RFC 8017
PKCS #1: RSA Cryptography Specifications Version 2.2
Appendix A. ASN.1 Syntax
A.1. RSA Key Representation
This section defines ASN.1 object identifiers for RSA public and private keys and defines the types RSAPublicKey and RSAPrivateKey. The intended application of these definitions includes X.509 certificates, PKCS #8 [RFC5958], and PKCS #12 [RFC7292]. The object identifier rsaEncryption identifies RSA public and private keys as defined in Appendices A.1.1 and A.1.2. The parameters field has associated with this OID in a value of type AlgorithmIdentifier SHALL have a value of type NULL. rsaEncryption OBJECT IDENTIFIER ::= { pkcs-1 1 } The definitions in this section have been extended to support multi- prime RSA, but they are backward compatible with previous versions.A.1.1. RSA Public Key Syntax
An RSA public key should be represented with the ASN.1 type RSAPublicKey: RSAPublicKey ::= SEQUENCE { modulus INTEGER, -- n publicExponent INTEGER -- e } The fields of type RSAPublicKey have the following meanings: o modulus is the RSA modulus n. o publicExponent is the RSA public exponent e.
A.1.2. RSA Private Key Syntax
An RSA private key should be represented with the ASN.1 type RSAPrivateKey: RSAPrivateKey ::= SEQUENCE { version Version, modulus INTEGER, -- n publicExponent INTEGER, -- e privateExponent INTEGER, -- d prime1 INTEGER, -- p prime2 INTEGER, -- q exponent1 INTEGER, -- d mod (p-1) exponent2 INTEGER, -- d mod (q-1) coefficient INTEGER, -- (inverse of q) mod p otherPrimeInfos OtherPrimeInfos OPTIONAL } The fields of type RSAPrivateKey have the following meanings: o version is the version number, for compatibility with future revisions of this document. It SHALL be 0 for this version of the document, unless multi-prime is used; in which case, it SHALL be 1. Version ::= INTEGER { two-prime(0), multi(1) } (CONSTRAINED BY {-- version must be multi if otherPrimeInfos present --}) o modulus is the RSA modulus n. o publicExponent is the RSA public exponent e. o privateExponent is the RSA private exponent d. o prime1 is the prime factor p of n. o prime2 is the prime factor q of n. o exponent1 is d mod (p - 1). o exponent2 is d mod (q - 1). o coefficient is the CRT coefficient q^(-1) mod p.
o otherPrimeInfos contains the information for the additional primes
r_3, ..., r_u, in order. It SHALL be omitted if version is 0 and
SHALL contain at least one instance of OtherPrimeInfo if version
is 1.
OtherPrimeInfos ::= SEQUENCE SIZE(1..MAX) OF OtherPrimeInfo
OtherPrimeInfo ::= SEQUENCE {
prime INTEGER, -- ri
exponent INTEGER, -- di
coefficient INTEGER -- ti
}
The fields of type OtherPrimeInfo have the following meanings:
o prime is a prime factor r_i of n, where i >= 3.
o exponent is d_i = d mod (r_i - 1).
o coefficient is the CRT coefficient t_i = (r_1 * r_2 * ... *
r_(i-1))^(-1) mod r_i.
Note: It is important to protect the RSA private key against both
disclosure and modification. Techniques for such protection are
outside the scope of this document. Methods for storing and
distributing private keys and other cryptographic data are described
in PKCS #12 and #15.
A.2. Scheme Identification
This section defines object identifiers for the encryption and signature schemes. The schemes compatible with PKCS #1 v1.5 have the same definitions as in PKCS #1 v1.5. The intended application of these definitions includes X.509 certificates and PKCS #7. Here are type identifier definitions for the PKCS #1 OIDs: PKCS1Algorithms ALGORITHM-IDENTIFIER ::= { { OID rsaEncryption PARAMETERS NULL } | { OID md2WithRSAEncryption PARAMETERS NULL } | { OID md5WithRSAEncryption PARAMETERS NULL } | { OID sha1WithRSAEncryption PARAMETERS NULL } | { OID sha224WithRSAEncryption PARAMETERS NULL } | { OID sha256WithRSAEncryption PARAMETERS NULL } | { OID sha384WithRSAEncryption PARAMETERS NULL } | { OID sha512WithRSAEncryption PARAMETERS NULL } | { OID sha512-224WithRSAEncryption PARAMETERS NULL } | { OID sha512-256WithRSAEncryption PARAMETERS NULL } | { OID id-RSAES-OAEP PARAMETERS RSAES-OAEP-params } | PKCS1PSourceAlgorithms | { OID id-RSASSA-PSS PARAMETERS RSASSA-PSS-params }, ... -- Allows for future expansion -- }A.2.1. RSAES-OAEP
The object identifier id-RSAES-OAEP identifies the RSAES-OAEP encryption scheme. id-RSAES-OAEP OBJECT IDENTIFIER ::= { pkcs-1 7 } The parameters field associated with this OID in a value of type AlgorithmIdentifier SHALL have a value of type RSAES-OAEP-params: RSAES-OAEP-params ::= SEQUENCE { hashAlgorithm [0] HashAlgorithm DEFAULT sha1, maskGenAlgorithm [1] MaskGenAlgorithm DEFAULT mgf1SHA1, pSourceAlgorithm [2] PSourceAlgorithm DEFAULT pSpecifiedEmpty } The fields of type RSAES-OAEP-params have the following meanings: o hashAlgorithm identifies the hash function. It SHALL be an algorithm ID with an OID in the set OAEP-PSSDigestAlgorithms. For a discussion of supported hash functions, see Appendix B.1.
