP]):
id-aes128-Wrap OID ::= { nistAlgorithm aes(1) aes128-Wrap(5) }
id-aes192-Wrap OID ::= { nistAlgorithm aes(1) aes192-Wrap(25) }
id-aes256-Wrap OID ::= { nistAlgorithm aes(1) aes256-Wrap(45) }
These object identifiers have no associated parameters.
aes128-Wrap ALGORITHM ::= { OID id-aes128-Wrap }
aes192-Wrap ALGORITHM ::= { OID id-aes192-Wrap }
aes256-Wrap ALGORITHM ::= { OID id-aes256-Wrap }
The object identifier for the Triple-DES Key Wrap (see
[3DES-WRAP]) is:
id-alg-CMS3DESwrap OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9)
smime(16) alg(3) 6
}
Randall, et al. Standards Track [Page 19]
RFC 5990 Use of RSA-KEM in CMS September 2010
This object identifier has a NULL parameter.
tdes-Wrap ALGORITHM ::=
{ OID id-alg-CMS3DESwrap PARMS NullParms }
NOTE: ASC X9 has not yet incorporated AES Key Wrap with Padding
[AES-WRAP-PAD] into ANS X9.44. When ASC X9.44 adds AES Key Wrap with
Padding, this document will also be updated.
The object identifiers for the Camellia Key Wrap depend on the size
of the key-encrypting key. There are three object identifiers:
id-camellia128-Wrap OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) 392 200011 61 security(1)
algorithm(1) key-wrap-algorithm(3)
camellia128-wrap(2) }
id-camellia192-Wrap OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) 392 200011 61 security(1)
algorithm(1) key-wrap-algorithm(3)
camellia192-wrap(3) }
id-camellia256-Wrap OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) 392 200011 61 security(1)
algorithm(1) key-wrap-algorithm(3)
camellia256-wrap(4) }
These object identifiers have no associated parameters.
camellia128-Wrap ALGORITHM ::= { OID id-camellia128-Wrap }
camellia192-Wrap ALGORITHM ::= { OID id-camellia192-Wrap }
camellia256-Wrap ALGORITHM ::= { OID id-camellia256-Wrap }
B.3. ASN.1 Module
CMS-RSA-KEM
{ iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
pkcs-9(9) smime(16) modules(0) cms-rsa-kem(21) }
DEFINITIONS ::=
BEGIN
-- EXPORTS ALL
-- IMPORTS None
-- Useful types and definitions
Randall, et al. Standards Track [Page 20]
RFC 5990 Use of RSA-KEM in CMS September 2010
OID ::= OBJECT IDENTIFIER -- alias
-- Unless otherwise stated, if an object identifier has associated
-- parameters (i.e., the PARMS element is specified), the
-- parameters field shall be included in algorithm identifier
-- values. The parameters field shall be omitted if and only if
-- the object identifier does not have associated parameters
-- (i.e., the PARMS element is omitted), unless otherwise stated.
ALGORITHM ::= CLASS {
&id OBJECT IDENTIFIER UNIQUE,
&Type OPTIONAL
}
WITH SYNTAX { OID &id [PARMS &Type] }
AlgorithmIdentifier { ALGORITHM:IOSet } ::= SEQUENCE {
algorithm ALGORITHM.&id( {IOSet} ),
parameters ALGORITHM.&Type( {IOSet}{@algorithm} ) OPTIONAL
}
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)
}
-- RSA-KEM Key Transport Algorithm
id-rsa-kem OID ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
pkcs-9(9) smime(16) alg(3) 14
}
Randall, et al. Standards Track [Page 21]
RFC 5990 Use of RSA-KEM in CMS September 2010
GenericHybridParameters ::= SEQUENCE {
kem KeyEncapsulationMechanism,
dem DataEncapsulationMechanism
}
KeyEncapsulationMechanism ::= AlgorithmIdentifier {{KEMAlgorithms}}
KEMAlgorithms ALGORITHM ::= { kem-rsa, ... }
kem-rsa ALGORITHM ::= { OID id-kem-rsa PARMS RsaKemParameters }
id-kem-rsa OID ::= {
is18033-2 key-encapsulation-mechanism(2) rsa(4)
}
RsaKemParameters ::= SEQUENCE {
keyDerivationFunction KeyDerivationFunction,
keyLength KeyLength
}
KeyDerivationFunction ::= AlgorithmIdentifier {{KDFAlgorithms}}
KDFAlgorithms ALGORITHM ::= {
kdf2 | kdf3,
... -- implementations may define other methods
}
KeyLength ::= INTEGER (1..MAX)
DataEncapsulationMechanism ::= AlgorithmIdentifier {{DEMAlgorithms}}
DEMAlgorithms ALGORITHM ::= {
X9-SymmetricKeyWrappingSchemes |
Camellia-KeyWrappingSchemes,
... -- implementations may define other methods
}
X9-SymmetricKeyWrappingSchemes ALGORITHM ::= {
aes128-Wrap | aes192-Wrap | aes256-Wrap | tdes-Wrap,
... -- allows for future expansion
}
X9-SymmetricKeyWrappingScheme ::=
AlgorithmIdentifier {{ X9-SymmetricKeyWrappingSchemes }}
Randall, et al. Standards Track [Page 22]
RFC 5990 Use of RSA-KEM in CMS September 2010
Camellia-KeyWrappingSchemes ALGORITHM ::= {
camellia128-Wrap | camellia192-Wrap | camellia256-Wrap,
... -- allows for future expansion
}
Camellia-KeyWrappingScheme ::=
AlgorithmIdentifier {{ Camellia-KeyWrappingSchemes }}
-- Key Derivation Functions
id-kdf-kdf2 OID ::= { x9-44-components kdf2(1) }
