Internet Draft Hemma Prafullchandra (XETI) Expires in 6 months Jim Schaad (Microsoft) February 25, 1999 Diffie-Hellman Proof-of-Possession Algorithms <draft-ietf-pkix-dhpop-00.txt> Status of this Memo This document is an Internet-Draft and is in full conformance with all provisions of Section 10 of RFC2026. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF), its areas, and its working groups. 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." To learn the current status of any Internet-Draft, please check the "1id-abstracts.txt" listing contained in the Internet-Drafts Shadow Directories on ftp.is.co.za (Africa), nic.nordu.net (Europe), munari.oz.au Pacific Rim), ds.internic.net (US East Coast), or ftp.isi.edu (US West Coast). Abstract This document describes two methods for producing a signature from a Diffie-Hellman key pair. This behavior is needed for such operations as creating a signature of a PKCS #10 certification request. These algorithms are designed to provide a proof-of-possession rather than general purpose signing. 1. Introduction PKCS #10 [RFC2314] defines a syntax for certification requests. It assumes that the public key being requested for certification corresponds to an algorithm that is capable of signing/encrypting. Diffie-Hellman (DH) is a key agreement algorithm and as such cannot be directly used for signing or encryption. This document describes two new signing algorithms using the Diffie- Hellman key agreement process to provide a shared secret as the basis of the signature. In the first signature algorithm, the signature is constructed for a specific recipient/verifier by using a public key of Prafullchandra, Schaad [Page 1]

INTERNET DRAFT February 1999 that verifier. In the second signature algorithm, the signature is constructed for arbitrary verifiers. This is done by creating an appropriate D-H key pair and encoding them as part of the signature value. 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). 3. DH Signature Process The steps for creating a DH signature are: 1. An entity (E) chooses the group parameters for a DH key agreement. In many cases this is done simply by selecting the group parameters from a certificate for the recipient of the signature process (static DH signatures) but they may be computed for other methods (ephemeral DH signatures). In the ephemeral DH signature scheme, a temporary DH key-pair is generated using the group parameters, which may be computed or acquired by some out-of-band means. In the static DH signature scheme, a certificate with the correct group parameters has to be available. Let these common DH parameters be g and p; and let this DH key-pair be known as the Recipient key pair (Rpub and Rpriv). Rpub = g^x mod p (where x=Rpriv, the private DH value and ^ denotes exponentiation) 2. The entity generates a DH public/private key-pair using the parameters from step 1. For an entity E: Epriv = DH private value = y Epub = DH public value = g^y mod p 3. The signature computation process will then consist of: a) The value to be signed is obtained. (For a RFC2314 object, the value is the DER encoded certificationRequestInfo field represented as an octet string.) This will be the `text' referred to in [RFC2104], the data to which HMAC-SHA1 is applied. b) A shared DH secret is computed, as follows, Prafullchandra, Schaad [Page 2]

INTERNET DRAFT February 1999 shared secret = ZZ = g^xy mod p [This is done by the entity E as g^(y.Rpub) and by the Recipient as g^(x.Epub), where Rpub is retrieved from the Recipient's DH certificate (or is the one that was locally generated by the Entity) and Epub is retrieved from the actual certification request. ] c) A temporary key K is derived from the shared secret ZZ as follows: K = SHA1(LeadingInfo | ZZ | TrailingInfo), where "|" means concatenation. d) Compute HMAC-SHA1 over the data `text' as per [RFC2104] as: SHA1(K XOR opad, SHA1(K XOR ipad, text)) where, opad (outer pad) = the byte 0x36 repeated 64 times and ipad (inner pad) = the byte 0x5C repeated 64 times. Namely, (1) Append zeros to the end of K to create a 64 byte string (e.g., if K is of length 16 bytes it will be appended with 48 zero bytes 0x00). (2) XOR (bitwise exclusive-OR) the 64 byte string computed in step (1) with ipad. (3) Append the data stream `text' to the 64 byte string resulting from step (2). (4) Apply SHA1 to the stream generated in step (3). (5) XOR (bitwise exclusive-OR) the 64 byte string computed in step (1) with opad. (6) Append the SHA1 result from step (4) to the 64 byte string resulting from step (5). (7) Apply SHA1 to the stream generated in step (6) and output the result. Sample code is also provided in [RFC2104]. e) The output of (d) is encoded as a BIT STRING (the Signature value). The signature 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: Prafullchandra, Schaad [Page 3]

INTERNET DRAFT February 1999 1) 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 2) For the static signature scheme, that only the Recipient that the entity sent the request to could actually verify the request because they would require their own private key to compute the same shared secret. In the case where the recipient is a Certification Authority, this protects the Entity from rogue CAs. 4. Static DH Signature In the static DH Signature scheme, the public key used in the key agreement process of step 2 is obtained from the entity that will be verifying the signature (i.e. the recipient). In the case of a certification request, the public key would normally be extracted from a certificate issued to the CA with the appropriate key parameters. The values used in step 3c for "LeadingInfo" and the "TrailingInfo" are: LeadingInfo ::= Subject Distinguished Name from certificate TrailingInfo ::= Issuer Distinguished Name from certificate The ASN.1 structures associated with the static Diffie-Hellman signature algorithms are: id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) <TBD> } DhPopStatic ::= SEQUENCE { issuerAndSerial IssuerAndSerialNumber OPTIONAL, hashValue MessageDigest } issuerAndSerial is 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 contains the result of the SHA-1 HMAC operation in step 3d. DhPopStatic is encoded as a BIT STRING and is the signature value (i.e. encodes the above sequence instead of the raw output from 3d). 5. Discrete Logarithm Signature The use of a single set of parameters for an entire public key infrastructure allows all keys in the group to be attacked together. Prafullchandra, Schaad [Page 4]

