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Internet Engineering Task Force (IETF) J. SchaadRequest for Comments: 6955 Soaring Hawk ConsultingObsoletes:2875 H. PrafullchandraCategory: Standards Track HyTrust, Inc.ISSN: 2070-1721 May 2013Diffie-Hellman Proof-of-Possession AlgorithmsAbstract This document describes two methods for producing an integrity check value from a Diffie-Hellman key pair and one method for producing an integrity check value from an Elliptic Curve key pair. This behavior is needed for such operations as creating the signature of a Public- Key Cryptography Standards (PKCS) #10 Certification Request. These algorithms are designed to provide a Proof-of-Possession of the private key and not to be a general purpose signing algorithm. This document obsoletesRFC 2875.Status of This Memo This is an Internet Standards Track document. This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Further information on Internet Standards is available inSection 2 of RFC 5741. Information about the current status of this document, any errata, and how to provide feedback on it may be obtained athttp://www.rfc-editor.org/info/rfc6955.Schaad & Prafullchandra Standards Track [Page 1]
RFC 6955 DH POP Algorithms May 2013Copyright Notice Copyright (c) 2013 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject toBCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. This document may contain material from IETF Documents or IETF Contributions published or made publicly available before November 10, 2008. The person(s) controlling the copyright in some of this material may not have granted the IETF Trust the right to allow modifications of such material outside the IETF Standards Process. Without obtaining an adequate license from the person(s) controlling the copyright in such materials, this document may not be modified outside the IETF Standards Process, and derivative works of it may not be created outside the IETF Standards Process, except to format it for publication as an RFC or to translate it into languages other than English.Schaad & Prafullchandra Standards Track [Page 2]
RFC 6955 DH POP Algorithms May 2013Table of Contents1. Introduction ....................................................31.1. Changes sinceRFC 2875 .....................................41.2. Requirements Terminology ...................................52. Terminology .....................................................53. Notation ........................................................54. Static DH Proof-of-Possession Process ...........................64.1. ASN.1 Encoding .............................................85. Discrete Logarithm Signature ...................................115.1. Expanding the Digest Value ................................115.2. Signature Computation Algorithm ...........................125.3. Signature Verification Algorithm ..........................135.4. ASN.1 Encoding ............................................146. Static ECDH Proof-of-Possession Process ........................166.1. ASN.1 Encoding ............................................187. Security Considerations ........................................208. References .....................................................218.1. Normative References ......................................218.2. Informative References ....................................21Appendix A. ASN.1 Modules .........................................23A.1. 2008 ASN.1 Module ..........................................23A.2. 1988 ASN.1 Module ..........................................28Appendix B. Example of Static DH Proof-of-Possession ..............30Appendix C. Example of Discrete Log Signature .....................381. Introduction Among the responsibilities of a Certification Authority (CA) in issuing certificates is a requirement that it verifies the identity for the entity to which it is issuing a certificate and that the private key for the public key to be placed in the certificate is in the possession of that entity. The process of validating that the private key is held by the requester of the certificate is called Proof-of-Possession (POP). Further details on why POP is important can be found inAppendix C of RFC 4211 [CRMF]. This document is designed to deal with the problem of how to support POP for encryption-only keys. PKCS #10 [RFC2986] and the Certificate Request Message Format (CRMF) [CRMF] both define syntaxes for Certification Requests. However, while CRMF supports an alternative method to support POP for encryption-only keys, PKCS #10 does not. PKCS #10 assumes that the public key being requested for certification corresponds to an algorithm that is capable of producing a POP by a signature operation. Diffie-Hellman (DH) and Elliptic Curve Diffie-Hellman (ECDH) are key agreement algorithms and, as such, cannot be directly used for signing or encryption.Schaad & Prafullchandra Standards Track [Page 3]
RFC 6955 DH POP Algorithms May 2013 This document describes a set of three POP algorithms. Two methods use the key agreement process (one for DH and one for ECDH) to provide a shared secret as the basis of an integrity check value. For these methods, the value is constructed for a specific recipient/ verifier by using a public key of that verifier. The third method uses a modified signature algorithm (for DH). This method allows for arbitrary verifiers. It should be noted that we did not create an algorithm that parallels the Elliptical Curve Digital Signature Algorithm (ECDSA) as was done for the Digital Signature Algorithm (DSA). When using ECDH, the common practice is to use one of a set of predefined curves; each of these curves has been designed to be paired with one of the commonly used hash algorithms. This differs in practice from the DH case where the common practice is to generate a set of group parameters, either on a single machine or for a given community, that are aligned to encryption algorithms rather than hash algorithms. The implication is that, if a key has the ability to perform the modified DSA algorithm for ECDSA, it should be able to use the correct hash algorithm and perform the regular ECDSA signature algorithm with the correctly sized hash.1.1. Changes sinceRFC 2875 The following changes have been made: o The Static DH POP algorithm has been rewritten for parameterization of the hash algorithm and the Message Authentication Code (MAC) algorithm. o New instances of the Static DH POP algorithm have been created using the Hashed Message Authentication Code (HMAC) paired with the SHA-224, SHA-256, SHA-384, and SHA-512 hash algorithms. However, the current SHA-1 algorithm remains identical. o The Discrete Logarithm Signature algorithm has been rewritten for parameterization of the hash algorithm. o New instances of the Discrete Logarithm Signature have been created for the SHA-224, SHA-256, SHA-384, and SHA-512 hash functions. However, the current SHA-1 algorithm remains identical. o A new Static ECDH POP algorithm has been added. o New instances of the Static ECDH POP algorithm have been created using HMAC paired with the SHA-224, SHA-256, SHA-384, and SHA-512 hash functions.Schaad & Prafullchandra Standards Track [Page 4]
