PKIX Working Group L. Bassham (NIST)
Internet Draft R. Housley (RSA Laboratories)
expires September, 2001 W. Polk (NIST)
July, 2001
Algorithms and Identifiers for the
Internet X.509 Public Key Infrastructure
Certificate and CRL Profile
<draft-ietf-pkix-ipki-pkalgs-03.txt>
Status of this Memo
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Abstract
This document specifies algorithm identifiers and ASN.1 encoding
formats for digital signatures and subject public keys used in the
Internet X.509 Public Key Infrastructure (PKI). Digital signatures
are used to sign certificates and certificate revocation lists
(CRLs). Certificates include the public key of the named subject.
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Table of Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Algorithm Support . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 One-Way Hash Functions . . . . . . . . . . . . . . . . . . . . 4
2.1.1 MD2 One-Way Hash Functions . . . . . . . . . . . . . . . . . 4
2.1.2 MD5 One-Way Hash Functions . . . . . . . . . . . . . . . . . 4
2.1.3 SHA-1 One-Way Hash Functions . . . . . . . . . . . . . . . . 4
2.2 Signature Algorithms . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 RSA Signature Algorithm . . . . . . . . . . . . . . . . . . . 5
2.2.2 DSA Signature Algorithm . . . . . . . . . . . . . . . . . . . 6
2.2.3 Elliptic Curve Digital Signature Algorithm . . . . . . . . . 7
2.3 Subject Public Key Algorithms . . . . . . . . . . . . . . . . . 8
2.3.1 RSA Keys . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 DSA Signature Keys . . . . . . . . . . . . . . . . . . . . . 9
2.3.3 Diffie-Hellman Key Exchange Keys . . . . . . . . . . . . . . 10
2.3.4 KEA Public Keys . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.5 ECDSA and ECDH Public Keys . . . . . . . . . . . . . . . . . 13
3 ASN.1 Module . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5 Security Considerations . . . . . . . . . . . . . . . . . . . . . 25
6 Intellectual Property Rights . . . . . . . . . . . . . . . . . . 25
7 Author Addresses . . . . . . . . . . . . . . . . . . . . . . . . 26
8 Full Copyright Statement . . . . . . . . . . . . . . . . . . . . 26
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1 Introduction
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].
This document specifies algorithm identifiers and ASN.1 encoding for-
mats for digital signatures and subject public keys used in the
Internet X.509 Public Key Infrastructure (PKI). This specification
supplements [RFC XXXX], "Internet Public Key Infrastructure: X.509
Certificate and CRL Profile". Implementations of this specification
must also conform to RFC XXXX.
This specification defines the contents of the signatureAlgorithm,
signatureValue, signature, and subjectPublicKeyInfo fields within
Internet X.509 certificates and CRLs.
This document identifies one-way hash functions for use in the gener-
ation of digital signatures. These algorithms are used in conjunc-
tion with digital signature algorithms.
This specification describes the encoding of digital signatures gen-
erated with the following cryptographic algorithms:
* Rivest-Shamir-Adelman (RSA);
* Digital Signature Algorithm (DSA); and
* Elliptic Curve Digital Signature Algorithm (ECDSA).
This document specifies the contents of the subjectPublicKeyInfo
field in Internet X.509 certificates. For each algorithm, the appro-
priate alternatives for the the keyUsage extension are provided.
This specification describes encoding formats for public keys used
with the following cryptographic algorithms:
* Rivest-Shamir-Adelman (RSA);
* Digital Signature Algorithm (DSA);
* Diffie-Hellman;
* Key Encryption Algorithm (KEA);
* Elliptic Curve Digital Signature Algorithm (ECDSA); and
* Elliptic Curve Diffie-Hellman (ECDH).
2 Algorithm Support
This section describes cryptographic algorithms which may be used
with the Internet X.509 certificate and CRL profile [RFC XXXX]. The
section describes one-way hash functions and digital signature algo-
rithms which may be used to sign certificates and CRLs, and identi-
fies OIDs for public keys contained in a certificate.
Conforming CAs and applications MUST, at a minimum, support digital
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signatures and public keys for one of the specified algorithms. When
using any of the algorithms identified in this specification, con-
forming CAs and applications MUST support them as described.
2.1 One-way Hash Functions
This section identifies one-way hash functions for use in the Inter-
net X.509 PKI. One-way hash functions are also called message digest
algorithms. SHA-1 is the preferred one-way hash function for the
Internet X.509 PKI. However, PEM uses MD2 for certificates [RFC
1422] [RFC 1423] and MD5 is used in other legacy applications. For
this reason, MD2 and MD5 are included in this profile.
2.1.1 MD2 One-way Hash Function
MD2 was developed by Ron Rivest for RSA Security. RSA Security has
recently placed the MD2 algorithm in the public domain. Previously,
RSA Data Security had granted license for use of MD2 for non-commer-
cial Internet Privacy-Enhanced Mail (PEM). MD2 may continue to be
used with PEM certificates, but SHA-1 is preferred. MD2 produces a
128-bit "hash" of the input. MD2 is fully described in [RFC 1319].
At the Selected Areas in Cryptography '95 conference in May 1995,
Rogier and Chauvaud presented an attack on MD2 that can nearly find
collisions [RC95]. Collisions occur when one can find two different
messages that generate the same message digest. A checksum operation
in MD2 is the only remaining obstacle to the success of the attack.
For this reason, the use of MD2 for new applications is discouraged.