HashAlgorithm ::= AlgorithmIdentifier {
{OAEP-PSSDigestAlgorithms}
}
OAEP-PSSDigestAlgorithms ALGORITHM-IDENTIFIER ::= {
{ OID id-sha1 PARAMETERS NULL }|
{ OID id-sha224 PARAMETERS NULL }|
{ OID id-sha256 PARAMETERS NULL }|
{ OID id-sha384 PARAMETERS NULL }|
{ OID id-sha512 PARAMETERS NULL }|
{ OID id-sha512-224 PARAMETERS NULL }|
{ OID id-sha512-256 PARAMETERS NULL },
... -- Allows for future expansion --
}
The default hash function is SHA-1:
sha1 HashAlgorithm ::= {
algorithm id-sha1,
parameters SHA1Parameters : NULL
}
SHA1Parameters ::= NULL
o maskGenAlgorithm identifies the mask generation function. It
SHALL be an algorithm ID with an OID in the set
PKCS1MGFAlgorithms, which for this version SHALL consist of
id-mgf1, identifying the MGF1 mask generation function (see
Appendix B.2.1). The parameters field associated with id-mgf1
SHALL be an algorithm ID with an OID in the set
OAEP-PSSDigestAlgorithms, identifying the hash function on which
MGF1 is based.
MaskGenAlgorithm ::= AlgorithmIdentifier { {PKCS1MGFAlgorithms} }
PKCS1MGFAlgorithms ALGORITHM-IDENTIFIER ::= {
{ OID id-mgf1 PARAMETERS HashAlgorithm },
... -- Allows for future expansion --
}
o The default mask generation function is MGF1 with SHA-1:
mgf1SHA1 MaskGenAlgorithm ::= {
algorithm id-mgf1,
parameters HashAlgorithm : sha1
}
o pSourceAlgorithm identifies the source (and possibly the value) of
the label L. It SHALL be an algorithm ID with an OID in the set
PKCS1PSourceAlgorithms, which for this version SHALL consist of
id-pSpecified, indicating that the label is specified explicitly.
The parameters field associated with id-pSpecified SHALL have a
value of type OCTET STRING, containing the label. In previous
versions of this specification, the term "encoding parameters" was
used rather than "label", hence the name of the type below.
PSourceAlgorithm ::= AlgorithmIdentifier {
{PKCS1PSourceAlgorithms}
}
PKCS1PSourceAlgorithms ALGORITHM-IDENTIFIER ::= {
{ OID id-pSpecified PARAMETERS EncodingParameters },
... -- Allows for future expansion --
}
id-pSpecified OBJECT IDENTIFIER ::= { pkcs-1 9 }
EncodingParameters ::= OCTET STRING(SIZE(0..MAX))
o The default label is an empty string (so that lHash will contain
the hash of the empty string):
pSpecifiedEmpty PSourceAlgorithm ::= {
algorithm id-pSpecified,
parameters EncodingParameters : emptyString
}
emptyString EncodingParameters ::= ''H
If all of the default values of the fields in RSAES-OAEP-params are
used, then the algorithm identifier will have the following value:
rSAES-OAEP-Default-Identifier RSAES-AlgorithmIdentifier ::= {
algorithm id-RSAES-OAEP,
parameters RSAES-OAEP-params : {
hashAlgorithm sha1,
maskGenAlgorithm mgf1SHA1,
pSourceAlgorithm pSpecifiedEmpty
}
}
RSAES-AlgorithmIdentifier ::= AlgorithmIdentifier {
{PKCS1Algorithms}
}
A.2.2. RSAES-PKCS-v1_5
The object identifier rsaEncryption (see Appendix A.1) identifies the RSAES-PKCS1-v1_5 encryption scheme. The parameters field associated with this OID in a value of type AlgorithmIdentifier SHALL have a value of type NULL. This is the same as in PKCS #1 v1.5. rsaEncryption OBJECT IDENTIFIER ::= { pkcs-1 1 }A.2.3. RSASSA-PSS
The object identifier id-RSASSA-PSS identifies the RSASSA-PSS encryption scheme. id-RSASSA-PSS OBJECT IDENTIFIER ::= { pkcs-1 10 } The parameters field associated with this OID in a value of type AlgorithmIdentifier SHALL have a value of type RSASSA-PSS-params: RSASSA-PSS-params ::= SEQUENCE { hashAlgorithm [0] HashAlgorithm DEFAULT sha1, maskGenAlgorithm [1] MaskGenAlgorithm DEFAULT mgf1SHA1, saltLength [2] INTEGER DEFAULT 20, trailerField [3] TrailerField DEFAULT trailerFieldBC } The fields of type RSASSA-PSS-params have the following meanings: o hashAlgorithm identifies the hash function. It SHALL be an algorithm ID with an OID in the set OAEP-PSSDigestAlgorithms (see Appendix A.2.1). The default hash function is SHA-1. o maskGenAlgorithm identifies the mask generation function. It SHALL be an algorithm ID with an OID in the set PKCS1MGFAlgorithms (see Appendix A.2.1). The default mask generation function is MGF1 with SHA-1. For MGF1 (and more generally, for other mask generation functions based on a hash function), it is RECOMMENDED that the underlying hash function be the same as the one identified by hashAlgorithm; see Note 2 in Section 9.1 for further comments. o saltLength is the octet length of the salt. It SHALL be an integer. For a given hashAlgorithm, the default value of saltLength is the octet length of the hash value. Unlike the other fields of type RSASSA-PSS-params, saltLength does not need to be fixed for a given RSA key pair.