RFC 6955 DH POP Algorithms May 20131.2. Requirements Terminology 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 [RFC2119]. When the words are in lower case they have their natural language meaning.2. Terminology The following definitions will be used in this document: DH certificate = a certificate whose SubjectPublicKey is a DH public value and is signed with any signature algorithm (e.g., RSA or DSA). ECDH certificate = a certificate whose SubjectPublicKey is an ECDH public value and is signed with any signature algorithm (e.g., RSA or ECDSA). Proof-of-Possession (POP) = a means that provides a method for a second party to perform an algorithm to establish with some degree of assurance that the first party does possess and has the ability to use a private key. The reasoning behind doing POP can be found inAppendix C in [CRMF].3. Notation This section describes mathematical notations, conventions, and symbols used throughout this document. a | b : Concatenation of a and b a ^ b : a raised to the power of b a mod b : a modulo b a / b : a divided by b using integer division a * b : a times b Depending on context, multiplication may be within an EC or normal multiplication KDF(a) : Key Derivation Function producing a value from a MAC(a, b) : Message Authentication Code function where a is the key and b is the text LEFTMOST(a, b) : Return the b left most bits of a FLOOR(a) : Return n where n is the largest integer such that n <= aSchaad & Prafullchandra Standards Track [Page 5]
RFC 6955 DH POP Algorithms May 2013 Details on how to implement the HMAC version of a MAC function used in this document can be found inRFC 2104 [RFC2104],RFC 6234 [RFC6234], andRFC 4231 [RFC4231].4. Static DH Proof-of-Possession Process The Static DH POP algorithm is set up to use a Key Derivation Function (KDF) and a MAC. This algorithm requires that a common set of group parameters be used by both the creator and verifier of the POP value. The steps for creating a DH POP are: 1. An entity (E) chooses the group parameters for a DH key agreement. This is done simply by selecting the group parameters from a certificate for the recipient of the POP process. A certificate with the correct group parameters has to be available. Let the common DH parameters be g and p; and let the DH key pair from the certificate be known as the recipient (R) key pair (Rpub and Rpriv). Rpub = g^x mod p (where x=Rpriv, the private DH value) 2. The entity generates a DH public/private key pair using the group parameters from step 1. For an entity (E): Epriv = DH private value = y Epub = DH public value = g^y mod pSchaad & Prafullchandra Standards Track [Page 6]
RFC 6955 DH POP Algorithms May 2013 3. The POP computation process will then consist of the following steps: (a) The value to be signed (text) is obtained. (For a PKCS #10 object, the value is the DER-encoded certificationRequestInfo field represented as an octet string.) (b) A shared DH secret is computed as follows: shared secret = ZZ = g^(x*y) mod p [This is done by E as Rpub^y and by the recipient as Epub^x, where Rpub is retrieved from the recipient's DH certificate (or is provided in the protocol) and Epub is retrieved from the Certification Request.] (c) A temporary key K is derived from the shared secret ZZ as follows: K = KDF(LeadingInfo | ZZ | TrailingInfo) LeadingInfo ::= Subject Distinguished Name from recipient's certificate TrailingInfo ::= Issuer Distinguished Name from recipient's certificate (d) Using the defined MAC function, compute MAC(K, text). The POP verification process requires the recipient to carry out steps (a) through (d) and then simply compare the result of step (d) with what it received as the signature component. If they match, then the following can be concluded: (a) The entity possesses the private key corresponding to the public key in the Certification Request because it needs the private key to calculate the shared secret; and (b) Only the recipient that the entity sent the request to could actually verify the request because it would require its own private key to compute the same shared secret. In the case where the recipient is a CA, this protects the entity from rogue CAs.Schaad & Prafullchandra Standards Track [Page 7]
RFC 6955 DH POP Algorithms May 20134.1. ASN.1 Encoding The algorithm outlined above allows for the use of an arbitrary hash function in computing the temporary key and the MAC algorithm. In this specification, we define object identifiers for the SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512 hash values and use HMAC for the MAC algorithm. The ASN.1 structures associated with the Static DH POP algorithm are: DhSigStatic ::= SEQUENCE { issuerAndSerial IssuerAndSerialNumber OPTIONAL, hashValue MessageDigest } sa-dhPop-static-sha1-hmac-sha1 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-dhPop-static-sha1-hmac-sha1 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } } id-dh-sig-hmac-sha1 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 3 } id-dhPop-static-sha1-hmac-sha1 OBJECT IDENTIFIER ::= id-dh-sig-hmac-sha1 sa-dhPop-static-sha224-hmac-sha224 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-static-sha224-hmac-sha224 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } } id-alg-dhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 15 } sa-dhPop-static-sha256-hmac-sha256 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-static-sha256-hmac-sha256 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } }Schaad & Prafullchandra Standards Track [Page 8]
RFC 6955 DH POP Algorithms May 2013 id-alg-dhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 16 } sa-dhPop-static-sha384-hmac-sha384 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-static-sha384-hmac-sha384 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } } id-alg-dhPop-static-sha384-hmac-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 17 } sa-dhPop-static-sha512-hmac-sha512 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-static-sha512-hmac-sha512 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } } id-alg-dhPop-static-sha512-hmac-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 18 } In the above ASN.1, the following items are defined: DhSigStatic This ASN.1 type structure holds the information describing the signature. The structure has the following fields: issuerAndSerial This field contains the issuer name and serial number of the certificate from which the public key was obtained. The issuerAndSerial field is omitted if the public key did not come from a certificate. hashValue This field contains the result of the MAC operation in step 3(d) (Section 4). sa-dhPop-static-sha1-hmac-sha1 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing a signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent.Schaad & Prafullchandra Standards Track [Page 9]
RFC 6955 DH POP Algorithms May 2013 id-dhPop-static-sha1-hmac-sha1 This OID identifies the Static DH POP algorithm that uses SHA-1 as the KDF and HMAC-SHA1 as the MAC function. The new OID was created for naming consistency with the other OIDs defined here. The value of the OID is the same value as id-dh-sig-hmac-sha1, which was defined in the previous version of this document [RFC2875]. sa-dhPop-static-sha224-hmac-sha224 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent. id-dhPop-static-sha224-hmac-sha224 This OID identifies the Static DH POP algorithm that uses SHA-224 as the KDF and HMAC-SHA224 as the MAC function. sa-dhPop-static-sha256-hmac-sha256 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent. id-dhPop-static-sha256-hmac-sha256 This OID identifies the Static DH POP algorithm that uses SHA-256 as the KDF and HMAC-SHA256 as the MAC function. sa-dhPop-static-sha384-hmac-sha384 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent. id-dhPop-static-sha384-hmac-sha384 This OID identifies the Static DH POP algorithm that uses SHA-384 as the KDF and HMAC-SHA384 as the MAC function. sa-dhPop-static-sha512-hmac-sha512 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent. id-dhPop-static-sha512-hmac-sha512 This OID identifies the Static DH POP algorithm that uses SHA-512 as the KDF and HMAC-SHA512 as the MAC function.Schaad & Prafullchandra Standards Track [Page 10]