It is still reasonable to use MD2 to verify existing signatures, as
the ability to find collisions in MD2 does not enable an attacker to
find new messages having a previously computed hash value.
2.1.2 MD5 One-way Hash Function
MD5 was developed by Ron Rivest for RSA Security. RSA Security has
placed the MD5 algorithm in the public domain. MD5 produces a
128-bit "hash" of the input. MD5 is fully described in [RFC 1321].
Den Boer and Bosselaers [DB94] have found pseudo-collisions for MD5,
but there are no other known cryptanalytic results. The use of MD5
for new applications is discouraged. It is still reasonable to use
MD5 to verify existing signatures.
2.1.3 SHA-1 One-way Hash Function
SHA-1 was developed by the U.S. Government. SHA-1 produces a 160-bit
"hash" of the input. SHA-1 is fully described in [FIPS 180-1].
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SHA-1 is the one-way hash function of choice for use with the RSA,
DSA, and ECDSA signature algorithms.
2.2 Signature Algorithms
Certificates and CRLs conforming to [RFC XXXX] may be signed with any
public key signature algorithm. The certificate or CRL indicates the
algorithm through an algorithm identifier which appears in the signa-
tureAlgorithm field within the Certificate or CertificateList. This
algorithm identifier is an OID and has optionally associated parame-
ters. This section identifies algorithm identifiers and parameters
that MUST be used in the signatureAlgorithm field in a Certificate or
CertificateList.
Signature algorithms are always used in conjunction with a one-way
hash function.
This section identifies OIDS for RSA, DSA, and ECDSA. The contents
of the parameters component for each algorithm vary; details are pro-
vided for each algorithm.
The data to be signed (e.g., the one-way hash function output value)
is formatted for the signature algorithm to be used. Then, a private
key operation (e.g., RSA encryption) is performed to generate the
signature value. This signature value is then ASN.1 encoded as a BIT
STRING and included in the Certificate or CertificateList in the sig-
nature field.
2.2.1 RSA Signature Algorithm
The RSA algorithm is named for its inventors: Rivest, Shamir, and
Adleman. This profile includes three signature algorithms based on
the RSA asymmetric encryption algorithm. The signature algorithms
combine RSA with either the MD2, MD5, or the SHA-1 one-way hash func-
tions.
The signature algorithm with SHA-1 and the RSA encryption algorithm
is implemented using the padding and encoding conventions described
in PKCS #1 [RFC 2313]. The message digest is computed using the SHA-1
hash algorithm.
The RSA signature algorithm, as specified in PKCS #1 [RFC 2313]
includes a data encoding step. In this step, the message digest and
the OID for the one-way hash function used to compute the digest are
combined. When performing the data encoding step, the md2, md5, and
id-sha1 OIDs MUST be used to specify the MD2, MD5, and SHA-1 one-way
hash functions respectively :
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md2 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) US(840) rsadsi(113549)
digestAlgorithm(2) 2 }
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 }
The signature algorithm with MD2 and the RSA encryption algorithm is
defined in PKCS #1 [RFC 2313]. As defined in PKCS #1 [RFC 2313], the
ASN.1 OID used to identify this signature algorithm is:
md2WithRSAEncryption OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
pkcs-1(1) 2 }
The signature algorithm with MD5 and the RSA encryption algorithm is
defined in PKCS #1 [RFC 2313]. As defined in PKCS #1 [RFC 2313], the
ASN.1 OID used to identify this signature algorithm is:
md5WithRSAEncryption OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
pkcs-1(1) 4 }
The ASN.1 object identifier used to identify this signature algorithm
is:
sha-1WithRSAEncryption OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
pkcs-1(1) 5 }
When any of these three OIDs appears within the ASN.1 type Algorith-
mIdentifier, the parameters component of that type SHALL be the ASN.1
type NULL.
The RSA signature generation process and the encoding of the result
is described in detail in PKCS #1 [RFC 2313].
2.2.2 DSA Signature Algorithm
The Digital Signature Algorithm (DSA) is defined in the Digital Sig-
nature Standard (DSS). DSA was developed by the U.S. Government, and
DSA is used in conjunction with the SHA-1 one-way hash function. DSA
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is fully described in [FIPS 186]. The ASN.1 OID used to identify
this signature algorithm is:
id-dsa-with-sha1 ID ::= {
iso(1) member-body(2) us(840) x9-57 (10040)
x9cm(4) 3 }
When the id-dsa-with-sha1 algorithm identifier appears as the algo-
rithm field in an AlgorithmIdentifier, the encoding SHALL omit the
parameters field. That is, the AlgorithmIdentifier shall be a
SEQUENCE of one component: the OBJECT IDENTIFIER id-dsa-with-sha1.
The DSA parameters in the subjectPublicKeyInfo field of the certifi-
cate of the issuer shall apply to the verification of the signature.
When signing, the DSA algorithm generates two values. These values
are commonly referred to as r and s. To easily transfer these two
values as one signature, they SHALL be ASN.1 encoded using the fol-
lowing ASN.1 structure:
Dss-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER }
2.2.3 ECDSA Signature Algorithm
The Elliptic Curve Digital Signature Algorithm (ECDSA) is defined in
[X9.62]. The ASN.1 object identifiers used to identify ECDSA are
defined in the following arc:
ansi-X9-62 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) us(840) 10045 }
ECDSA is used in conjunction with the SHA-1 one-way hash function.