o trailerField is the trailer field number, for compatibility with
IEEE 1363a [IEEE1363A]. It SHALL be 1 for this version of the
document, which represents the trailer field with hexadecimal
value 0xbc. Other trailer fields (including the trailer field
HashID || 0xcc in IEEE 1363a) are not supported in this document.
TrailerField ::= INTEGER { trailerFieldBC(1) }
If the default values of the hashAlgorithm, maskGenAlgorithm, and
trailerField fields of RSASSA-PSS-params are used, then the algorithm
identifier will have the following value:
rSASSA-PSS-Default-Identifier RSASSA-AlgorithmIdentifier ::= {
algorithm id-RSASSA-PSS,
parameters RSASSA-PSS-params : {
hashAlgorithm sha1,
maskGenAlgorithm mgf1SHA1,
saltLength 20,
trailerField trailerFieldBC
}
}
RSASSA-AlgorithmIdentifier ::= AlgorithmIdentifier {
{PKCS1Algorithms}
}
Note: In some applications, the hash function underlying a signature
scheme is identified separately from the rest of the operations in
the signature scheme. For instance, in PKCS #7 [RFC2315], a hash
function identifier is placed before the message and a "digest
encryption" algorithm identifier (indicating the rest of the
operations) is carried with the signature. In order for PKCS #7 to
support the RSASSA-PSS signature scheme, an object identifier would
need to be defined for the operations in RSASSA-PSS after the hash
function (analogous to the RSAEncryption OID for the
RSASSA-PKCS1-v1_5 scheme). S/MIME Cryptographic Message Syntax (CMS)
[RFC5652] takes a different approach. Although a hash function
identifier is placed before the message, an algorithm identifier for
the full signature scheme may be carried with a CMS signature (this
is done for DSA signatures). Following this convention, the
id-RSASSA-PSS OID can be used to identify RSASSA-PSS signatures in
CMS. Since CMS is considered the successor to PKCS #7 and new
developments such as the addition of support for RSASSA-PSS will be
pursued with respect to CMS rather than PKCS #7, an OID for the "rest
of" RSASSA-PSS is not defined in this version of PKCS #1.
A.2.4. RSASSA-PKCS-v1_5
The object identifier for RSASSA-PKCS1-v1_5 SHALL be one of the following. The choice of OID depends on the choice of hash algorithm: MD2, MD5, SHA-1, SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, or SHA-512/256. Note that if either MD2 or MD5 is used, then the OID is just as in PKCS #1 v1.5. For each OID, the parameters field associated with this OID in a value of type AlgorithmIdentifier SHALL have a value of type NULL. The OID should be chosen in accordance with the following table: Hash algorithm OID ------------------------------------------------------------ MD2 md2WithRSAEncryption ::= {pkcs-1 2} MD5 md5WithRSAEncryption ::= {pkcs-1 4} SHA-1 sha1WithRSAEncryption ::= {pkcs-1 5} SHA-256 sha224WithRSAEncryption ::= {pkcs-1 14} SHA-256 sha256WithRSAEncryption ::= {pkcs-1 11} SHA-384 sha384WithRSAEncryption ::= {pkcs-1 12} SHA-512 sha512WithRSAEncryption ::= {pkcs-1 13} SHA-512/224 sha512-224WithRSAEncryption ::= {pkcs-1 15} SHA-512/256 sha512-256WithRSAEncryption ::= {pkcs-1 16} The EMSA-PKCS1-v1_5 encoding method includes an ASN.1 value of type DigestInfo, where the type DigestInfo has the syntax DigestInfo ::= SEQUENCE { digestAlgorithm DigestAlgorithm, digest OCTET STRING } digestAlgorithm identifies the hash function and SHALL be an algorithm ID with an OID in the set PKCS1-v1-5DigestAlgorithms. For a discussion of supported hash functions, see Appendix B.1.
