S/MIME Working Group B. Kaliski
Internet Draft RSA Laboratories
Document: draft-ietf-smime-cms-rsa-kem-00.txt May 2003
Category: Standards
Use of the RSA-KEM Key Transport Algorithm in CMS
Status of this Memo
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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. This document specifies the
conventions for using the RSA-KEM Key Transport Algorithm with the
Cryptographic Message Syntax (CMS).
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].
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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
KD.
5. Output c and KD as the encrypted keying data.
This different approach provides higher security assurance because
the input to the underlying RSA operation is random and independent
of the message, and the key-encrypting key KEK is derived from it in
a strong way. As a result, the algorithm enjoys a "tight" security
proof in the random oracle model. It is also architecturally
convenient because the public-key operations are separate from the
symmetric operations on the keying data. One 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 including ANSI X9.44 [ANSI-X9.44]
and ISO/IEC 18033-2 [ISO-IEC-18033-2]. It has also been recommended
by the NESSIE project [NESSIE]. Although the other standards are
still in development, the algorithm is fairly stable across the
drafts. For completeness, a specification of the algorithm is given
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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 a result of research by Victor Shoup leading to the
development of the ISO/IEC 18033-2 standard [SHOUP].
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.
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 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.
2.1 Underlying Components
A CMS implementation that supports the RSA-KEM Key Transport
Algorithm MUST support at least the following underlying components:
* For the key derivation function, KDF2 (see [ANSI-X9.44][IEEE-
P1363a]) based on SHA-1 (see [NIST-SHA2]) (this function is
also specified as the key derivation function in [ANSI-X9.63])
* 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 based on SHA-256 (see
[NIST-SHA2]), and the Triple-DES Key Wrap (see [3DES-WRAP]). It MAY
support other underlying components.
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:
* keyEncryptionAlgorithm.algorithm MUST be id-kts2-basic (see
Appendix B)
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* keyEncryptionAlgorithm.parameters MUST be a value of type
KTS2-Parms (see Appendix B)
* encryptedKey MUST be the encrypted keying data output by the
algorithm (see Appendix A)
2.3 Certificate Conventions
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].
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-kts2-basic object
identifier (see Appendix B) where the KTS2-Params value indicates
the underlying components with which the algorithm is to be
employed.
[[matching rules to be added]]
2.4 SMIMECapabilities Attribute Conventions
[[to be added]]
3. Security Considerations
The security of the RSA-KEM Key Transport Algorithm described in
this document has been 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 [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 [NIST-
GUIDELINES]. For brevity, the first three levels are mentioned here:
* 80-bit security. The RSA key size SHOULD be at least 1024
bits, the hash function underlying KDF2 SHOULD be SHA-1 or
above, and the symmetric key-wrapping scheme SHOULD be AES Key
Wrap or Triple-DES Key Wrap.
* 112-bit security. The RSA key size SHOULD be at least 2048
bits, the hash function underlying KDF2 SHOULD be SHA-224 or
above, and the symmetric key-wrapping scheme SHOULD be AES Key
Wrap or Triple-DES Key Wrap.
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* 128-bit security. The RSA key size SHOULD be at least 3072
bits, the hash function underlying KDF2 SHOULD be SHA-256 or
above, and the symmetric key-wrapping scheme SHOULD be AES Key
Wrap.
Note that the AES Key Wrap MAY be used at all three of these levels;
the use of AES does not require a 128-bit security level for other
components.
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 it practical to,
unless analysis specifically indicates that the information would
not be useful.
Parties MAY wish to formalize the assurance that one another's
implementations are correct through implementation validation, e.g.
NIST's Cryptographic Module Validation Program (CMVP).
4. References
4.1 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.
ANSI-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.
CMS Housley, R. Cryptographic Message Syntax. RFC
3369. August 2002.
CMSALGS Housley, R. Cryptographic Message Syntax (CMS)
Algorithms. RFC 3370. August 2002.
NIST-SHA2 National Institute of Standards and Technology
(NIST). FIPS 180-2: Secure Hash Standard. August
2002.
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STDWORDS Bradner, S. Key Words for Use in RFCs to Indicate
Requirement Levels. RFC 2119. March 1997.
4.2 Informative References
ANSI-X9.44 ANSI X9F1 Working Group. ANSI X9.44: Public Key
Cryptography for the Financial Services Industry -
- Key Establishment Using Integer Factorization
Cryptography. Draft D4.1, April 1, 2003.
CMS-OAEP Housley, R. Use of the RSAES-OAEP Key Transport
Algorithm in CMS. Internet Draft . December 2002.
IEEE-P1363a IEEE P1363 Working Group. IEEE P1363a: Standard
Specifications for Public Key Cryptography:
Additional Techniques. Draft D12, May 12, 2003.
Available via http://grouper.ieee.org/groups/1363.