The ASN.1 object identifier used to identify ECDSA with SHA-1 is:
id-ecSigType OBJECT IDENTIFIER ::= { ansi-X9-62 signatures(4) }
ecdsa-with-SHA1 OBJECT IDENTIFIER ::= { id-ecSigType 1 }
When the ecdsa-with-SHA1 algorithm identifier appears as the algo-
rithm field in an AlgorithmIdentifier, the encoding MUST omit the
parameters field. That is, the AlgorithmIdentifier shall be a
SEQUENCE of one component: the OBJECT IDENTIFIER ecdsa-with-SHA1.
The elliptic curve parameters in the subjectPublicKeyInfo field of
the certificate of the issuer shall apply to the verification of the
signature.
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When signing, the ECDSA algorithm generates two values. These values
are commonly referred to as r and s. To easily transfer these two
values as one signature, they MUST be ASN.1 encoded using the follow-
ing ASN.1 structure:
Ecdsa-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER }
2.3 Subject Public Key Algorithms
Certificates conforming to [RFC XXXX] may convey a public key for any
public key algorithm. The certificate indicates the algorithm through
an algorithm identifier. This algorithm identifier is an OID and
optionally associated parameters.
This section identifies preferred OIDs and parameters for the RSA,
DSA, Diffie-Hellman, KEA, ECDSA, and ECDH algorithms. Conforming CAs
MUST use the identified OIDs when issuing certificates containing
public keys for these algorithms. Conforming applications supporting
any of these algorithms MUST, at a minimum, recognize the OID identi-
fied in this section.
2.3.1 RSA Keys
The OID rsaEncryption identifies RSA public keys.
pkcs-1 OBJECT IDENTIFIER ::= { iso(1) member-body(2) us(840)
rsadsi(113549) pkcs(1) 1 }
rsaEncryption OBJECT IDENTIFIER ::= { pkcs-1 1}
The rsaEncryption OID is intended to be used in the algorithm field
of a value of type AlgorithmIdentifier. The parameters field MUST
have ASN.1 type NULL for this algorithm identifier.
The RSA public key MUST be encoded using the ASN.1 type RSAPublicKey:
RSAPublicKey ::= SEQUENCE {
modulus INTEGER, -- n
publicExponent INTEGER } -- e
where modulus is the modulus n, and publicExponent is the public
exponent e. The DER encoded RSAPublicKey is the value of the BIT
STRING subjectPublicKey.
This OID is used in public key certificates for both RSA signature
keys and RSA encryption keys. The intended application for the key
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MAY be indicated in the key usage field (see [RFC XXXX]). The use of
a single key for both signature and encryption purposes is not recom-
mended, but is not forbidden.
If the keyUsage extension is present in an end entity certificate
which conveys an RSA public key, any combination of the following
values MAY be present:
digitalSignature;
nonRepudiation;
keyEncipherment; and
dataEncipherment.
If the keyUsage extension is present in a CA certificate which con-
veys an RSA public key, any combination of the following values MAY
be present:
digitalSignature;
nonRepudiation;
keyEncipherment;
dataEncipherment;
keyCertSign; and
cRLSign.
However, this specification RECOMMENDS that if keyCertSign or cRLSign
is present, both keyEncipherment and dataEncipherment SHOULD NOT be
present.
2.3.2 DSA Signature Keys
The Digital Signature Algorithm (DSA) is defined in the Digital Sig-
nature Standard (DSS) [FIPS 186]. The DSA OID supported by this pro-
file is
id-dsa ID ::= { iso(1) member-body(2) us(840) x9-57(10040)
x9cm(4) 1 }
The id-dsa algorithm syntax includes optional domain parameters.
These parameters are commonly referred to as p, q, and g. When omit-
ted, the parameters component MUST be omitted entirely. That is, the
AlgorithmIdentifier MUST be a SEQUENCE of one component: the OBJECT
IDENTIFIER id-dsa.
If the DSA domain parameters are present in the subjectPublicKeyInfo
AlgorithmIdentifier, the parameters are included using the following
ASN.1 structure:
Dss-Parms ::= SEQUENCE {
p INTEGER,
q INTEGER,
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g INTEGER }
The AlgorithmIdentifier within subjectPublicKeyInfo is the only place
within a certificate where the parameters may be used. If the DSA
algorithm parameters are omitted from the subjectPublicKeyInfo Algo-
rithmIdentifier and the CA signed the subject certificate using DSA,
then the certificate issuer's DSA parameters apply to the subject's
DSA key. If the DSA domain parameters are omitted from the subject-
PublicKeyInfo AlgorithmIdentifier and the CA signed the subject cer-
tificate using a signature algorithm other than DSA, then the sub-
ject's DSA domain parameters are distributed by other means. If the
subjectPublicKeyInfo AlgorithmIdentifier field omits the parameters
component, the CA signed the subject with a signature algorithm other
than DSA, and the subject's DSA parameters are not available through
other means, then clients MUST reject the certificate.
The DSA public key MUST be ASN.1 DER encoded as an INTEGER; this
encoding shall be used as the contents (i.e., the value) of the sub-
jectPublicKey component (a BIT STRING) of the SubjectPublicKeyInfo
data element.
DSAPublicKey ::= INTEGER -- public key, Y
If the keyUsage extension is present in an end entity certificate
which conveys a DSA public key, any combination of the following val-
ues MAY be present:
digitalSignature;
nonRepudiation;
If the keyUsage extension is present in a CA certificate which con-
veys a DSA public key, any combination of the following values MAY be
present:
digitalSignature;
nonRepudiation;
keyCertSign; and
cRLSign.