DigestAlgorithm ::= AlgorithmIdentifier {
{PKCS1-v1-5DigestAlgorithms}
}
PKCS1-v1-5DigestAlgorithms ALGORITHM-IDENTIFIER ::= {
{ OID id-md2 PARAMETERS NULL }|
{ OID id-md5 PARAMETERS NULL }|
{ OID id-sha1 PARAMETERS NULL }|
{ OID id-sha224 PARAMETERS NULL }|
{ OID id-sha256 PARAMETERS NULL }|
{ OID id-sha384 PARAMETERS NULL }|
{ OID id-sha512 PARAMETERS NULL }|
{ OID id-sha512-224 PARAMETERS NULL }|
{ OID id-sha512-256 PARAMETERS NULL }
}
Appendix B. Supporting Techniques
This section gives several examples of underlying functions
supporting the encryption schemes in Section 7 and the encoding
methods in Section 9. A range of techniques is given here to allow
compatibility with existing applications as well as migration to new
techniques. While these supporting techniques are appropriate for
applications to implement, none of them is required to be
implemented. It is expected that profiles for PKCS #1 v2.2 will be
developed that specify particular supporting techniques.
This section also gives object identifiers for the supporting
techniques.
B.1. Hash Functions
Hash functions are used in the operations contained in Sections 7 and
9. Hash functions are deterministic, meaning that the output is
completely determined by the input. Hash functions take octet
strings of variable length and generate fixed-length octet strings.
The hash functions used in the operations contained in Sections 7 and
9 should generally be collision-resistant. This means that it is
infeasible to find two distinct inputs to the hash function that
produce the same output. A collision-resistant hash function also
has the desirable property of being one-way; this means that given an
output, it is infeasible to find an input whose hash is the specified
output. In addition to the requirements, the hash function should
yield a mask generation function (Appendix B.2) with pseudorandom
output.
Nine hash functions are given as examples for the encoding methods in this document: MD2 [RFC1319] (which was retired by [RFC6149]), MD5 [RFC1321], SHA-1, SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, and SHA-512/256 [SHS]. For the RSAES-OAEP encryption scheme and EMSA-PSS encoding method, only SHA-1, SHA-224, SHA-256, SHA-384, SHA- 512, SHA-512/224, and SHA-512/256 are RECOMMENDED. For the EMSA- PKCS1-v1_5 encoding method, SHA-224, SHA-256, SHA-384, SHA-512, SHA- 512/224, and SHA-512/256 are RECOMMENDED for new applications. MD2, MD5, and SHA-1 are recommended only for compatibility with existing applications based on PKCS #1 v1.5. The object identifiers id-md2, id-md5, id-sha1, id-sha224, id-sha256, id-sha384, id-sha512, id-sha512/224, and id-sha512/256 identify the respective hash functions: id-md2 OBJECT IDENTIFIER ::= { iso (1) member-body (2) us (840) rsadsi (113549) digestAlgorithm (2) 2 } id-md5 OBJECT IDENTIFIER ::= { iso (1) member-body (2) us (840) rsadsi (113549) digestAlgorithm (2) 5 } id-sha1 OBJECT IDENTIFIER ::= { iso(1) identified-organization(3) oiw(14) secsig(3) algorithms(2) 26 } id-sha224 OBJECT IDENTIFIER ::= { joint-iso-itu-t (2) country (16) us (840) organization (1) gov (101) csor (3) nistalgorithm (4) hashalgs (2) 4 } id-sha256 OBJECT IDENTIFIER ::= { joint-iso-itu-t (2) country (16) us (840) organization (1) gov (101) csor (3) nistalgorithm (4) hashalgs (2) 1 } id-sha384 OBJECT IDENTIFIER ::= { joint-iso-itu-t (2) country (16) us (840) organization (1) gov (101) csor (3) nistalgorithm (4) hashalgs (2) 2 }
id-sha512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t (2) country (16) us (840) organization (1)
gov (101) csor (3) nistalgorithm (4) hashalgs (2) 3
}
id-sha512-224 OBJECT IDENTIFIER ::= {
joint-iso-itu-t (2) country (16) us (840) organization (1)
gov (101) csor (3) nistalgorithm (4) hashalgs (2) 5
}
id-sha512-256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t (2) country (16) us (840) organization (1)
gov (101) csor (3) nistalgorithm (4) hashalgs (2) 6
}
The parameters field associated with these OIDs in a value of type
AlgorithmIdentifier SHALL have a value of type NULL.
The parameters field associated with id-md2 and id-md5 in a value of
type AlgorithmIdentifier shall have a value of type NULL.
The parameters field associated with id-sha1, id-sha224, id-sha256,
id-sha384, id-sha512, id-sha512/224, and id-sha512/256 should
generally be omitted, but if present, it shall have a value of type
NULL.
This is to align with the definitions originally promulgated by NIST.
For the SHA algorithms, implementations MUST accept
AlgorithmIdentifier values both without parameters and with NULL
parameters.
Exception: When formatting the DigestInfoValue in EMSA-PKCS1-v1_5
(see Section 9.2), the parameters field associated with id-sha1,
id-sha224, id-sha256, id-sha384, id-sha512, id-sha512/224, and
id-sha512/256 shall have a value of type NULL. This is to maintain
compatibility with existing implementations and with the numeric
information values already published for EMSA-PKCS1-v1_5, which are
also reflected in IEEE 1363a [IEEE1363A].