ISO-IEC-18033-2 ISO/IEC 18033-2: Information technology --
Security techniques -- Encryption algorithms --
Part 2: Asymmetric Ciphers. Committee Draft,
December 18, 2002.
NESSIE NESSIE Consortium. Portfolio of Recommended
Cryptographic Primitives. February 27, 2003.
Available via http://www.cryptonessie.org/.
NIST-GUIDELINES National Institute of Standards and Technology.
Special Publication 800-57: Recommendation for Key
Management. Part 1: General Guideline. Draft,
January 2003. Available via
http://csrc.nist.gov/CryptoToolkit/tkkeymgmt.html.
NIST-SCHEMES National Institute of Standards and Technology.
Special Publication 800-56: Recommendation on Key
Establishment Schemes. Draft 2.0, January 2003.
Available via
http://csrc.nist.gov/CryptoToolkit/tkkeymgmt.html.
PKCS1 Jonsson, J. and B. Kaliski. PKCS #1: RSA
Cryptography Specifications Version 2.1. RFC 3447.
February 2003.
RANDOM Eastlake, D., S. Crocker, and J. Schiller.
Randomness Recommendations for Security. RFC 1750.
December 1994.
SHOUP Shoup, V. A Proposal for an ISO Standard for
Public Key Encryption. Version 2.1, December 20,
2001. Available via http://www.shoup.net/papers/.
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5. IANA Considerations
Within the CMS, algorithms are identified by object identifiers
(OIDs). All of the OIDs used in this document were assigned in
Public-Key Cryptography Standards (PKCS) documents, Accredited
Standards Committee (ASC) X9 documents, or by the National Institute
of Standards and Technology (NIST). No further action by the IANA is
necessary for this document or any anticipated updates.
6. Acknowledgments
This document is one part of a strategy to align algorithm standards
produced by ASC X9, ISO/IEC JTC1 SC27, NIST, and the IETF. I would
like to thank the members of the ANSI X9F1 working group for their
contributions to drafts of ANSI X9.44 which led to this
specification. My thanks as well to Russ Housley as well for his
guidance and encouragement.
7. Author Address
Burt Kaliski
RSA Laboratories
174 Middlesex Turnpike
Bedford, MA 01730
USA
bkaliski@rsasecurity.com
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:
* KDF, a key derivation function, which derives keying data of a
specified length from a shared secret value
* 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
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wrapping scheme. (The AES Key Wrap, for instance, requires 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.
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 using the underlying key wrapping
scheme with the key-encrypting key KEK 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
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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.
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 using the underlying key
wrapping scheme with the key-encrypting key KEK to recover the
keying data K:
K = Unwrap (KEK, WK)
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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
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 intemediate 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 a special case of the syntax for Key Transport Scheme 2 (KTS2) in
the draft ANSI X9.44 [ANSI-X9.44]. The syntax for the scheme is
given in Section B.1. The syntax for selected underlying components
including those mentioned above is given in B.2.
The following object identifier prefixes are used in the definitions
below:
x9-44 OID ::= {
iso(1) identified-organization(3) tc68(133) country(16)
x9(840) x9Standards(9) x9-44(44)
}
pkcs-1 OID ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1)
}
nistAlgorithm OID ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
gov(101) csor(3) nistAlgorithm(4)
}
The material in this Appendix is based on a draft standard and is
SUBJECT TO CHANGE as that standard is developed.
B.1 RSA-KEM Key Transport Algorithm
The object identifier for the RSA-KEM Key Transport Algorithm is the
same as for the basic KTS2 scheme in the draft ANSI X9.44, id-kts2-
basic, which is defined in the draft as
id-kts2-basic OID ::= { x9-44 schemes(2) kts2-basic(7) }
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The associated parameters for id-kts2-basic have type KTS2-Parms:
KTS2-Parms ::= SEQUENCE {
kas [0] KTS2-KeyAgreementScheme,
kws [1] KTS2-SymmetricKeyWrappingScheme,
labelMethod [2] KTS2-LabelMethod
}
The fields of type KTS2-Parms have the following meanings:
* kas identifies the underlying key agreement scheme. For the
RSA-KEM Key Transport Algorithm, the scheme is the basic Key
Agreement Scheme 1 (KAS1) from the draft ANSI X9.44.
The object identifier for the basic KAS1 is id-kas1-basic,
which is defined in the draft ANSI X9.44 as
id-kas1-basic OID ::= { x9-44 schemes(2) kas1-basic(1) }
The associated parameters for id-kas1-basic have type KAS1-
Parms:
KAS1-Parms ::= SEQUENCE {
sves [0] KAS1-SecretValueEncapsulationScheme,
kdf [1] KAS1-KeyDerivationFunction,
otherInfoMethod [2] KAS1-OtherInfoMethod
}
The fields of type KAS1-Parms have the following meanings:
* sves identifies the underlying secret-value
encapsulation mechanism. (In the draft ANSI X9.44, the
term "Secret Value Encapsulation Scheme" refers to the
first _two_ steps of the RSA-KEM Key Transport
Algorithm, which are separated from the key derivation
function for architectural reasons.) For the RSA-KEM Key
Transport Algorithm, the mechanism is RSASVES1 from the
draft ANSI X9.44.