RFC 6955 DH POP Algorithms May 20135. Discrete Logarithm Signature When a single set of parameters is used for a large group of keys, the chance that a collision will occur in the set of keys, either by accident or design, increases as the number of keys used increases. A large number of keys from a single parameter set also encourages the use of brute force methods of attack, as the entire set of keys in the parameters can be attacked in a single operation rather than having to attack each key parameter set individually. For this reason, we need to create a POP for DH keys that does not require the use of a common set of parameters. This POP algorithm is based on DSA, but we have removed the restrictions dealing with the hash and key sizes imposed by the [FIPS-186-3] standard. The use of this method does impose some additional restrictions on the set of keys that may be used; however, if the key-generation algorithm documented in [RFC2631] is used, the required restrictions are met. The additional restrictions are the requirement for the existence of a q parameter. Adding the q parameter is generally accepted as a good practice, as it allows for checking of small subgroup attacks. The following definitions are used in the rest of this section: p is a large prime g = h^((p-1)/q) mod p, where h is any integer 1 < h < p-1 such that h^((p-1)/q) mod p > 1 (g has order q mod p) q is a large prime j is a large integer such that p = q*j + 1 x is a randomly or pseudo-randomly generated integer with 1 < x < q y = g^x mod p HASH is a hash function such that b = the output size of HASH in bits Note: These definitions match the ones in [RFC2631].5.1. Expanding the Digest Value Besides the addition of a q parameter, [FIPS-186-3] also imposes size restrictions on the parameters. The length of q must be 160 bits (matching the output length of the SHA-1 digest algorithm), and the length of p must be 1024 bits. The size restriction on p is eliminated in this document, but the size restriction on q is replaced with the requirement that q must be at least b bits in length. (If the hash function is SHA-1, then b=160 bits and the size restriction on b is identical with that in [FIPS-186-3].) Given thatSchaad & Prafullchandra Standards Track [Page 11]
RFC 6955 DH POP Algorithms May 2013 there is not a random length-hashing algorithm, a hash value of the message will need to be derived such that the hash is in the range from 0 to q-1. If the length of q is greater than b, then a method must be provided to expand the hash. The method for expanding the digest value used in this section does not provide any additional security beyond the b bits provided by the hash algorithm. For this reason, the hash algorithm should be the largest size possible to match q. The value being signed is increased mainly to enhance the difficulty of reversing the signature process. This algorithm produces m, the value to be signed. Let L = the size of q (i.e., 2^L <= q < 2^(L+1)). Let M be the original message to be signed. Let b be the length of HASH output. 1. Compute d = HASH(M), the digest of the original message. 2. If L == b, then m = d. 3. If L > b, then follow steps (a) through (d) below. (a) Set n = FLOOR(L / b) (b) Set m = d, the initial computed digest value (c) For i = 0 to n - 1 m = m | HASH(m) (d) m = LEFTMOST(m, L-1) Thus, the final result of the process meets the criteria that 0 <= m < q.5.2. Signature Computation Algorithm The signature algorithm produces the pair of values (r, s), which is the signature. The signature is computed as follows: Given m, the value to be signed, as well as the parameters defined earlier inSection 5: 1. Generate a random or pseudo-random integer k, such that 0 < k-1 < q. 2. Compute r = (g^k mod p) mod q.Schaad & Prafullchandra Standards Track [Page 12]
RFC 6955 DH POP Algorithms May 2013 3. If r is zero, repeat from step 1. 4. Compute s = ((k^-1) * (m + x*r)) mod q. 5. If s is zero, repeat from step 1.5.3. Signature Verification Algorithm The signature verification process is far more complicated than is normal for DSA, as some assumptions about the validity of parameters cannot be taken for granted. Given a value m to be validated, the signature value pair (r, s) and the parameters for the key: 1. Perform a strong verification that p is a prime number. 2. Perform a strong verification that q is a prime number. 3. Verify that q is a factor of p-1; if any of the above checks fail, then the signature cannot be verified and must be considered a failure. 4. Verify that r and s are in the range [1, q-1]. 5. Compute w = (s^-1) mod q. 6. Compute u1 = m*w mod q. 7. Compute u2 = r*w mod q. 8. Compute v = ((g^u1 * y^u2) mod p) mod q. 9. Compare v and r; if they are the same, then the signature verified correctly.Schaad & Prafullchandra Standards Track [Page 13]
RFC 6955 DH POP Algorithms May 20135.4. ASN.1 Encoding The signature algorithm is parameterized by the hash algorithm. The ASN.1 structures associated with the Discrete Logarithm Signature algorithm are: sa-dhPop-SHA1 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dh-pop VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha1 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha1 OBJECT IDENTIFIER ::= id-alg-dh-pop id-alg-dh-pop OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 4 } sa-dhPop-sha224 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-sha224 VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha224 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 5 } sa-dhPop-sha256 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-sha256 VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha256 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 6 }Schaad & Prafullchandra Standards Track [Page 14]
RFC 6955 DH POP Algorithms May 2013 sa-dhPop-sha384 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-sha384 VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha384 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 7 } sa-dhPop-sha512 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-sha512 VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha512 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 8 } In the above ASN.1, the following items are defined: sa-dhPop-sha1 A SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DSA-Sig-Value represents the signature value, and the structure DomainParameters SHOULD be omitted in the signature but MUST be present in the associated key request. id-alg-dhPop-sha1 This OID identifies the Discrete Logarithm Signature using SHA-1 as the hash algorithm. The new OID was created for naming consistency with the others defined here. The value of the OID is the same as id-alg-dh-pop, which was defined in the previous version of this document [RFC2875]. sa-dhPop-sha224 A SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DSA-Sig-Value represents the signature value, and the structure DomainParameters SHOULD be omitted in the signature but MUST be present in the associated key request.Schaad & Prafullchandra Standards Track [Page 15]
