PKIX Working Group L. Bassham (NIST) Internet Draft R. Housley (SPYRUS) expires September, 2001 W. Polk (NIST) March, 2001 Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and CRL Profile <draft-ietf-pkix-ipki-pkalgs-02.txt> Status of this Memo This document is an Internet-Draft and is in full conformance with all provisions of Section 10 of RFC 2026. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as Internet-Drafts. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at http://www.ietf.org/ietf/1id-abstracts.txt. The list of Internet-Drafts Shadow Directories can be accessed at http://www.ietf.org/shadow.html. 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. Bassham, Housley & Polk [Page 1]

INTERNET DRAFT March, 2001 Table Of Contents 1 Introduction ................................................ 3 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 ............................. 7 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 ............................................ 25 8 Full Copyright Statement .................................... 26 Bassham, Housley & Polk [Page 2]

INTERNET DRAFT March, 2001 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 gen- eration 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 appropriate 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. The section describes one-way hash functions and digital signature algorithms which may be used to sign certificates and CRLs, and identifies OIDs for public keys contained in a certificate. Conforming CAs and applications are not required to support the Bassham, Housley & Polk [Page 3]

INTERNET DRAFT March, 2001 algorithms or algorithm identifiers described in this section. How- ever, conforming CAs and applications that use the algorithms identi- fied here MUST support them as specified. 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- commercial 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]. Bassham, Housley & Polk [Page 4]

INTERNET DRAFT March, 2001 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 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: Bassham, Housley & Polk [Page 5]

INTERNET DRAFT March, 2001 md5WithRSAEncryption OBJECT IDENTIFIER ::= { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1) 4 } 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. The following OID MUST be used to specify the SHA-1 one- way hash function when performing the data encoding step: id-sha1 OBJECT IDENTIFIER ::= { iso(1) identified-organization(3) oiw(14) secsig(3) algorithms(2) 26 } 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 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 Bassham, Housley & Polk [Page 6]

INTERNET DRAFT March, 2001 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 is used the parameters MUST be NULL. 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. Bassham, Housley & Polk [Page 7]

INTERNET DRAFT March, 2001 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 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; Bassham, Housley & Polk [Page 8]

INTERNET DRAFT March, 2001 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, g INTEGER } If the DSA algorithm parameters are absent from the subjectPublicKey- Info AlgorithmIdentifier 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 absent from the subjectPublicKeyInfo AlgorithmIdentifier and the CA signed the sub- ject certificate using a signature algorithm other than DSA, then the subject's DSA domain parameters are distributed by other means. If the subjectPublicKeyInfo AlgorithmIdentifier field omits the parame- ters component and the CA signed the subject with a signature algo- rithm other than DSA, then clients MUST reject the certificate. The AlgorithmIdentifier within subjectPublicKeyInfo is the only place within a certificate where the parameters may be used. If the DSA Bassham, Housley & Polk [Page 9]

INTERNET DRAFT March, 2001 domain parameters are absent from the subjectPublicKeyInfo Algorith- mIdentifier and the CA signed the subject certificate using DSA, then the certificate issuer's DSA domain parameters apply to the subject's DSA key. If the DSA domain parameters are absent from the sub- jectPublicKeyInfo AlgorithmIdentifier and the CA signed the certifi- cate using a signature algorithm other than DSA, then clients shall not validate the certificate. When signing, 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 are ASN.1 encoded using the following ASN.1 structure: Dss-Sig-Value ::= SEQUENCE { r INTEGER, s INTEGER } The encoded signature is conveyed as the value of the BIT STRING sig- nature in a Certificate or CertificateList. 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 The key usage extension MAY optionally appear in certificates which convey a DSA public key. If a certificate containing a DSA public key includes the keyUsage extension, only the following values may be asserted: digitalSignature; nonRepudiation; keyCertSign; and cRLSign. These values MAY be asserted in any combination. However, the key- CertSign and cRLSign values MAY only be asserted if the basicCon- straints extension is present and cA is TRUE. 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 } Bassham, Housley & Polk [Page 10]

INTERNET DRAFT March, 2001 The dhpublicnumber OID is intended to be used in the algorithm field 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 Bassham, Housley & Polk [Page 11]

INTERNET DRAFT March, 2001 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. 2.3.4 KEA Public Keys This section identifies the preferred OID and parameters for the inclusion of a KEA public key in a certificate. Conforming CAs MUST use the identified OID when issuing certificates containing public keys for the KEA algorithm. Conforming applications supporting the KEA algorithm MUST, at a minimum, recognize the OID identified in this section. The Key Exchange Algorithm (KEA) is a key agreement algorithm. Two parties may generate a "pairwise key" if and only if they share the same KEA parameters. The KEA parameters are not included in a certi- ficate; 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- Bassham, Housley & Polk [Page 12]