The object identifier for RSASVES1 is id-rsasves1, which
is defined in the draft ANSI X9.44 as
id-rsasves1 OID ::= {
x9-44 components(1) rsasves1(2)
}
This object identifier has no associated parameters.
* kdf identifies the underlying key derivation function.
For alignment with the draft ANSI X9.44, it MUST be
KDF2. However, other key derivation functions MAY be
used with CMS. Please see B.2.1 for the syntax for KDF2.
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KAS1-KeyDerivationFunction ::= AlgorithmIdentifier
* otherInfoMethod specifies the method for formatting
other information to be included in the input to the key
derivation function. For this version of the document,
the method MUST be the "specified other information"
method.
KAS1-OtherInfoMethod ::= AlgorithmIdentifier
The object identifier for the "specified other
information" method is id-specifiedOtherInfo:
id-specifiedOtherInfo OID ::= [[to be defined]]
The associated parameters for id-specifiedOtherInfo have
type SpecifiedOtherInfo:
SpecifiedOtherInfo ::= OCTET STRING SIZE((0..MAX))
For this version of the document, the value of the other
information MUST be the empty string.
* kws identifies the underlying symmetric key-wrapping scheme.
For alignment with the draft ANSI X9.44, it MUST be an X9-
approved symmetric key-wrapping scheme. (See Note.) However,
other schemes MAY be used with CMS. Please see B.2.2 for the
syntax for the AES and Triple-DES Key Wraps.
KTS2-SymmetricKeyWrappingScheme ::= AlgorithmIdentifier
* labelMethod specifies the method for formatting a label to be
associated with the keying data. For this version of the
document, the method MUST be the "specified label" method.
KTS2-LabelMethod ::= AlgorithmIdentifier
The object identifier for the "specified label" method is id-
specifiedLabel, which is defined in the draft ANSI X9.44 as
id-specifiedLabel OID ::= { pkcs-1 specifiedLabel(9) }
The associated parameters for id-specifiedLabel have type
SpecifiedLabel:
SpecifiedLabel ::= OCTET STRING SIZE((0..MAX))
For this version of the document, the value of the label MUST
be the empty string.
NOTE: As of this writing, the AES Key Wrap and the Triple-DES Key
Wrap are in the process of being approved by X9.
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DISCUSSION TOPIC: In NIST's key establishment schemes recommendation
[NIST-SCHEMES], the parties' names are included in the "other
information" for key derivation. Should they be included here as
well?
B.2 Selected Underlying Components
B.2.1 Key Derivation Functions
The object identifier for KDF2 (see [ANSI-X9.44]) is
id-kdf2 OID ::= { x9-44 components(1) kdf2(1) }
The associated parameters identify the underlying hash function. For
alignment with the draft ANSI X9.44, the hash function MUST be an
X9-approved hash function. (See Note.) However, other hash functions
MAY be used with CMS.
KDF2-Parms ::= AlgorithmIdentifier
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-256, SHA-384 and SHA-512 are
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.
NOTE: As of this writing, only SHA-1 is an X9-approved hash
function; SHA-224 and above are in the process of being approved.
The object identifier for SHA-224 has not yet been assigned.
B.2.2 Symmetric Key Wrapping Schemes
The object identifier for the AES Key Wrap depends 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) }
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These object identifiers have no associated parameters.
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
}
This object identifier has a NULL parameter.
B.3 Example
As an example, if the key derivation function is KDF2 based on SHA-1
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-kts2-basic, -- basic KTS2
SEQUENCE { -- KTS2-Parms
[0] SEQUENCE { -- key agreement scheme
id-kas1-basic, -- basic KAS1
SEQUENCE { -- KAS1-Parms
[0] SEQUENCE { -- secret value encapsulation scheme
id-rsasves1 -- RSASVES1; no parameters
},
[1] SEQUENCE { -- key derivation function
id-kdf2, -- KDF2
SEQUENCE { -- KDF2-Parms
id-sha1 -- no parameters (preferred)
}
},
[2] SEQUENCE { -- other information method
id-specifiedOtherInfo, -- specified other info.
''H -- empty string
}
}
},
[1] SEQUENCE { -- symmetric key wrapping scheme
id-aes128-Wrap -- AES-128 Wrap; no parameters
},
[2] SEQUENCE { -- label method
id-specifiedLabel, -- specified label
''H -- empty string
}
}
}
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