RFC 6955 DH POP Algorithms May 2013 id-alg-dhPop-sha224 This OID identifies the Discrete Logarithm Signature using SHA-224 as the hash algorithm. sa-dhPop-sha256 A SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DSA-Sig-Value represents the signature value, and the structure DomainParameters SHOULD be omitted in the signature but MUST be present in the associated key request. id-alg-dhPop-sha256 This OID identifies the Discrete Logarithm Signature using SHA-256 as the hash algorithm. sa-dhPop-sha384 A SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DSA-Sig-Value represents the signature value, and the structure DomainParameters SHOULD be omitted in the signature but MUST be present in the associated key request. id-alg-dhPop-sha384 This OID identifies the Discrete Logarithm Signature using SHA-384 as the hash algorithm. sa-dhPop-sha512 A SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DSA-Sig-Value represents the signature value, and the structure DomainParameters SHOULD be omitted in the signature but MUST be present in the associated key request. id-alg-dhPop-sha512 This OID identifies the Discrete Logarithm Signature using SHA-512 as the hash algorithm.6. Static ECDH Proof-of-Possession Process The Static ECDH POP algorithm is set up to use a KDF and a MAC. This algorithm requires that a common set of group parameters be used by both the creator and the verifier of the POP value. Full details of how Elliptic Curve Cryptography (ECC) works can be found inRFC 6090 [RFC6090].Schaad & Prafullchandra Standards Track [Page 16]
RFC 6955 DH POP Algorithms May 2013 The steps for creating an ECDH POP are: 1. An entity (E) chooses the group parameters for an ECDH key agreement. This is done simply by selecting the group parameters from a certificate for the recipient of the POP process. A certificate with the correct group parameters has to be available. The ECDH parameters can be identified either by a named group or by a set of curve parameters.Section 2.3.5 of RFC 3279 [RFC3279] documents how the parameters are encoded for PKIX certificates. For PKIX-based applications, the parameters will almost always be defined by a named group. Designate G as the group from the ECDH parameters. Let the ECDH key pair associated with the certificate be known as the recipient key pair (Rpub and Rpriv). Rpub = Rpriv * G 2. The entity generates an ECDH public/private key pair using the parameters from step 1. For an entity (E): Epriv = entity private value Epub = ECDH public point = Epriv * G 3. The POP computation process will then consist of the following steps: (a) The value to be signed (text) is obtained. (For a PKCS #10 object, the value is the DER-encoded certificationRequestInfo field represented as an octet string.) (b) A shared ECDH secret is computed as follows: shared secret point (x, y) = Epriv * Rpub = Rpriv * Epub shared secret value ZZ is the x coordinate of the computed pointSchaad & Prafullchandra Standards Track [Page 17]
RFC 6955 DH POP Algorithms May 2013 (c) A temporary key K is derived from the shared secret ZZ as follows: K = KDF(LeadingInfo | ZZ | TrailingInfo) LeadingInfo ::= Subject Distinguished Name from certificate TrailingInfo ::= Issuer Distinguished Name from certificate (d) Compute MAC(K, text). The POP verification process requires the recipient to carry out steps (a) through (d) and then simply compare the result of step (d) with what it received as the signature component. If they match, then the following can be concluded: (a) The entity possesses the private key corresponding to the public key in the Certification Request because it needed the private key to calculate the shared secret; and (b) Only the recipient that the entity sent the request to could actually verify the request because it would require its own private key to compute the same shared secret. In the case where the recipient is a CA, this protects the entity from rogue CAs.6.1. ASN.1 Encoding The algorithm outlined above allows for the use of an arbitrary hash function in computing the temporary key and the MAC value. In this specification, we define object identifiers for the SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512 hash values. The ASN.1 structures associated with the Static ECDH POP algorithm are: id-alg-ecdhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 25 } sa-ecdhPop-sha224-hmac-sha224 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-ecdhPop-static-sha224-hmac-sha224 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-ec } }Schaad & Prafullchandra Standards Track [Page 18]
RFC 6955 DH POP Algorithms May 2013 id-alg-ecdhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 26 } sa-ecdhPop-sha256-hmac-sha256 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-ecdhPop-static-sha256-hmac-sha256 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-ec } } id-alg-ecdhPop-static-sha384-hmac-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 27 } sa-ecdhPop-sha384-hmac-sha384 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-ecdhPop-static-sha384-hmac-sha384 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-ec } } id-alg-ecdhPop-static-sha512-hmac-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 28 } sa-ecdhPop-sha512-hmac-sha512 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-ecdhPop-static-sha512-hmac-sha512 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-ec } } These items reuse the DhSigStatic structure defined inSection 4. When used with these algorithms, the value to be placed in the field hashValue is that computed in step 3(d) (Section 6). In the above ASN.1, the following items are defined: sa-ecdhPop-static-sha224-hmac-sha224 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent. id-ecdhPop-static-sha224-hmac-sha224 This OID identifies the Static ECDH POP algorithm that uses SHA-224 as the KDF and HMAC-SHA224 as the MAC function.Schaad & Prafullchandra Standards Track [Page 19]
RFC 6955 DH POP Algorithms May 2013 sa-ecdhPop-static-sha256-hmac-sha256 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent. id-ecdhPop-static-sha256-hmac-sha256 This OID identifies the Static ECDH POP algorithm that uses SHA-256 as the KDF and HMAC-SHA256 as the MAC function. sa-ecdhPop-static-sha384-hmac-sha384 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent. id-ecdhPop-static-sha384-hmac-sha384 This OID identifies the Static ECDH POP algorithm that uses SHA-384 as the KDF and HMAC-SHA384 as the MAC function. sa-ecdhPop-static-sha512-hmac-sha512 An ASN.1 SIGNATURE-ALGORITHM object that associates together the information describing this signature algorithm. The structure DhSigStatic represents the signature value, and the parameters MUST be absent. id-ecdhPop-static-sha512-hmac-sha512 This OID identifies the Static ECDH POP algorithm that uses SHA-512 as the KDF and HMAC-SHA512 as the MAC function.7. Security Considerations None of the algorithms defined in this document are meant for use in general purpose situations. These algorithms are designed and purposed solely for use in doing POP with PKCS #10 and CRMF constructs. In the Static DH POP and Static ECDH POP algorithms, an appropriate value can be produced by either party. Thus, these algorithms only provide integrity and not origination service. The Discrete Logarithm Signature algorithm provides both integrity checking and origination checking. All the security in this system is provided by the secrecy of the private keying material. If either sender or recipient private keys are disclosed, all messages sent or received using those keys are compromised. Similarly, the loss of a private key results in an inability to read messages sent using that key.Schaad & Prafullchandra Standards Track [Page 20]