INTERNET DRAFT March, 2001 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: 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. Con- forming CAs MUST use these object identifiers and data formats when issuing certificates conveying an ECDSA or ECDH public key. Conform- ing applications MUST recognize the object identifiers and process the data formats when processing such certificates. The Elliptic Curve Digital Signature Algorithm (ECDSA) is defined in [X9.62]. ECDSA is the elliptic curve mathematical analog of the Digital Signature Algorithm [FIPS 186]. The Elliptic Curve Diffie Hellman (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 specifications 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 } Bassham, Housley & Polk [Page 13]

INTERNET DRAFT March, 2001 When certificates contain an ECDSA or ECDH public key, the id- ecPublicKey algorithm identifier MUST be used. The id-ecPublicKey algorithm 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 recom- mended, 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, Bassham, Housley & Polk [Page 14]

INTERNET DRAFT March, 2001 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. Implementa- tions that support elliptic curve according to this specification MUST support the uncompressed form and MAY support the compressed 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 parameterized type FieldID, constrained to the values of the objects defined in the information object set FieldTypes. Addi- tional 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. Parameter 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 Bassham, Housley & Polk [Page 15]

INTERNET DRAFT March, 2001 elliptic curve parameters are specified as implicitlyCA in the sub- jectPublicKeyInfo AlgorithmIdentifier and the CA signed the subject certificate using ECDSA, then the certificate issuer's ECDSA parame- ters apply to the subject's ECDSA key. If the elliptic curve parame- ters are specified as implicitlyCA in the subjectPublicKeyInfo Algor- ithmIdentifier and the CA signed the certificate using a signature algorithm other than ECDSA, then clients MUST not make use of the elliptic curve public key. FieldID ::= SEQUENCE { fieldType OBJECT IDENTIFIER, parameters ANY DEFINED BY fieldType } 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 Bassham, Housley & Polk [Page 16]

INTERNET DRAFT March, 2001 [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 } -- 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. The key usage extension may optionally appear in certificates which convey an ECDSA public key. If a certificate containing an ECDSA public key includes the keyUsage extension, only the following values may be asserted: digitalSignature; nonRepudiation; keyCertSign; and cRLSign. These values MAY be asserted in any combination. However, the key- CertSign and cRLSign values MAY only be asserted if the basicCon- straints extension is present and cA is TRUE. The key usage extension may optionally appear in certificates which convey an ECDH public key. If a certificate containing an ECDH pub- lic key includes the keyUsage extension, only the following values may be asserted: keyAgreement; Bassham, Housley & Polk [Page 17]

INTERNET DRAFT March, 2001 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. 3 ASN.1 Module PKIX1Algorithms88 { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-algorithms-88(?) } 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 ---- ---- Bassham, Housley & Polk [Page 18]

INTERNET DRAFT March, 2001 -- arc for RSA public key and RSA signature OIDs 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 } 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 Bassham, Housley & Polk [Page 19]

INTERNET DRAFT March, 2001 ---- ---- ECDSA 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 } -- 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 -- 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 Bassham, Housley & Polk [Page 20]

INTERNET DRAFT March, 2001 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 } -- The object identifiers gnBasis, tpBasis and ppBasis name -- three kinds of basis for characteristic-two finite fields FieldElement ::= OCTET STRING -- Finite field element Bassham, Housley & Polk [Page 21]

INTERNET DRAFT March, 2001 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. ellipticCurve OBJECT IDENTIFIER ::= { ansi-X9-62 curves(3) } c-TwoCurve OBJECT IDENTIFIER ::= { ellipticCurve characteristicTwo(0) } primeCurve OBJECT IDENTIFIER ::= { ellipticCurve prime(1) } Bassham, Housley & Polk [Page 22]

INTERNET DRAFT March, 2001 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] Federal Information Processing Standards Publication (FIPS PUB) 186, Digital Signature Standard, 18 May 1994. [P1363] IEEE P1363, "Standard for Public-Key Cryptography", draft standard, 1997. [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 Bassham, Housley & Polk [Page 23]

INTERNET DRAFT March, 2001 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" (Working Draft), 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. [X9.63] ANSI X9.63-199x, "Public Key Cryptography For The Financial Services Industry: Key Agreement and Key Transport Using Elliptic Curve Cryptography" (Working Draft). Bassham, Housley & Polk [Page 24]

INTERNET DRAFT March, 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 Appen- dix 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. 7 Author Addresses: Larry Bassham NIST 100 Bureau Drive, Stop 8930 Gaithersburg, MD 20899-8930 Bassham, Housley & Polk [Page 25]

INTERNET DRAFT March, 2001 USA lbassham@nist.gov Russ Housley SPYRUS 381 Elden Street Suite 1120 Herndon, VA 20170 housley@spyrus.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 NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Bassham, Housley & Polk [Page 26]