Note: Version 1.5 of PKCS #1 also allowed for the use of MD4 in
signature schemes. The cryptanalysis of MD4 has progressed
significantly in the intervening years. For example, Dobbertin [MD4]
demonstrated how to find collisions for MD4 and that the first two
rounds of MD4 are not one-way [MD4FIRST]. Because of these results
and others (e.g., [MD4LAST]), MD4 is NOT RECOMMENDED.
Further advances have been made in the cryptanalysis of MD2 and MD5,
especially after the findings of Stevens et al. [PREFIX] on chosen-
prefix collisions on MD5. MD2 and MD5 should be considered cryptographically broken and removed from existing applications. This version of the standard supports MD2 and MD5 just for backwards- compatibility reasons. There have also been advances in the cryptanalysis of SHA-1. Particularly, the results of Wang et al. [SHA1CRYPT] (which have been independently verified by M. Cochran in his analysis [COCHRAN]) on using a differential path to find collisions in SHA-1, which conclude that the security strength of the SHA-1 hashing algorithm is significantly reduced. However, this reduction is not significant enough to warrant the removal of SHA-1 from existing applications, but its usage is only recommended for backwards-compatibility reasons. To address these concerns, only SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, and SHA-512/256 are RECOMMENDED for new applications. As of today, the best (known) collision attacks against these hash functions are generic attacks with complexity 2L/2, where L is the bit length of the hash output. For the signature schemes in this document, a collision attack is easily translated into a signature forgery. Therefore, the value L / 2 should be at least equal to the desired security level in bits of the signature scheme (a security level of B bits means that the best attack has complexity 2B). The same rule of thumb can be applied to RSAES-OAEP; it is RECOMMENDED that the bit length of the seed (which is equal to the bit length of the hash output) be twice the desired security level in bits.B.2. Mask Generation Functions
A mask generation function takes an octet string of variable length and a desired output length as input and outputs an octet string of the desired length. There may be restrictions on the length of the input and output octet strings, but such bounds are generally very large. Mask generation functions are deterministic; the octet string output is completely determined by the input octet string. The output of a mask generation function should be pseudorandom: Given one part of the output but not the input, it should be infeasible to predict another part of the output. The provable security of RSAES-OAEP and RSASSA-PSS relies on the random nature of the output of the mask generation function, which in turn relies on the random nature of the underlying hash. One mask generation function is given here: MGF1, which is based on a hash function. MGF1 coincides with the mask generation functions defined in IEEE 1363 [IEEE1363] and ANSI X9.44 [ANSIX944]. Future versions of this document may define other mask generation functions.
B.2.1. MGF1
MGF1 is a mask generation function based on a hash function. MGF1 (mgfSeed, maskLen) Options: Hash hash function (hLen denotes the length in octets of the hash function output) Input: mgfSeed seed from which mask is generated, an octet string maskLen intended length in octets of the mask, at most 2^32 hLen Output: mask mask, an octet string of length maskLen Error: "mask too long" Steps: 1. If maskLen > 2^32 hLen, output "mask too long" and stop. 2. Let T be the empty octet string. 3. For counter from 0 to \ceil (maskLen / hLen) - 1, do the following: A. Convert counter to an octet string C of length 4 octets (see Section 4.1): C = I2OSP (counter, 4) . B. Concatenate the hash of the seed mgfSeed and C to the octet string T: T = T || Hash(mgfSeed || C) . 4. Output the leading maskLen octets of T as the octet string mask. The object identifier id-mgf1 identifies the MGF1 mask generation function: id-mgf1 OBJECT IDENTIFIER ::= { pkcs-1 8 }
The parameters field associated with this OID in a value of type AlgorithmIdentifier shall have a value of type hashAlgorithm, identifying the hash function on which MGF1 is based.Appendix C. ASN.1 Module
-- PKCS #1 v2.2 ASN.1 Module -- Revised October 27, 2012 -- This module has been checked for conformance with the -- ASN.1 standard by the OSS ASN.1 Tools PKCS-1 { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1) modules(0) pkcs-1(1) } DEFINITIONS EXPLICIT TAGS ::= BEGIN -- EXPORTS ALL -- All types and values defined in this module are exported for use -- in other ASN.1 modules. IMPORTS id-sha224, id-sha256, id-sha384, id-sha512, id-sha512-224, id-sha512-256 FROM NIST-SHA2 { joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistalgorithm(4) hashAlgs(2) }; -- ============================ -- Basic object identifiers -- ============================ -- The DER encoding of this in hexadecimal is: -- (0x)06 08 -- 2A 86 48 86 F7 0D 01 01 -- pkcs-1 OBJECT IDENTIFIER ::= { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) 1 } -- -- When rsaEncryption is used in an AlgorithmIdentifier,
-- the parameters MUST be present and MUST be NULL.
--
rsaEncryption OBJECT IDENTIFIER ::= { pkcs-1 1 }
--
-- When id-RSAES-OAEP is used in an AlgorithmIdentifier, the
-- parameters MUST be present and MUST be RSAES-OAEP-params.