RFC 6955 DH POP Algorithms May 2013 Selection of parameters can be of paramount importance. In the selection of parameters, one must take into account the community/ group of entities that one wishes to be able to communicate with. In choosing a set of parameters, one must also be sure to avoid small groups. [FIPS-186-3] Appendixes A and B.2 contain information on the selection of parameters for DH.Section 10 of [RFC6090] contains information on the selection of parameters for ECC. The practices outlined in these documents will lead to better selection of parameters.8. References8.1. Normative References [RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-Hashing for Message Authentication",RFC 2104, February 1997. [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels",BCP 14,RFC 2119, March 1997. [RFC2631] Rescorla, E., "Diffie-Hellman Key Agreement Method",RFC 2631, June 1999. [RFC2986] Nystrom, M. and B. Kaliski, "PKCS #10: Certification Request Syntax Specification Version 1.7",RFC 2986, November 2000. [RFC4231] Nystrom, M., "Identifiers and Test Vectors for HMAC- SHA-224, HMAC-SHA-256, HMAC-SHA-384, and HMAC-SHA-512",RFC 4231, December 2005. [RFC6234] Eastlake, D. and T. Hansen, "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)",RFC 6234, May 2011.8.2. Informative References [CRMF] Schaad, J., "Internet X.509 Public Key Infrastructure Certificate Request Message Format (CRMF)",RFC 4211, September 2005. [FIPS-186-3] National Institute of Standards and Technology, "Digital Signature Standard (DSS)", Federal Information Processing Standards Publication 186-3, June 2009, <http://www.nist.gov/>. [RFC2875] Prafullchandra, H. and J. Schaad, "Diffie-Hellman Proof-of-Possession Algorithms",RFC 2875, July 2000.Schaad & Prafullchandra Standards Track [Page 21]
RFC 6955 DH POP Algorithms May 2013 [RFC3279] Bassham, L., Polk, W., and R. Housley, "Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile",RFC 3279, April 2002. [RFC5912] Hoffman, P. and J. Schaad, "New ASN.1 Modules for the Public Key Infrastructure Using X.509 (PKIX)",RFC 5912, June 2010. [RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic Curve Cryptography Algorithms",RFC 6090, February 2011.Schaad & Prafullchandra Standards Track [Page 22]
RFC 6955 DH POP Algorithms May 2013Appendix A. ASN.1 ModulesA.1. 2008 ASN.1 Module This appendix contains an ASN.1 module that is conformant with the 2008 version of ASN.1. This module references the object classes defined by [RFC5912] to more completely describe all of the associations between the elements defined in this document. Where a difference exists between the module in this section and the 1988 module, the 2008 module is the definitive module. DH-Sign { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-dhSign-2012-08(80) } DEFINITIONS IMPLICIT TAGS ::= BEGIN -- EXPORTS ALL -- The types and values defined in this module are exported for use -- in the other ASN.1 modules. Other applications may use them -- for their own purposes. IMPORTS SIGNATURE-ALGORITHM FROM AlgorithmInformation-2009 { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-algorithmInformation-02(58) } IssuerAndSerialNumber, MessageDigest FROM CryptographicMessageSyntax-2010 { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16) modules(0) id-mod-cms-2009(58) } DSA-Sig-Value, DomainParameters, ECDSA-Sig-Value, mda-sha1, mda-sha224, mda-sha256, mda-sha384, mda-sha512, pk-dh, pk-ec FROM PKIXAlgs-2009 { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-pkix1-algorithms2008-02(56) } id-pkix FROM PKIX1Explicit-2009 { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-pkix1-explicit-02(51) };Schaad & Prafullchandra Standards Track [Page 23]
RFC 6955 DH POP Algorithms May 2013 DhSigStatic ::= SEQUENCE { issuerAndSerial IssuerAndSerialNumber OPTIONAL, hashValue MessageDigest } sa-dhPop-static-sha1-hmac-sha1 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-dhPop-static-sha1-hmac-sha1 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } } id-dh-sig-hmac-sha1 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 3 } id-dhPop-static-sha1-hmac-sha1 OBJECT IDENTIFIER ::= id-dh-sig-hmac-sha1 sa-dhPop-static-sha224-hmac-sha224 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-static-sha224-hmac-sha224 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } } id-alg-dhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 15 } sa-dhPop-static-sha256-hmac-sha256 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-static-sha256-hmac-sha256 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } } id-alg-dhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 16 } sa-dhPop-static-sha384-hmac-sha384 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-static-sha384-hmac-sha384 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } }Schaad & Prafullchandra Standards Track [Page 24]
RFC 6955 DH POP Algorithms May 2013 id-alg-dhPop-static-sha384-hmac-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 17 } sa-dhPop-static-sha512-hmac-sha512 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-static-sha512-hmac-sha512 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-dh } } id-alg-dhPop-static-sha512-hmac-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 18 } sa-dhPop-SHA1 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dh-pop VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha1 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha1 OBJECT IDENTIFIER ::= id-alg-dh-pop id-alg-dh-pop OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 4 } sa-dhPop-sha224 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-sha224 VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha224 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 5 } sa-dhPop-sha256 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-sha256 VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha256 } PUBLIC-KEYS { pk-dh } }Schaad & Prafullchandra Standards Track [Page 25]
RFC 6955 DH POP Algorithms May 2013 id-alg-dhPop-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 6 } sa-dhPop-sha384 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-sha384 VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha384 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 7 } sa-dhPop-sha512 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-dhPop-sha512 VALUE DSA-Sig-Value PARAMS TYPE DomainParameters ARE preferredAbsent HASHES { mda-sha512 } PUBLIC-KEYS { pk-dh } } id-alg-dhPop-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 8 } id-alg-ecdhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 25 } sa-ecdhPop-sha224-hmac-sha224 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-ecdhPop-static-sha224-hmac-sha224 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-ec } } id-alg-ecdhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 26 }Schaad & Prafullchandra Standards Track [Page 26]
RFC 6955 DH POP Algorithms May 2013 sa-ecdhPop-sha256-hmac-sha256 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-ecdhPop-static-sha256-hmac-sha256 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-ec } } id-alg-ecdhPop-static-sha384-hmac-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 27 } sa-ecdhPop-sha384-hmac-sha384 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-ecdhPop-static-sha384-hmac-sha384 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-ec } } id-alg-ecdhPop-static-sha512-hmac-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 28 } sa-ecdhPop-sha512-hmac-sha512 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-ecdhPop-static-sha512-hmac-sha512 VALUE DhSigStatic PARAMS ARE absent PUBLIC-KEYS { pk-ec } } ENDSchaad & Prafullchandra Standards Track [Page 27]