2.3.3 Diffie-Hellman Key Exchange Keys
The Diffie-Hellman OID supported by this profile is
defined in [X9.42].
dhpublicnumber OBJECT IDENTIFIER ::= { iso(1) member-body(2)
us(840) ansi-x942(10046) number-type(2) 1 }
The dhpublicnumber OID is intended to be used in the algorithm field
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of a value of type AlgorithmIdentifier. The parameters field of that
type, which has the algorithm-specific syntax ANY DEFINED BY algo-
rithm, have the ASN.1 type DomainParameters for this algorithm.
DomainParameters ::= SEQUENCE {
p INTEGER, -- odd prime, p=jq +1
g INTEGER, -- generator, g
q INTEGER, -- factor of p-1
j INTEGER OPTIONAL, -- subgroup factor
validationParms ValidationParms OPTIONAL }
ValidationParms ::= SEQUENCE {
seed BIT STRING,
pgenCounter INTEGER }
The fields of type DomainParameters have the following meanings:
p identifies the prime p defining the Galois field;
g specifies the generator of the multiplicative subgroup of order
g;
q specifies the prime factor of p-1;
j optionally specifies the value that satisfies the equation
p=jq+1 to support the optional verification of group parameters;
seed optionally specifies the bit string parameter used as the
seed for the domain parameter generation process; and
pgenCounter optionally specifies the integer value output as part
of the of the domain parameter prime generation process.
If either of the domain parameter generation components (pgencounter
or seed) is provided, the other MUST be present as well.
The Diffie-Hellman public key MUST be ASN.1 encoded as an INTEGER;
this encoding shall be used as the contents (i.e., the value) of the
subjectPublicKey component (a BIT STRING) of the subjectPublicKeyInfo
data element.
DHPublicKey ::= INTEGER -- public key, y = g^x mod p
If the keyUsage extension is present in a certificate which conveys a
DH public key, the following values may be present:
keyAgreement;
encipherOnly; and
decipherOnly.
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If present, the keyUsage extension MUST assert keyAgreement and MAY
assert either encipherOnly and decipherOnly. The keyUsage extension
MUST NOT assert both encipherOnly and decipherOnly.
2.3.4 KEA Public Keys
This section identifies the preferred OID and parameters for the
inclusion of a KEA public key in a certificate. The Key Exchange
Algorithm (KEA) is a key agreement algorithm. Two parties may gener-
ate a "pairwise key" if and only if they share the same KEA parame-
ters. The KEA parameters are not included in a certificate; instead
a domain identifier is supplied in the parameters field.
When the subjectPublicKeyInfo field contains a KEA key, the algorithm
identifier and parameters shall be as defined in [SDN.701r]:
id-keyExchangeAlgorithm OBJECT IDENTIFIER ::=
{ 2 16 840 1 101 2 1 1 22 }
KEA-Parms-Id ::= OCTET STRING
CAs MUST populate the parameters field of the AlgorithmIdentifier
within the subjectPublicKeyInfo field of each certificate containing
a KEA public key with an 80-bit parameter identifier (OCTET STRING),
also known as the domain identifier. The domain identifier is com-
puted in three steps:
1) the KEA domain parameters (p, q, and g) are DER encoded using
the Dss-Parms structure;
(2) a 160-bit SHA-1 hash is generated from the parameters; and
(3) the 160-bit hash is reduced to 80-bits by performing an
"exclusive or" of the 80 high order bits with the 80 low order
bits.
The resulting value is encoded such that the most significant byte of
the 80-bit value is the first octet in the octet string. The Dss-
Parms is provided above in Section 2.3.2.
A KEA public key, y, is conveyed in the subjectPublicKey BIT STRING
such that the most significant bit (MSB) of y becomes the MSB of the
BIT STRING value field and the least significant bit (LSB) of y
becomes the LSB of the BIT STRING value field. This results in the
following encoding:
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BIT STRING tag;
BIT STRING length;
0 (indicating that there are zero unused bits in the final octet
of y); and
BIT STRING value field including y.
The key usage extension may optionally appear in a KEA certificate.
If a KEA certificate includes the keyUsage extension, only the fol-
lowing values may be asserted:
keyAgreement;
encipherOnly; and
decipherOnly.
If present, the keyUsage extension MUST assert keyAgreement and MAY
assert either encipherOnly and decipherOnly. The keyUsage extension
MUST NOT assert both encipherOnly and decipherOnly.
2.3.5 ECDSA and ECDH Keys
This section identifies the preferred OID and parameter encoding for
the inclusion of an ECDSA or ECDH public key in a certificate. The
Elliptic Curve Digital Signature Algorithm (ECDSA) is defined in
[X9.62]. ECDSA is the elliptic curve mathematical analog of the Dig-
ital Signature Algorithm [FIPS 186]. The Elliptic Curve Diffie Hell-
man (ECDH) algorithm is a key agreement algorithm defined in [X9.63].
ECDH is the elliptic curve mathemetical analog of the Diffie-Hellman
key agreement algorithm as specified in [X9.42]. These specifica-
tions use the same OIDs and parameter encodings. The ASN.1 object
identifiers used to identify these public keys are defined in the
following arc:
ansi-X9-62 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) us(840) 10045 }
When certificates contain an ECDSA or ECDH public key, the id-ecPub-
licKey algorithm identifier MUST be used. The id-ecPublicKey algo-
rithm identifier is defined as follows:
id-public-key-type OBJECT IDENTIFIER ::= { ansi-X9.62 2 }
id-ecPublicKey OBJECT IDENTIFIER ::= { id-publicKeyType 1 }
This OID is used in public key certificates for both ECDSA signature
keys and ECDH encryption keys. The intended application for the key
may be indicated in the key usage field (see [RFC XXXX]). The use of
a single key for both signature and encryption purposes is not
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recommended, but is not forbidden.