--
id-RSAES-OAEP OBJECT IDENTIFIER ::= { pkcs-1 7 }
--
-- When id-pSpecified is used in an AlgorithmIdentifier, the
-- parameters MUST be an OCTET STRING.
--
id-pSpecified OBJECT IDENTIFIER ::= { pkcs-1 9 }
--
-- When id-RSASSA-PSS is used in an AlgorithmIdentifier, the
-- parameters MUST be present and MUST be RSASSA-PSS-params.
--
id-RSASSA-PSS OBJECT IDENTIFIER ::= { pkcs-1 10 }
--
-- When the following OIDs are used in an AlgorithmIdentifier,
-- the parameters MUST be present and MUST be NULL.
--
md2WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 2 }
md5WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 4 }
sha1WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 5 }
sha224WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 14 }
sha256WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 11 }
sha384WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 12 }
sha512WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 13 }
sha512-224WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 15 }
sha512-256WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 16 }
--
-- This OID really belongs in a module with the secsig OIDs.
--
id-sha1 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) oiw(14) secsig(3) algorithms(2)
26
}
--
-- OIDs for MD2 and MD5, allowed only in EMSA-PKCS1-v1_5.
--
id-md2 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) digestAlgorithm(2) 2
}
id-md5 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) digestAlgorithm(2) 5
}
--
-- When id-mgf1 is used in an AlgorithmIdentifier, the parameters
-- MUST be present and MUST be a HashAlgorithm, for example, sha1.
--
id-mgf1 OBJECT IDENTIFIER ::= { pkcs-1 8 }
-- ================
-- Useful types
-- ================
ALGORITHM-IDENTIFIER ::= CLASS {
&id OBJECT IDENTIFIER UNIQUE,
&Type OPTIONAL
}
WITH SYNTAX { OID &id [PARAMETERS &Type] }
-- Note: the parameter InfoObjectSet in the following definitions
-- allows a distinct information object set to be specified for sets
-- of algorithms such as:
-- DigestAlgorithms ALGORITHM-IDENTIFIER ::= {
-- { OID id-md2 PARAMETERS NULL }|
-- { OID id-md5 PARAMETERS NULL }|
-- { OID id-sha1 PARAMETERS NULL }
-- }
--
AlgorithmIdentifier { ALGORITHM-IDENTIFIER:InfoObjectSet } ::=
SEQUENCE {
algorithm
ALGORITHM-IDENTIFIER.&id({InfoObjectSet}),
parameters
ALGORITHM-IDENTIFIER.&Type({InfoObjectSet}{@.algorithm})
OPTIONAL
}
-- ==============
-- Algorithms
-- ==============
--
-- Allowed EME-OAEP and EMSA-PSS digest algorithms.
--
OAEP-PSSDigestAlgorithms ALGORITHM-IDENTIFIER ::= {
{ OID id-sha1 PARAMETERS NULL }|
{ OID id-sha224 PARAMETERS NULL }|
{ OID id-sha256 PARAMETERS NULL }|
{ OID id-sha384 PARAMETERS NULL }|
{ OID id-sha512 PARAMETERS NULL }|
{ OID id-sha512-224 PARAMETERS NULL }|
{ OID id-sha512-256 PARAMETERS NULL },
... -- Allows for future expansion --
}
--
-- Allowed EMSA-PKCS1-v1_5 digest algorithms.
--
PKCS1-v1-5DigestAlgorithms ALGORITHM-IDENTIFIER ::= {
{ OID id-md2 PARAMETERS NULL }|
{ OID id-md5 PARAMETERS NULL }|
{ OID id-sha1 PARAMETERS NULL }|
{ OID id-sha224 PARAMETERS NULL }|
{ OID id-sha256 PARAMETERS NULL }|
{ OID id-sha384 PARAMETERS NULL }|
{ OID id-sha512 PARAMETERS NULL }|
{ OID id-sha512-224 PARAMETERS NULL }|
{ OID id-sha512-256 PARAMETERS NULL }
}
-- When id-md2 and id-md5 are used in an AlgorithmIdentifier, the
-- parameters field shall have a value of type NULL.
-- When id-sha1, id-sha224, id-sha256, id-sha384, id-sha512,
-- id-sha512-224, and id-sha512-256 are used in an
-- AlgorithmIdentifier, the parameters (which are optional) SHOULD be
-- omitted, but if present, they SHALL have a value of type NULL.
-- However, implementations MUST accept AlgorithmIdentifier values
-- both without parameters and with NULL parameters.
-- Exception: When formatting the DigestInfoValue in EMSA-PKCS1-v1_5
-- (see Section 9.2), the parameters field associated with id-sha1,
-- id-sha224, id-sha256, id-sha384, id-sha512, id-sha512-224, and
-- id-sha512-256 SHALL have a value of type NULL. This is to
-- maintain compatibility with existing implementations and with the
-- numeric information values already published for EMSA-PKCS1-v1_5,
-- which are also reflected in IEEE 1363a.
sha1 HashAlgorithm ::= {
algorithm id-sha1,
parameters SHA1Parameters : NULL
}
HashAlgorithm ::= AlgorithmIdentifier { {OAEP-PSSDigestAlgorithms} }
SHA1Parameters ::= NULL
--
-- Allowed mask generation function algorithms.