RFC 6955 DH POP Algorithms May 2013A.2. 1988 ASN.1 Module This appendix contains an ASN.1 module that is conformant with the 1988 version of ASN.1, which represents an informational version of the ASN.1 module for this document. Where a difference exists between the module in this section and the 2008 module, the 2008 module is the definitive module. DH-Sign { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-dhSign-2012-88(79) } DEFINITIONS IMPLICIT TAGS ::= BEGIN -- EXPORTS ALL -- The types and values defined in this module are exported for use -- in the other ASN.1 modules. Other applications may use them -- for their own purposes. IMPORTS IssuerAndSerialNumber, MessageDigest FROM CryptographicMessageSyntax2004 { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16) modules(0) cms-2004(24) } id-pkix FROM PKIX1Explicit88 { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-pkix1-explicit(18) } Dss-Sig-Value, DomainParameters FROM PKIX1Algorithms88 { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-pkix1-algorithms(17) }; id-dh-sig-hmac-sha1 OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 3} DhSigStatic ::= SEQUENCE { issuerAndSerial IssuerAndSerialNumber OPTIONAL, hashValue MessageDigest } id-alg-dh-pop OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 4 }Schaad & Prafullchandra Standards Track [Page 28]
RFC 6955 DH POP Algorithms May 2013 id-dhPop-static-sha1-hmac-sha1 OBJECT IDENTIFIER ::= id-dh-sig-hmac-sha1 id-alg-dhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 15 } id-alg-dhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 16 } id-alg-dhPop-static-sha384-hmac-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 17 } id-alg-dhPop-static-sha512-hmac-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 18 } id-alg-dhPop-sha1 OBJECT IDENTIFIER ::= id-alg-dh-pop id-alg-dhPop-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 5 } id-alg-dhPop-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 6 } id-alg-dhPop-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 7 } id-alg-dhPop-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 8 } id-alg-ecdhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 25 } id-alg-ecdhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 26 } id-alg-ecdhPop-static-sha384-hmac-sha384 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 27 } id-alg-ecdhPop-static-sha512-hmac-sha512 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 28 } ENDSchaad & Prafullchandra Standards Track [Page 29]
RFC 6955 DH POP Algorithms May 2013Appendix B. Example of Static DH Proof-of-Possession The following example follows the steps described earlier inSection 4. Step 1. Establishing common DH parameters: Assume the parameters are as in the DER-encoded certificate. The certificate contains a DH public key signed by a CA with a DSA signing key. 0 30 939: SEQUENCE { 4 30 872: SEQUENCE { 8 A0 3: [0] { 10 02 1: INTEGER 2 : } 13 02 6: INTEGER : 00 DA 39 B6 E2 CB 21 30 11: SEQUENCE { 23 06 7: OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3) 32 05 0: NULL : } 34 30 72: SEQUENCE { 36 31 11: SET { 38 30 9: SEQUENCE { 40 06 3: OBJECT IDENTIFIER countryName (2 5 4 6) 45 13 2: PrintableString 'US' : } : } 49 31 17: SET { 51 30 15: SEQUENCE { 53 06 3: OBJECT IDENTIFIER organizationName (2 5 4 10) 58 13 8: PrintableString 'XETI Inc' : } : } 68 31 16: SET { 70 30 14: SEQUENCE { 72 06 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4 11) 77 13 7: PrintableString 'Testing' : } : } 86 31 20: SET { 88 30 18: SEQUENCE { 90 06 3: OBJECT IDENTIFIER commonName (2 5 4 3) 95 13 11: PrintableString 'Root DSA CA' : } : } : }Schaad & Prafullchandra Standards Track [Page 30]
RFC 6955 DH POP Algorithms May 2013108 3030: SEQUENCE {110 1713: UTCTime '990914010557Z'125 1713: UTCTime '991113010557Z' : }140 3070: SEQUENCE {142 3111: SET {144 30 9: SEQUENCE {146 06 3: OBJECT IDENTIFIER countryName (2 5 4 6)151 13 2: PrintableString 'US' : } : }155 3117: SET {157 3015: SEQUENCE {159 06 3: OBJECT IDENTIFIER organizationName (2 5 4 10)164 13 8: PrintableString 'XETI Inc' : } : }174 3116: SET {176 3014: SEQUENCE {178 06 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4 11)183 13 7: PrintableString 'Testing' : } : }192 3118: SET {194 3016: SEQUENCE {196 06 3: OBJECT IDENTIFIER commonName (2 5 4 3)201 13 9: PrintableString 'DH TestCA' : } : } : }212 30 577: SEQUENCE {216 30 438: SEQUENCE {220 06 7: OBJECT IDENTIFIER dhPublicKey (1 2 840 10046 2 1)229 30 425: SEQUENCE {233 02 129: INTEGER : 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 : C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 : F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 : 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 : 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 : 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 : 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 : D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 : 27Schaad & Prafullchandra Standards Track [Page 31]
RFC 6955 DH POP Algorithms May 2013365 02 128: INTEGER : 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 : 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 : 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 : 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 : 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE : 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 : 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 : 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD496 0233: INTEGER : 00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 : B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 : FB531 0297: INTEGER : 00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 : B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D : AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 : 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 : B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 : 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 : 92630 3026: SEQUENCE {632 0321: BIT STRING 0 unused bits : 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB : 09 E4 98 34655 02 1: INTEGER 55 : } : } : }658 03 132: BIT STRING 0 unused bits : 02 81 80 5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1 : E6 A7 01 4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0 : 46 79 50 A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69 : B7 11 A1 C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22 : 4D 0A 11 6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF : D8 59 92 C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21 : E1 AF 7A 3A CF 20 0A B4 2C 69 5F CF 79 67 20 31 : 4D F2 C6 ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0 : 8F C5 1A : }793 A385: [3] {795 3083: SEQUENCE {797 3029: SEQUENCE {799 06 3: OBJECT IDENTIFIER subjectKeyIdentifier (2 5 29 14)804 0422: OCTET STRING : 04 14 80 DF 59 88 BF EB 17 E1 AD 5E C6 40 A3 42 : E5 AC D3 B4 88 78 : }Schaad & Prafullchandra Standards Track [Page 32]
RFC 6955 DH POP Algorithms May 2013828 3034: SEQUENCE {830 06 3: OBJECT IDENTIFIER authorityKeyIdentifier (2 5 2935)835 01 1: BOOLEAN TRUE838 0424: OCTET STRING : 30 16 80 14 6A 23 37 55 B9 FD 81 EA E8 4E D3 C9 : B7 09 E5 7B 06 E3 68 AA : }864 3014: SEQUENCE {866 06 3: OBJECT IDENTIFIER keyUsage (2 5 29 15)871 01 1: BOOLEAN TRUE874 04 4: OCTET STRING : 03 02 03 08 : } : } : } : }880 3011: SEQUENCE {882 06 7: OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3)891 05 0: NULL : }893 0348: BIT STRING 0 unused bits : 30 2D 02 14 7C 6D D2 CA 1E 32 D1 30 2E 29 66 BC : 06 8B 60 C7 61 16 3B CA 02 15 00 8A 18 DD C1 83 : 58 29 A2 8A 67 64 03 92 AB 02 CE 00 B5 94 6A : } Step 2. End entity/user generates a DH key pair using the parameters from the CA certificate. End entity DH public key: Y: 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8 93 74 AE FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18 FE 94 B8 A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC 33 FD 1A 0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A BE B2 5C DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E 0B 59 4A 93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8 29 98 EC D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E 7E AF 33 62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53 EF B2 E8 End entity DH private key: X: 32 CC BD B4 B7 7C 44 26 BB 3C 83 42 6E 7D 1B 00 86 35 09 71 07 A0 A4 76 B8 DB 5F EC 00 CE 6F C3Schaad & Prafullchandra Standards Track [Page 33]