ECDSA and ECDH require use of certain parameters with the public key.
The parameters may be inherited from the issuer, implicitly included
through reference to a "named curve," or explicitly included in the
certificate.
ecpkParameters ::= CHOICE {
ecParameters ECParameters,
namedCurve OBJECT IDENTIFIER,
implicitlyCA NULL }
When the parameters are inherited, the parameters field shall contain
implictlyCA, which is the ASN.1 value NULL. When parameters are
specified by reference, the parameters field shall contain the named-
Curve choice, which is an object identifier. When the parameters are
explicitly included, they shall be encoded in the ASN.1 structure
ECParameters:
ECParameters ::= SEQUENCE {
version ECPVer, -- version is always 1
fieldID FieldID, -- identifies the finite field over
-- which the curve is defined
curve Curve, -- coefficients a and b of the
-- elliptic curve
base ECPoint, -- specifies the base point P
-- on the elliptic curve
order INTEGER, -- the order n of the base point
cofactor INTEGER OPTIONAL, -- The integer h = #E(Fq)/n
}
ECPVer ::= INTEGER {ecpVer1(1)}
Curve ::= SEQUENCE {
a FieldElement,
b FieldElement,
seed BIT STRING OPTIONAL }
FieldElement ::= OCTET STRING
ECPoint ::= OCTET STRING
The value of FieldElement shall be the octet string representation of
a field element following the conversion routine in [X9.62], Section
4.3.3. The value of ECPoint shall be the octet string representation
of an elliptic curve point following the conversion routine in
[X9.62], Section 4.3.6. Note that this octet string may represent an
elliptic curve point in compressed or uncompressed form.
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Implementations that support elliptic curve according to this speci-
fication MUST support the uncompressed form and MAY support the com-
pressed form.
The components of type ECParameters have the following meanings:
version specifies the version number of the elliptic curve parame-
ters. It MUST have the value 1 (ecpVer1).
fieldID identifies the finite field over which the elliptic curve
is defined. Finite fields are represented by values of the parame-
terized type FieldID, constrained to the values of the objects
defined in the information object set FieldTypes. Additional
detail regarding fieldID is provided below.
curve specifies the coefficients a and b of the elliptic curve E.
Each coefficient shall be represented as a value of type FieldEle-
ment, an OCTET STRING. seed is an optional parameter used to
derive the coefficients of a randomly generated elliptic curve.
base specifies the base point P on the elliptic curve. The base
point shall be represented as a value of type ECPoint, an OCTET
STRING.
order specifies the order n of the base point.
cofactor is the integer h = #E(Fq)/n. This parameter is specified
as OPTIONAL. However, the cofactor MUST be included in ECDH pub-
lic key parameters. The cofactor is not required to support
ECDSA, except in parameter validation. The cofactor MAY be
included to support parameter validation for ECDSA keys. Parame-
ter validation is not required by this specification.
The AlgorithmIdentifier within subjectPublicKeyInfo is the only place
within a certificate where the parameters may be used. If the ellip-
tic curve parameters are specified as implicitlyCA in the subjectPub-
licKeyInfo AlgorithmIdentifier and the CA signed the subject certifi-
cate using ECDSA, then the certificate issuer's ECDSA parameters
apply to the subject's ECDSA key. If the elliptic curve parameters
are specified as implicitlyCA in the subjectPublicKeyInfo AlgorithmI-
dentifier and the CA signed the certificate using a signature algo-
rithm other than ECDSA, then clients MUST not make use of the ellip-
tic curve public key.
FieldID ::= SEQUENCE {
fieldType OBJECT IDENTIFIER,
parameters ANY DEFINED BY fieldType
}
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FieldID is a SEQUENCE of two components, fieldType and parameters.
The fieldType contains an object identifier value that uniquely iden-
tifies the type contained in the parameters.
The object identifier id-fieldType specifies an arc containing the
object identifiers of each field type. It has the following value:
id-fieldType OBJECT IDENTIFIER ::= { ansi-X9-62 fieldType(1) }
The object identifiers prime-field and characteristic-two-field name
the two kinds of fields defined in this Standard. They have the fol-
lowing values:
prime-field OBJECT IDENTIFIER ::= { id-fieldType 1 }
Prime-p ::= INTEGER -- Field size p (p in bits)
characteristic-two-field OBJECT IDENTIFIER ::= { id-fieldType 2 }
Characteristic-two ::= SEQUENCE {
m INTEGER, -- Field size 2^m
basis OBJECT IDENTIFIER,
parameters ANY DEFINED BY basis
}
The object identifier id-characteristic-two-basis specifies an arc
containing the object identifiers for each type of basis for the
characteristic-two finite fields. It has the following value:
id-characteristic-two-basis OBJECT IDENTIFIER ::= {
characteristic-two-field basisType(1) }
The object identifiers gnBasis, tpBasis and ppBasis name the three
kinds of basis for characteristic-two finite fields defined by
[X9.62]. They have the following values:
gnBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 1 }
-- for gnBasis, the value of the parameters field is NULL
tpBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 2 }
-- type of parameters field for tpBasis is Trinomial
Trinomial ::= INTEGER
ppBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 3 }
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-- type of parameters field for ppBasis is Pentanomial
Pentanomial ::= SEQUENCE {
k1 INTEGER,
k2 INTEGER,
k3 INTEGER
}
The elliptic curve public key (an ECPoint which is an OCTET STRING)
is mapped to a subjectPublicKey (a BIT STRING) as follows: the most
significant bit of the OCTET STRING becomes the most significant bit
of the BIT STRING, and the least significant bit of the OCTET STRING
becomes the least significant bit of the BIT STRING. Note that this
octet string may represent an elliptic curve point in compressed or
uncompressed form. Implementations that support elliptic curve
according to this specification MUST support the uncompressed form
and MAY support the compressed form.