-- If the identifier is id-mgf1, the parameters are a HashAlgorithm.
--
PKCS1MGFAlgorithms ALGORITHM-IDENTIFIER ::= {
{ OID id-mgf1 PARAMETERS HashAlgorithm },
... -- Allows for future expansion --
}
--
-- Default AlgorithmIdentifier for id-RSAES-OAEP.maskGenAlgorithm and
-- id-RSASSA-PSS.maskGenAlgorithm.
--
mgf1SHA1 MaskGenAlgorithm ::= {
algorithm id-mgf1,
parameters HashAlgorithm : sha1
}
MaskGenAlgorithm ::= AlgorithmIdentifier { {PKCS1MGFAlgorithms} }
--
-- Allowed algorithms for pSourceAlgorithm.
--
PKCS1PSourceAlgorithms ALGORITHM-IDENTIFIER ::= {
{ OID id-pSpecified PARAMETERS EncodingParameters },
... -- Allows for future expansion --
}
EncodingParameters ::= OCTET STRING(SIZE(0..MAX))
--
-- This identifier means that the label L is an empty string, so the
-- digest of the empty string appears in the RSA block before
-- masking.
--
pSpecifiedEmpty PSourceAlgorithm ::= {
algorithm id-pSpecified,
parameters EncodingParameters : emptyString
}
PSourceAlgorithm ::= AlgorithmIdentifier { {PKCS1PSourceAlgorithms} }
emptyString EncodingParameters ::= ''H
--
-- Type identifier definitions for the PKCS #1 OIDs.
--
PKCS1Algorithms ALGORITHM-IDENTIFIER ::= {
{ OID rsaEncryption PARAMETERS NULL } |
{ OID md2WithRSAEncryption PARAMETERS NULL } |
{ OID md5WithRSAEncryption PARAMETERS NULL } |
{ OID sha1WithRSAEncryption PARAMETERS NULL } |
{ OID sha224WithRSAEncryption PARAMETERS NULL } |
{ OID sha256WithRSAEncryption PARAMETERS NULL } |
{ OID sha384WithRSAEncryption PARAMETERS NULL } |
{ OID sha512WithRSAEncryption PARAMETERS NULL } |
{ OID sha512-224WithRSAEncryption PARAMETERS NULL } |
{ OID sha512-256WithRSAEncryption PARAMETERS NULL } |
{ OID id-RSAES-OAEP PARAMETERS RSAES-OAEP-params } |
PKCS1PSourceAlgorithms |
{ OID id-RSASSA-PSS PARAMETERS RSASSA-PSS-params },
... -- Allows for future expansion --
}
-- ===================
-- Main structures
-- ===================
RSAPublicKey ::= SEQUENCE {
modulus INTEGER, -- n
publicExponent INTEGER -- e
}
--
-- Representation of RSA private key with information for the CRT
-- algorithm.
--
RSAPrivateKey ::= SEQUENCE {
version Version,
modulus INTEGER, -- n
publicExponent INTEGER, -- e
privateExponent INTEGER, -- d
prime1 INTEGER, -- p
prime2 INTEGER, -- q
exponent1 INTEGER, -- d mod (p-1)
exponent2 INTEGER, -- d mod (q-1)
coefficient INTEGER, -- (inverse of q) mod p
otherPrimeInfos OtherPrimeInfos OPTIONAL
}
Version ::= INTEGER { two-prime(0), multi(1) }
(CONSTRAINED BY
{-- version MUST
be multi if otherPrimeInfos present --})
OtherPrimeInfos ::= SEQUENCE SIZE(1..MAX) OF OtherPrimeInfo
OtherPrimeInfo ::= SEQUENCE {
prime INTEGER, -- ri
exponent INTEGER, -- di
coefficient INTEGER -- ti
}
--
-- AlgorithmIdentifier.parameters for id-RSAES-OAEP.
-- Note that the tags in this Sequence are explicit.
--
RSAES-OAEP-params ::= SEQUENCE {
hashAlgorithm [0] HashAlgorithm DEFAULT sha1,
maskGenAlgorithm [1] MaskGenAlgorithm DEFAULT mgf1SHA1,
pSourceAlgorithm [2] PSourceAlgorithm DEFAULT pSpecifiedEmpty
}
--
-- Identifier for default RSAES-OAEP algorithm identifier.
-- The DER encoding of this is in hexadecimal:
-- (0x)30 0D
-- 06 09
-- 2A 86 48 86 F7 0D 01 01 07
-- 30 00
-- Notice that the DER encoding of default values is "empty".