RFC 6955 DH POP Algorithms May 2013 Step 3. Compute the shared secret ZZ. 56 b6 01 39 42 8e 09 16 30 b0 31 4d 12 90 af 03 c7 92 65 c2 9c ba 88 bb 0a d5 94 02 ed 6f 54 cb 22 e5 94 b4 d6 60 72 bc f6 a5 2b 18 8d df 28 72 ac e0 41 dd 3b 03 2a 12 9e 5d bd 72 a0 1e fb 6b ee c5 b2 16 59 ee 12 00 3b c8 e0 cb c5 08 8e 2d 40 5f 2d 37 62 8c 4f bb 49 76 69 3c 9e fc 2c f7 f9 50 c1 b9 f7 01 32 4c 96 b9 c3 56 c0 2c 1b 77 3f 2f 36 e8 22 c8 2e 07 76 d0 4f 7f aa d5 c0 59 Step 4. Compute K and the signature. LeadingInfo: DER-encoded Subject/Requester Distinguished Name (DN), as in the generated Certificate Signing Request 30 46 31 0B 30 09 06 03 55 04 06 13 02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73 74 69 6E 67 31 12 30 10 06 03 55 04 03 13 09 44 48 20 54 65 73 74 43 41 TrailingInfo: DER-encoded Issuer/recipient DN (from the certificate described in step 1) 30 48 31 0B 30 09 06 03 55 04 06 13 02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73 74 69 6E 67 31 14 30 12 06 03 55 04 03 13 0B 52 6F 6F 74 20 44 53 41 20 43 41 K: B1 91 D7 DB 4F C5 EF EF AC 9A C5 44 5A 6D 42 28 DC 70 7B DASchaad & Prafullchandra Standards Track [Page 34]
RFC 6955 DH POP Algorithms May 2013 TBS: the "text" for computing the SHA-1 HMAC. 30 82 02 98 02 01 00 30 4E 31 0B 30 09 06 03 55 04 06 13 02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73 74 69 6E 67 31 1A 30 18 06 03 55 04 03 13 11 50 4B 49 58 20 45 78 61 6D 70 6C 65 20 55 73 65 72 30 82 02 41 30 82 01 B6 06 07 2A 86 48 CE 3E 02 01 30 82 01 A9 02 81 81 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 27 02 81 80 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD 02 21 00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 FB 02 61 00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 92 30 1A 03 15 00 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB 09 E4 98 34 02 01 37 03 81 84 00 02 81 80 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8 93 74 AE FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18 FE 94 B8 A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC 33 FD 1A 0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A BE B2 5C DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E 0B 59 4A 93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8 29 98 EC D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E 7E AF 33 62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53 EF B2 E8Schaad & Prafullchandra Standards Track [Page 35]
RFC 6955 DH POP Algorithms May 2013 Certification Request: 0 30 793: SEQUENCE { 4 30 664: SEQUENCE { 8 02 1: INTEGER 0 11 30 78: SEQUENCE { 13 31 11: SET { 15 30 9: SEQUENCE { 17 06 3: OBJECT IDENTIFIER countryName (2 5 4 6) 22 13 2: PrintableString 'US' : } : } 26 31 17: SET { 28 30 15: SEQUENCE { 30 06 3: OBJECT IDENTIFIER organizationName (2 5 4 10) 35 13 8: PrintableString 'XETI Inc' : } : } 45 31 16: SET { 47 30 14: SEQUENCE { 49 06 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4 11) 54 13 7: PrintableString 'Testing' : } : } 63 31 26: SET { 65 30 24: SEQUENCE { 67 06 3: OBJECT IDENTIFIER commonName (2 5 4 3) 72 13 17: PrintableString 'PKIX Example User' : } : } : } 91 30 577: SEQUENCE { 95 30 438: SEQUENCE { 99 06 7: OBJECT IDENTIFIER dhPublicKey (1 2 840 10046 2 1) 108 30 425: SEQUENCE { 112 02 129: INTEGER : 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 : C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 : F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 : 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 : 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 : 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 : 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 : D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 : 27Schaad & Prafullchandra Standards Track [Page 36]
RFC 6955 DH POP Algorithms May 2013 244 02 128: INTEGER : 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 : 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 : 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 : 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 : 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE : 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 : 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 : 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD 375 02 33: INTEGER : 00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 : B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 : FB 410 02 97: INTEGER : 00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 : B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D : AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 : 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 : B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 : 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 : 92 509 30 26: SEQUENCE { 511 03 21: BIT STRING 0 unused bits : 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E : DB 09 E4 98 34 534 02 1: INTEGER 55 : } : } : } 537 03 132: BIT STRING 0 unused bits : 02 81 80 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8 : 93 74 AE FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18 : FE 94 B8 A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC : 33 FD 1A 0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A : BE B2 5C DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E : 0B 59 4A 93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8 : 29 98 EC D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E : 7E AF 33 62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53 : EF B2 E8 : } : } 672 30 12: SEQUENCE { 674 06 8: OBJECT IDENTIFIER dh-sig-hmac-sha1 (1 3 6 1 5 5 7 6 3) 684 05 0: NULL : }Schaad & Prafullchandra Standards Track [Page 37]
RFC 6955 DH POP Algorithms May 2013 686 03 109: BIT STRING 0 unused bits : 30 6A 30 52 30 48 31 0B 30 09 06 03 55 04 06 13 : 02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45 : 54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13 : 07 54 65 73 74 69 6E 67 31 14 30 12 06 03 55 04 : 03 13 0B 52 6F 6F 74 20 44 53 41 20 43 41 02 06 : 00 DA 39 B6 E2 CB 04 14 2D 05 77 FE 5E 8F 65 F5 : AF AD C9 5C 9B 02 C0 A8 88 29 61 63 : } Signature verification requires CA's private key, the CA certificate, and the generated Certification Request. CA DH private key: x: 3E 5D AD FD E5 F4 6B 1B 61 5E 18 F9 0B 84 74 a7 52 1E D6 92 BC 34 94 56 F3 0C BE DA 67 7A DD 7DAppendix C. Example of Discrete Log Signature Step 1. Generate a DH key with length of q being 256 bits. p: 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 27 q: E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 FB g: 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CDSchaad & Prafullchandra Standards Track [Page 38]