If the keyUsage extension is present in an end entity certificate
which conveys an elliptic curve public key, any combination of the
following values MAY be present:
digitalSignature;
nonRepudiation; and
keyAgreement.
If the keyAgreement value is present, either of the following values
MAY be present:
encipherOnly; and
decipherOnly.
The keyUsage extension MUST NOT assert both encipherOnly and deci-
pherOnly.
If the keyUsage extension is present in a CA certificate which con-
veys an elliptic curve public key, any combination of the following
values MAY be present:
digitalSignature;
nonRepudiation;
keyAgreement;
keyCertSign; and
cRLSign.
As above, if the keyUsage extension asserts keyAgreement then it MAY
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assert either encipherOnly and decipherOnly. However, this specifi-
cation RECOMMENDS that if keyCertSign or cRLSign is present, keyA-
greement, encipherOnly, and decipherOnly SHOULD NOT be present.
3 ASN.1 Module
PKIX1Algorithms88 { iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-pkix1-algorithms(17) }
DEFINITIONS EXPLICIT TAGS ::= BEGIN
-- EXPORTS All;
-- IMPORTS NONE;
----
---- DSA Keys and Signatures
----
-- OID for DSA public key
id-dsa OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) x9-57(10040) x9algorithm(4) 1 }
-- encoding for DSA public key
Dss-Parms ::= SEQUENCE {
p INTEGER,
q INTEGER,
g INTEGER }
-- OID for DSA signature generated with SHA-1 hash
id-dsa-with-sha1 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) x9-57 (10040) x9algorithm(4) 3 }
-- encoding for DSA signature generated with SHA-1 hash
Dss-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER }
----
---- RSA Keys and Signatures
----
----
-- arc for RSA public key and RSA signature OIDs
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pkcs-1 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) 1 }
-- OID for RSA public keys
rsaEncryption OBJECT IDENTIFIER ::= { pkcs-1 1 }
-- OID for RSA signature generated with MD2 hash
md2WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 2 }
-- OID for RSA signature generated with MD5 hash
md5WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 4 }
-- OID for RSA signature generated with SHA-1 hash
sha1WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 5 }
----
---- Diffie-Hellman Keys
----
----
dhpublicnumber OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) ansi-x942(10046) number-type(2) 1 }
DomainParameters ::= SEQUENCE {
p INTEGER, -- odd prime, p=jq +1
g INTEGER, -- generator, g
q INTEGER, -- factor of p-1
j INTEGER OPTIONAL, -- subgroup factor, j>= 2
validationParms ValidationParms OPTIONAL }
ValidationParms ::= SEQUENCE {
seed BIT STRING,
pgenCounter INTEGER }
----
---- KEA Keys
----
----
id-keyExchangeAlgorithm OBJECT IDENTIFIER ::=
{ 2 16 840 1 101 2 1 1 22 }
KEA-Parms-Id ::= OCTET STRING
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----
---- Elliptic Curve Keys, Signatures, and Curves
----
----
ansi-X9-62 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) 10045 }
FieldID ::= SEQUENCE { -- Finite field
fieldType OBJECT IDENTIFIER,
parameters ANY DEFINED BY fieldType
}
--
-- ECDSA signatures
--
--
-- Arc for ECDSA signature OIDS
id-ecSigType OBJECT IDENTIFIER ::= { ansi-X9-62 signatures(4) }
-- OID for ECDSA signatures with SHA-1
ecdsa-with-SHA1 OBJECT IDENTIFIER ::= { id-ecSigType 1 }
-- OID for an elliptic curve signature
-- format for the value of an ECDSA signature value
ECDSA-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER
}
--
-- Elliptic Curve Keys
--
--
-- recognized field type OIDs are defined in the following arc
id-fieldType OBJECT IDENTIFIER ::= { ansi-X9-62 fieldType(1) }
-- where fieldType is prime-field, the parameters are of type Prime-p
prime-field OBJECT IDENTIFIER ::= { id-fieldType 1 }
Prime-p ::= INTEGER -- Finite field F(p), where p is an odd prime
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-- where fieldType is characteristic-two-field, the parameters are
-- of type Characteristic-two
characteristic-two-field OBJECT IDENTIFIER ::= { id-fieldType 2 }
Characteristic-two ::= SEQUENCE {
m INTEGER, -- Field size 2^m
basis OBJECT IDENTIFIER,
parameters ANY DEFINED BY basis
}
-- recognized basis type OIDs are defined in the following arc
id-characteristic-two-basis OBJECT IDENTIFIER ::= {