INTERNET DRAFT February 1999 For this reason we need to create a proof of possession for Diffie- Hellman keys that does not require the use of a common set of parameters. The method outlined in this document is the same as used by the Digital Signature Algorithm, but we have removed the restrictions imposed by the [FIPS-186] 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 [DH-X9.42] 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 group 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) mod q > 1 (g has order q mod p) q is a large prime j is a large integer such that p = qj + 1 x is a randomly or pseudo-randomly generated integer with 1 < x < q y = g^x mod p Note: These definitions match the ones in [DH-X9.42]. 5.1 Expanding the Digest Value Besides the addition of a q parameter, [FIPS-186] also imposes size restrictions on the parameters. The length of q must be 160-bits (matching output of the SHA-1 digest algorithm) and 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 160-bits. (The size restriction on q is identical with that in [DH-X9.42].) Given that 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 160-bits then a method must be provided to expand the hash length. The method for expanding the digest value used in this section does not add any additional security beyond the 160-bits provided by SHA. 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. Prafullchandra, Schaad [Page 5]

INTERNET DRAFT February 1999 Let L = the size of q (i.e. 2^L <= q < 2^(L+1)). Let M be the original message to be signed. 1. Compute d = SHA-1(M), the SHA-1 digest of the original message. 2. If L == 160 then m = d. 3. If L @ 160 then follow steps (a) through (d) below. a) Set n = L / 160, where / represents integer division, consequently, if L = 200, n = 1. b) Set m = d, the initial computed digest value. c) For i = 0 to n - - 1 m = m | SHA(d), where "|" means concatenation. d) m = LEFTMOST(m, L-1), where LEFTMOST returns the L-1 left most bits of m. 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 in section 5. 1. Generate a random or pseudorandom integer k, such that 0 < k^-1 < q. 2. Compute r = (g^k mod p) mod q. 3. If r is zero, repeat from step 1. 4. Compute s = (k^-1 (m + xr)) 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 the Digital Signature Algorithm, as some assumptions about the validity of parameters cannot be taken for granted. Given a message m to be validated, the signature value pair (r, s) and the parameters for the key. Prafullchandra, Schaad [Page 6]

INTERNET DRAFT February 1999 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. 5.4 ASN Encoding The signature is encoded using id-alg-dhPOP OBJECT IDENTIFIER ::= {id-pkix id-alg(6) <TBD> } The parameters for id-alg-dhPOP are encoded as DomainParameters (imported from [PROFILE]). The parameters may be omitted in the signature, as they must exist in the associated key request. The signature value pair r and s are encoded using Dss-Sig-Value (imported from [PROFILE]). 5. Security Considerations 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 that key are compromised. Similarly, loss of the private key results in an inability to read messages sent using that key. 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 Prafullchandra, Schaad [Page 7]

INTERNET DRAFT February 1999 groups. [FIPS-186] Appendixes 2 and 3 contain information on the selection of parameters. The practices outlined in this document will lead to better selection of parameters. 6. Open Issues There are no known open issues. 7. References [FIPS-186] Federal Information Processing Standards Publication (FIPS PUB) 186, "Digital Signature Standard", 1994 May 19. [RFC2314] B. Kaliski, "PKCS #10: Certification Request Syntax v1.5", RFC 2314, October 1997 [RFC2104] H. Krawczyk, M. Bellare, R. Canetti, "HMAC: Keyed-Hashing for Message Authentication", RFC 2104, February 1997. [PROFILE] R. Housley, W. Ford, W. Polk, D. Solo, "Internet X.509 Public Key Infrastructure: Certificate and CRL Profile", RFC 2459, January 1999. [DH-X9.42] E. Rescorla, "Diffie-Hellman Key Agreement Method". (currently draft-ietf-smime-x942-*.txt) 8. Author's Addresses Hemma Prafullchandra XETI Inc. 5150 El Camino Real, #A-32 Los Altos, CA 94022 (640) 694-6812 hemma@xeti.com Jim Schaad Microsoft Corporation One Microsoft Way Redmond, WA 98052-6399 (425) 936-3101 jimsch@microsoft.com Appendix A. ASN.1 Module DH-Sign DEFINITIONS IMPLICIT TAGS ::= BEGIN Prafullchandra, Schaad [Page 8]

```
INTERNET DRAFT February 1999
--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 CryptographicMessageSyntax { iso(1) member-body(2)
us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16)
modules(0) cms(1) }
Dss-Sig-Value, DomainParameters
FROM PKIX1Explicit88 {iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-pkix1-explicit-88(1)};
id-dhSig-static-HMAC-SHA1 OBJECT IDENTIFIER ::= {id-pkix id-alg(6)
<TBD> }
DhSigStatic ::= SEQUENCE {
IssuerAndSerial IssuerAndSerialNumber OPTIONAL,
hashValue MessageDigest
}
id-alg-dhPOP OBJECT IDENTIFIER ::= {id-pkix id-alg(6) <TBD> }
END
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```