--
rSAES-OAEP-Default-Identifier RSAES-AlgorithmIdentifier ::= {
algorithm id-RSAES-OAEP,
parameters RSAES-OAEP-params : {
hashAlgorithm sha1,
maskGenAlgorithm mgf1SHA1,
pSourceAlgorithm pSpecifiedEmpty
}
}
RSAES-AlgorithmIdentifier ::= AlgorithmIdentifier {
{PKCS1Algorithms}
}
--
-- AlgorithmIdentifier.parameters for id-RSASSA-PSS.
-- Note that the tags in this Sequence are explicit.
--
RSASSA-PSS-params ::= SEQUENCE {
hashAlgorithm [0] HashAlgorithm DEFAULT sha1,
maskGenAlgorithm [1] MaskGenAlgorithm DEFAULT mgf1SHA1,
saltLength [2] INTEGER DEFAULT 20,
trailerField [3] TrailerField DEFAULT trailerFieldBC
}
TrailerField ::= INTEGER { trailerFieldBC(1) }
--
-- Identifier for default RSASSA-PSS algorithm identifier
-- The DER encoding of this is in hexadecimal:
-- (0x)30 0D
-- 06 09
-- 2A 86 48 86 F7 0D 01 01 0A
-- 30 00
-- Notice that the DER encoding of default values is "empty".
--
rSASSA-PSS-Default-Identifier RSASSA-AlgorithmIdentifier ::= {
algorithm id-RSASSA-PSS,
parameters RSASSA-PSS-params : {
hashAlgorithm sha1,
maskGenAlgorithm mgf1SHA1,
saltLength 20,
trailerField trailerFieldBC
}
}
RSASSA-AlgorithmIdentifier ::= AlgorithmIdentifier {
{PKCS1Algorithms}
}
--
-- Syntax for the EMSA-PKCS1-v1_5 hash identifier.
--
DigestInfo ::= SEQUENCE {
digestAlgorithm DigestAlgorithm,
digest OCTET STRING
}
DigestAlgorithm ::= AlgorithmIdentifier {
{PKCS1-v1-5DigestAlgorithms}
}
END
Appendix D. Revision History of PKCS #1
Versions 1.0 - 1.5: Versions 1.0 - 1.3 were distributed to participants in RSA Data Security, Inc.'s Public-Key Cryptography Standards meetings in February and March 1991. Version 1.4 was part of the June 3, 1991 initial public release of PKCS. Version 1.4 was published as NIST/OSI Implementors' Workshop document SEC-SIG-91-18. Version 1.5 incorporated several editorial changes, including updates to the references and the addition of a revision history. The following substantive changes were made: * Section 10: "MD4 with RSA" signature and verification processes were added. * Section 11: md4WithRSAEncryption object identifier was added. Version 1.5 was republished as [RFC2313] (which was later obsoleted by [RFC2437]). Version 2.0: Version 2.0 incorporated major editorial changes in terms of the document structure and introduced the RSAES-OAEP encryption scheme. This version continued to support the encryption and signature processes in version 1.5, although the hash algorithm MD4 was no longer allowed due to cryptanalytic advances in the intervening years. Version 2.0 was republished as [RFC2437] (which was later obsoleted by [RFC3447]). Version 2.1: Version 2.1 introduced multi-prime RSA and the RSASSA-PSS signature scheme with appendix along with several editorial improvements. This version continued to support the schemes in version 2.0. Version 2.1 was republished as [RFC3447].
Version 2.2:
Version 2.2 updates the list of allowed hashing algorithms to
align them with FIPS 180-4 [SHS], therefore adding SHA-224,
SHA-512/224, and SHA-512/256. The following substantive changes
were made:
* Object identifiers for sha224WithRSAEncryption,
sha512-224WithRSAEncryption, and sha512-256WithRSAEncryption
were added.
* This version continues to support the schemes in version 2.1.
Appendix E. About PKCS
The Public-Key Cryptography Standards are specifications produced by
RSA Laboratories in cooperation with secure systems developers
worldwide for the purpose of accelerating the deployment of public-
key cryptography. First published in 1991 as a result of meetings
with a small group of early adopters of public-key technology, the
PKCS documents have become widely referenced and implemented.
Contributions from the PKCS series have become part of many formal
and de facto standards, including ANSI X9 and IEEE P1363 documents,
PKIX, Secure Electronic Transaction (SET), S/MIME, SSL/TLS, and
Wireless Application Protocol (WAP) / WAP Transport Layer Security
(WTLS).
Further development of most PKCS documents occurs through the IETF.
Suggestions for improvement are welcome.
Acknowledgements
This document is based on a contribution of RSA Laboratories, the research center of RSA Security Inc.Authors' Addresses
Kathleen M. Moriarty (editor) EMC Corporation 176 South Street Hopkinton, MA 01748 United States of America Email: kathleen.moriarty@emc.com Burt Kaliski Verisign 12061 Bluemont Way Reston, VA 20190 United States of America Email: bkaliski@verisign.com URI: http://verisignlabs.com Jakob Jonsson Subset AB Munkbrogtan 4 Stockholm SE-11127 Sweden Phone: +46 8 428 687 43 Email: jakob.jonsson@subset.se Andreas Rusch RSA 345 Queen Street Brisbane, QLD 4000 Australia Email: andreas.rusch@rsa.com