characteristic-two-field basisType(3) }
-- gnbasis is identified by OID gnBasis and indicates
-- parameters are NULL
gnBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 1 }
-- parameters for this basis are NULL
-- trinomial basis is identified by OID tpBasis and indicates
-- parameters of type Pentanomial
tpBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 2 }
-- Trinomial basis representation of F2^m
-- Integer k for reduction polynomial xm + xk + 1
--
Trinomial ::= INTEGER
-- for pentanomial basis is identified by OID ppBasis and indicates
-- parameters of type Pentanomial
ppBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 3 }
Pentanomial ::= SEQUENCE {
--
-- Pentanomial basis representation of F2^m
-- reduction polynomial integers k1, k2, k3
-- f(x) = x**m + x**k3 + x**k2 + x**k1 + 1
--
k1 INTEGER,
k2 INTEGER,
k3 INTEGER
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}
-- The object identifiers gnBasis, tpBasis and ppBasis name
-- three kinds of basis for characteristic-two finite fields
FieldElement ::= OCTET STRING -- Finite field element
ECPoint ::= OCTET STRING -- Elliptic curve point
-- Elliptic Curve parameters may be specfied explicitly,
-- specified implicitly through a "named curve", or
-- inherited from the CA
ecpkParameters ::= CHOICE {
ecParameters ECParameters,
namedCurve OBJECT IDENTIFIER,
implicitlyCA NULL
}
ECParameters ::= SEQUENCE { -- Elliptic curve parameters
version ECPVer,
fieldID FieldID,
curve Curve,
base ECPoint, -- Base point G
order INTEGER, -- Order n of the base point
cofactor INTEGER OPTIONAL, -- The integer h = #E(Fq)/n
}
ECPVer ::= INTEGER {ecpVer1(1)}
Curve ::= SEQUENCE {
a FieldElement, -- Elliptic curve coefficient a
b FieldElement, -- Elliptic curve coefficient b
seed BIT STRING OPTIONAL
}
id-publicKeyType OBJECT IDENTIFIER ::= { ansi-X9-62 keyType(2) }
id-ecPublicKey OBJECT IDENTIFIER ::= { id-publicKeyType 1 }
-- Named Elliptic Curves
--
-- Standards bodies may define OIDs to represent common
-- elliptic curve parameters. Users are encouraged
-- to consult relevant standards and specifications to
-- determine which OIDs (if any) are appropriate for their
-- applications.
-- The following OIDS are defined in ANSI X9.62.
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ellipticCurve OBJECT IDENTIFIER ::= { ansi-X9-62 curves(3) }
c-TwoCurve OBJECT IDENTIFIER ::= {
ellipticCurve characteristicTwo(0) }
primeCurve OBJECT IDENTIFIER ::= { ellipticCurve prime(1) }
c2pnb163v1 OBJECT IDENTIFIER ::= { c-TwoCurve 1 }
c2pnb163v2 OBJECT IDENTIFIER ::= { c-TwoCurve 2 }
c2pnb163v3 OBJECT IDENTIFIER ::= { c-TwoCurve 3 }
c2pnb176w1 OBJECT IDENTIFIER ::= { c-TwoCurve 4 }
c2tnb191v1 OBJECT IDENTIFIER ::= { c-TwoCurve 5 }
c2tnb191v2 OBJECT IDENTIFIER ::= { c-TwoCurve 6 }
c2tnb191v3 OBJECT IDENTIFIER ::= { c-TwoCurve 7 }
c2onb191v4 OBJECT IDENTIFIER ::= { c-TwoCurve 8 }
c2onb191v5 OBJECT IDENTIFIER ::= { c-TwoCurve 9 }
c2pnb208w1 OBJECT IDENTIFIER ::= { c-TwoCurve 10 }
c2tnb239v1 OBJECT IDENTIFIER ::= { c-TwoCurve 11 }
c2tnb239v2 OBJECT IDENTIFIER ::= { c-TwoCurve 12 }
c2tnb239v3 OBJECT IDENTIFIER ::= { c-TwoCurve 13 }
c2onb239v4 OBJECT IDENTIFIER ::= { c-TwoCurve 14 }
c2onb239v5 OBJECT IDENTIFIER ::= { c-TwoCurve 15 }
c2pnb272w1 OBJECT IDENTIFIER ::= { c-TwoCurve 16 }
c2pnb304w1 OBJECT IDENTIFIER ::= { c-TwoCurve 17 }
c2tnb359v1 OBJECT IDENTIFIER ::= { c-TwoCurve 18 }
c2pnb368w1 OBJECT IDENTIFIER ::= { c-TwoCurve 19 }
c2tnb431r1 OBJECT IDENTIFIER ::= { c-TwoCurve 20 }
prime192v1 OBJECT IDENTIFIER ::= { primeCurve 1 }
prime192v2 OBJECT IDENTIFIER ::= { primeCurve 2 }
prime192v3 OBJECT IDENTIFIER ::= { primeCurve 3 }
prime239v1 OBJECT IDENTIFIER ::= { primeCurve 4 }
prime239v2 OBJECT IDENTIFIER ::= { primeCurve 5 }
prime239v3 OBJECT IDENTIFIER ::= { primeCurve 6 }
prime256v1 OBJECT IDENTIFIER ::= { primeCurve 7 }
END
4 References
[FIPS 180-1] Federal Information Processing Standards Publication
(FIPS PUB) 180-1, Secure Hash Standard, 17 April 1995.
[Supersedes FIPS PUB 180 dated 11 May 1993.]
[FIPS 186-2] Federal Information Processing Standards Publication
(FIPS PUB) 186, Digital Signature Standard, 27 January
2000. [Supersedes FIPS PUB 186-1 dated 15 December 1998.]
Bassham, Housley & Polk [Page 23]
INTERNET DRAFT July, 2001
[P1363] IEEE P1363, "Standard Specifications for Public-Key
Cryptography", 2001.