-- Base 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) }
kdf2 ALGORITHM ::= { OID id-kdf-kdf2 PARMS KDF2-HashFunction }
KDF2-HashFunction ::= AlgorithmIdentifier {{ KDF2-HashFunctions }}
KDF2-HashFunctions ALGORITHM ::= {
X9-HashFunctions,
... -- implementations may define other methods
}
id-kdf-kdf3 OID ::= { x9-44-components kdf3(2) }
kdf3 ALGORITHM ::= { OID id-kdf-kdf3 PARMS KDF3-HashFunction }
KDF3-HashFunction ::= AlgorithmIdentifier {{ KDF3-HashFunctions }}
KDF3-HashFunctions ALGORITHM ::= {
X9-HashFunctions,
... -- implementations may define other methods
}
-- Hash Functions
X9-HashFunctions ALGORITHM ::= {
sha1 | sha224 | sha256 | sha384 | sha512,
... -- allows for future expansion
}
Randall, et al. Standards Track [Page 23]
RFC 5990 Use of RSA-KEM in CMS September 2010
id-sha1 OID ::= {
iso(1) identified-organization(3) oiw(14) secsig(3)
algorithms(2) sha1(26)
}
id-sha224 OID ::= { nistAlgorithm hashAlgs(2) sha224(4) }
id-sha256 OID ::= { nistAlgorithm hashAlgs(2) sha256(1) }
id-sha384 OID ::= { nistAlgorithm hashAlgs(2) sha384(2) }
id-sha512 OID ::= { nistAlgorithm hashAlgs(2) sha512(3) }
sha1 ALGORITHM ::= { OID id-sha1 } -- NullParms MUST be
sha224 ALGORITHM ::= { OID id-sha224 } -- accepted for these
sha256 ALGORITHM ::= { OID id-sha256 } -- OIDs
sha384 ALGORITHM ::= { OID id-sha384 } -- ""
sha512 ALGORITHM ::= { OID id-sha512 } -- ""
-- Symmetric Key-Wrapping Schemes
id-aes128-Wrap OID ::= { nistAlgorithm aes(1) aes128-Wrap(5) }
id-aes192-Wrap OID ::= { nistAlgorithm aes(1) aes192-Wrap(25) }
id-aes256-Wrap OID ::= { nistAlgorithm aes(1) aes256-Wrap(45) }
aes128-Wrap ALGORITHM ::= { OID id-aes128-Wrap }
aes192-Wrap ALGORITHM ::= { OID id-aes192-Wrap }
aes256-Wrap ALGORITHM ::= { OID id-aes256-Wrap }
id-alg-CMS3DESwrap OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9)
smime(16) alg(3) 6
}
tdes-Wrap ALGORITHM ::= { OID id-alg-CMS3DESwrap PARMS NullParms }
id-camellia128-Wrap OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) 392 200011 61 security(1)
algorithm(1) key-wrap-algorithm(3)
camellia128-wrap(2) }
Randall, et al. Standards Track [Page 24]
RFC 5990 Use of RSA-KEM in CMS September 2010
id-camellia192-Wrap OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) 392 200011 61 security(1)
algorithm(1) key-wrap-algorithm(3)
camellia192-wrap(3) }
id-camellia256-Wrap OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) 392 200011 61 security(1)
algorithm(1) key-wrap-algorithm(3)
camellia256-wrap(4) }
camellia128-Wrap ALGORITHM ::= { OID id-camellia128-Wrap }
camellia192-Wrap ALGORITHM ::= { OID id-camellia192-Wrap }
camellia256-Wrap ALGORITHM ::= { OID id-camellia256-Wrap }
END
B.4. Examples
As an example, if the key derivation function is KDF3 based on
SHA-256 and the symmetric key-wrapping scheme is the AES Key Wrap
with a 128-bit KEK, the AlgorithmIdentifier for the RSA-KEM Key
Transport Algorithm will have the following value:
SEQUENCE {
id-rsa-kem, -- RSA-KEM cipher
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
}
}
}
Randall, et al. Standards Track [Page 25]
RFC 5990 Use of RSA-KEM in CMS September 2010
This AlgorithmIdentifier value has the following DER encoding:
30 47
06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e -- id-rsa-kem
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
The DER encodings for other typical sets of underlying components are
as follows:
o KDF3 based on SHA-384, AES Key Wrap with a 192-bit KEK
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
o KDF3 based on SHA-512, AES Key Wrap with a 256-bit KEK
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
o KDF2 based on SHA-1, Triple-DES Key Wrap with a 128-bit KEK (two-
key Triple-DES)
30 45 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e 30
36 30 25 06 07 28 81 8c 71 02 02 04 30 1a 30 15
06 0a 2b 81 05 10 86 48 09 2c 01 01 30 07 06 05
2b 0e 03 02 1a 02 01 10 30 0d 06 0b 2a 86 48 86
f7 0d 01 09 10 03 06
Randall, et al. Standards Track [Page 26]
RFC 5990 Use of RSA-KEM in CMS September 2010
Authors' Addresses
James Randall
Randall Consulting
55 Sandpiper Drive
Dover, NH 03820
USA
EMail: jdrandall@comcast.net
Burt Kaliski
EMC
176 South Street
Hopkinton, MA 01748
USA
EMail: burt.kaliski@emc.com
John Brainard
RSA, The Security Division of EMC
174 Middlesex Turnpike
Bedford, MA 01730
USA
EMail: jbrainard@rsa.com
Sean Turner
IECA, Inc.
3057 Nutley Street, Suite 106
Fairfax, VA 22031
USA
EMail: turners@ieca.com
Randall, et al. Standards Track [Page 27]