RFC 6955 DH POP Algorithms May 2013 j: A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 92 y: 5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1 E6 A7 01 4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0 46 79 50 A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69 B7 11 A1 C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22 4D 0A 11 6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF D8 59 92 C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21 E1 AF 7A 3A CF 20 0A B4 2C 69 5F CF 79 67 20 31 4D F2 C6 ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0 8F C5 1A seed: 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB 09 E4 98 34 C: 00000037 x: 3E 5D AD FD E5 F4 6B 1B 61 5E 18 F9 0B 84 74 a7 52 1E D6 92 BC 34 94 56 F3 0C BE DA 67 7A DD 7D Step 2. Form the value to be signed and hash with SHA1. The result of the hash for this example is: 5f a2 69 b6 4b 22 91 22 6f 4c fe 68 ec 2b d1 c6 d4 21 e5 2c Step 3. The hash value needs to be expanded, since |q| = 256. This is done by hashing the hash with SHA1 and appending it to the original hash. The value after this step is: 5f a2 69 b6 4b 22 91 22 6f 4c fe 68 ec 2b d1 c6 d4 21 e5 2c 64 92 8b c9 5e 34 59 70 bd 62 40 ad 6f 26 3b f7 1c a3 b2 cbSchaad & Prafullchandra Standards Track [Page 39]
RFC 6955 DH POP Algorithms May 2013 Next, the first 255 bits of this value are taken to be the resulting "hash" value. Note that in this case a shift of one bit right is done, since the result is to be treated as an integer: 2f d1 34 db 25 91 48 91 37 a6 7f 34 76 15 e8 e3 6a 10 f2 96 32 49 45 e4 af 1a 2c b8 5e b1 20 56 Step 4. The signature value is computed. In this case, you get the values: r: A1 B5 B4 90 01 34 6B A0 31 6A 73 F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E 5A 77 FF C3 4B s: 59 40 45 BC 6F 0D DC FF 9D 55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68 75 81 F7 EC 9E BE A1 The encoded signature value is then: 30 45 02 21 00 A1 B5 B4 90 01 34 6B A0 31 6A 73 F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E 5A 77 FF C3 4B 02 20 59 40 45 BC 6F 0D DC FF 9D 55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68 75 81 F7 EC 9E BE A1 Result: 30 82 02 c2 30 82 02 67 02 01 00 30 1b 31 19 30 17 06 03 55 04 03 13 10 49 45 54 46 20 50 4b 49 58 20 53 41 4d 50 4c 45 30 82 02 41 30 82 01 b6 06 07 2a 86 48 ce 3e 02 01 30 82 01 a9 02 81 81 00 94 84 e0 45 6c 7f 69 51 62 3e 56 80 7c 68 e7 c5 a9 9e 9e 74 74 94 ed 90 8c 1d c4 e1 4a 14 82 f5 d2 94 0c 19 e3 b9 10 bb 11 b9 e5 a5 fb 8e 21 51 63 02 86 aa 06 b8 21 36 b6 7f 36 df d1 d6 68 5b 79 7c 1d 5a 14 75 1f 6a 93 75 93 ce bb 97 72 8a f0 0f 23 9d 47 f6 d4 b3 c7 f0 f4 e6 f6 2b c2 32 e1 89 67 be 7e 06 ae f8 d0 01 6b 8b 2a f5 02 d7 b6 a8 63 94 83 b0 1b 31 7d 52 1a de e5 03 85 27 02 81 80 26 a6 32 2c 5a 2b d4 33 2b 5c dc 06 87 53 3f 90 06 61 50 38 3e d2 b9 7d 81 1c 12 10 c5 0c 53 d4 64 d1 8e 30 07 08 8c dd 3f 0a 2f 2c d6 1b 7f 57 86 d0 da bb 6e 36 2a 18 e8 d3 bc 70 31 7a 48 b6 4e 18 6e dd 1f 22 06 eb 3f ea d4 41 69 d9 9b de 47 95 7a 72 91 d2 09 7f 49 5c 3b 03 33 51 c8 f1 39 9a ff 04 d5 6e 7e 94 3d 03 b8 f6 31 15 26 48 95 a8 5c de 47 88 b4 69 3a 00 a7 86 9e da d1 cd 02 21 00 e8 72 fa 96 f0 11 40 f5 f2Schaad & Prafullchandra Standards Track [Page 40]
RFC 6955 DH POP Algorithms May 2013 dc fd 3b 5d 78 94 b1 85 01 e5 69 37 21 f7 25 b9 ba 71 4a fc 60 30 fb 02 61 00 a3 91 01 c0 a8 6e a4 4d a0 56 fc 6c fe 1f a7 b0 cd 0f 94 87 0c 25 be 97 76 8d eb e5 a4 09 5d ab 83 cd 80 0b 35 67 7f 0c 8e a7 31 98 32 85 39 40 9d 11 98 d8 de b8 7f 86 9b af 8d 67 3d b6 76 b4 61 2f 21 e1 4b 0e 68 ff 53 3e 87 dd d8 71 56 68 47 dc f7 20 63 4b 3c 5f 78 71 83 e6 70 9e e2 92 30 1a 03 15 00 1c d5 3a 0d 17 82 6d 0a 81 75 81 46 10 8e 3e db 09 e4 98 34 02 01 37 03 81 84 00 02 81 80 5f cf 39 ad 62 cf 49 8e d1 ce 66 e2 b1 e6 a7 01 4d 05 c2 77 c8 92 52 42 a9 05 a4 db e0 46 79 50 a3 fc 99 3d 3d a6 9b a9 ad bc 62 1c 69 b7 11 a1 c0 2a f1 85 28 f7 68 fe d6 8f 31 56 22 4d 0a 11 6e 72 3a 02 af 0e 27 aa f9 ed ce 05 ef d8 59 92 c0 18 d7 69 6e bd 70 b6 21 d1 77 39 21 e1 af 7a 3a cf 20 0a b4 2c 69 5f cf 79 67 20 31 4d f2 c6 ed 23 bf c4 bb 1e d1 71 40 2c 07 d6 f0 8f c5 1a a0 00 30 0c 06 08 2b 06 01 05 05 07 06 04 05 00 03 47 00 30 44 02 20 54 d9 43 8d 0f 9d 42 03 d6 09 aa a1 9a 3c 17 09 ae bd ee b3 d1 a0 00 db 7d 8c b8 e4 56 e6 57 7b 02 20 44 89 b1 04 f5 40 2b 5f e7 9c f9 a4 97 50 0d ad c3 7a a4 2b b2 2d 5d 79 fb 38 8a b4 df bb 88 bc Decoded version of result: 0 30 707: SEQUENCE { 4 30 615: SEQUENCE { 8 02 1: INTEGER 0 11 30 27: SEQUENCE { 13 31 25: SET { 15 30 23: SEQUENCE { 17 06 3: OBJECT IDENTIFIER commonName (2 5 4 3) 22 13 16: PrintableString 'IETF PKIX SAMPLE' : } : } : } 40 30 577: SEQUENCE { 44 30 438: SEQUENCE { 48 06 7: OBJECT IDENTIFIER dhPublicNumber (1 2 840 10046 2 1)Schaad & Prafullchandra Standards Track [Page 41]
RFC 6955 DH POP Algorithms May 2013 57 30 425: SEQUENCE { 61 02 129: INTEGER : 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 : C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 : F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 : 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 : 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 : 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 : 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 : D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 : 27 193 02 128: INTEGER : 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 : 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 : 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 : 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 : 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE : 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 : 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 : 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD 324 02 33: INTEGER : 00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 : B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 : FB 359 02 97: INTEGER : 00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 : B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D : AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 : 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 : B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 : 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 : 92 458 30 26: SEQUENCE { 460 03 21: BIT STRING 0 unused bits : 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB : 09 E4 98 34 483 02 1: INTEGER 55 : } : } : }Schaad & Prafullchandra Standards Track [Page 42]
RFC 6955 DH POP Algorithms May 2013 486 03 132: BIT STRING 0 unused bits : 02 81 80 5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1 : E6 A7 01 4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0 : 46 79 50 A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69 : B7 11 A1 C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22 : 4D 0A 11 6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF : D8 59 92 C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21 : E1 AF 7A 3A CF 20 0A B4 2C 69 5F CF 79 67 20 31 : 4D F2 C6 ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0 : 8F C5 1A : } 621 A0 0: [0] : } 623 30 12: SEQUENCE { 625 06 8: OBJECT IDENTIFIER '1 3 6 1 5 5 7 6 4' 635 05 0: NULL : } 637 03 72: BIT STRING 0 unused bits : 30 45 02 21 00 A1 B5 B4 90 01 34 6B A0 31 6A 73 : F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E : 5A 77 FF C3 4B 02 20 59 40 45 BC 6F 0D DC FF 9D : 55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68 : 75 81 F7 EC 9E BE A1 : }Authors' Addresses Jim Schaad Soaring Hawk Consulting EMail: ietf@augustcellars.com Hemma Prafullchandra HyTrust, Inc. 1975 W. El Camino Real, Suite 203 Mountain View, CA 94040 USA Phone: (650) 681-8100 EMail: HPrafullchandra@hytrust.comSchaad & Prafullchandra Standards Track [Page 43]
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