[RC95] Rogier, N. and Chauvaud, P., "The compression function of
MD2 is not collision free," Presented at Selected Areas in
Cryptography '95, May 1995.
[RFC 1034] P.V. Mockapetris, "Domain names - concepts and
facilities", November 1987.
[RFC 1319] Kaliski, B., "The MD2 Message-Digest Algorithm," RFC 1319,
RSA Laboratories, April 1992.
[RFC 1321] Rivest, R., "The MD5 Message-Digest Algorithm," RFC 1321,
MIT and RSA Data Security, April 1992.
[RFC 1422] Kent, S., "Privacy Enhancement for Internet Electronic
Mail: Part II: Certificate-Based Key Management," RFC
1422, BBN Communications, February 1993.
[RFC 1423] Balenson, D., "Privacy Enhancement for Internet Electronic
Mail: Part III: Algorithms, Modes, and Identifiers,"
RFC 1423, Trusted Information Systems, February 1993.
[RFC 2119] S. Bradner, "Key Words for Use in RFCs to Indicate
Requirement Levels", RFC 2219, Harvard University, March
1997.
[RFC 2313] B. Kaliski, "PKCS #1: RSA Encryption Version 1.5",
RFC 2313, March 1998.
[RFC 2459] R. Housley, W. Ford, W. Polk and D. Solo "Internet X.509
Public Key Infrastructure: Certificate and CRL Profile",
January, 1999.
[SDN.701r] SDN.701, "Message Security Protocol 4.0", Revision A
1997-02-06.
[X.208] CCITT Recommendation X.208: Specification of Abstract
Syntax Notation One (ASN.1), 1988.
[X9.42] ANSI X9.42-2000, "Public Key Cryptography for The Financial
Services Industry: Agreement of Symmetric Keys Using
Discrete Logarithm Cryptography", December, 1999.
[X9.62] X9.62-1998, "Public Key Cryptography For The Financial
Services Industry: The Elliptic Curve Digital Signature
Algorithm (ECDSA)", January 7, 1999.
Bassham, Housley & Polk [Page 24]
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[X9.63] ANSI X9.63-2001, "Public Key Cryptography For The Financial
Services Industry: Key Agreement and Key Transport
Using Elliptic Curve Cryptography" (Working Draft),
May 8, 2001.
5 Security Considerations
This specification does not constrain the size of public keys or
their parameters for use in the Internet PKI. However, the key size
selected impacts the strength achieved when implementing crypto-
graphic services. Selection of appropriate key sizes is critical to
implementing appropriate security.
This specification does not identify particular elliptic curves for
use in the Internet PKI. However, the particular curve selected
impact the the strength of the digital signatures. Some curves are
cryptographically stronger than others!
In general, use of "well-known" curves, such as the "named curves"
from ANSI X9.62 is a sound strategy. For additional information,
refer to X9.62 Appendix H.1.3, "Key Length Considerations" and
Appendix A.1, "Avoiding Cryptographically Weak Keys".
This specification supplements RFC XXXX. The security considerations
section of that document applies to this specification as well.
6 Intellectual Property Rights
The IETF has been notified of intellectual property rights claimed in
regard to some or all of the specification contained in this docu-
ment. For more information consult the online list of claimed
rights.
The IETF takes no position regarding the validity or scope of any
intellectual property or other rights that might be claimed to per-
tain to the implementation or use of the technology described in this
document or the extent to which any license under such rights might
or might not be available; neither does it represent that it has made
any effort to identify any such rights. Information on the IETF's
procedures with respect to rights in standards-track and standards-
related documentation can be found in BCP-11. Copies of claims of
rights made available for publication and any assurances of licenses
to be made available, or the result of an attempt made to obtain a
general license or permission for the use of such proprietary rights
by implementors or users of this specification can be obtained from
the IETF Secretariat.
Bassham, Housley & Polk [Page 25]
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7 Author Addresses:
Larry Bassham
NIST
100 Bureau Drive, Stop 8930
Gaithersburg, MD 20899-8930
USA
lbassham@nist.gov
Russell Housley
RSA Laboratories
918 Spring Knoll Drive
Herndon, VA 20170
USA
rhousley@rsasecurity.com
Tim Polk
NIST
100 Bureau Drive, Stop 8930
Gaithersburg, MD 20899-8930
USA
tim.polk@nist.gov
8 Full Copyright Statement
Copyright (C) The Internet Society (date). All Rights Reserved.
This document and translations of it may be copied and furnished to
others, and derivative works that comment on or otherwise explain it
or assist in its implementation may be prepared, copied, published
and distributed, in whole or in part, without restriction of any
kind, provided that the above copyright notice and this paragraph are
included on all such copies and derivative works. In addition, the
ASN.1 modules presented in Appendices A and B may be used in whole or
in part without inclusion of the copyright notice. However, this
document itself may not be modified in any way, such as by removing
the copyright notice or references to the Internet Society or other
Internet organizations, except as needed for the purpose of develop-
ing Internet standards in which case the procedures for copyrights
defined in the Internet Standards process shall be followed, or as
required to translate it into languages other than English.
The limited permissions granted above are perpetual and will not be
revoked by the Internet Society or its successors or assigns. This
document and the information contained herein is provided on an "AS
IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING TASK
FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT
LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION HEREIN WILL
Bassham, Housley & Polk [Page 26]
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NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF MERCHANTABILITY
OR FITNESS FOR A PARTICULAR PURPOSE.
Bassham, Housley & Polk [Page 27]
