Network Working Group A. Brusilovsky Internet-Draft I. Faynberg Expires: April, 2007 S. Patel Z. Zeltsan October 23, 2006 Lucent Technologies Password Authenticated Diffie-Hellman Exchange (PAK) draft-brusilovsky-pak-03.txt Status of this Memo By submitting this Internet-Draft, each author represents that any applicable patent or other IPR claims of which he or she is aware have been or will be disclosed, and any of which he or she becomes aware will be disclosed, in accordance with Section 6 of BCP 79. 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-Draft Shadow Directories can be accessed at http://www.ietf.org/shadow.html. This Internet-Draft will expire on August 15, 2006. Copyright Notice Copyright (C) The Internet Society (2006). Abstract This document proposes to add mutual authentication, based on human-memorizable password, to the basic unauthenticated Diffie-Hellman key exchange. The proposed algorithm is called Password Authenticated Key exchange (PAK). PAK allows two parties to authenticate themselves while performing the Diffie-Hellman exchange. The protocol is secure against all passive and active attacks. In particular, it does not allow either type of attackers to obtain any information that would enable an off-line dictionary attack on the password. The use of Diffie-Hellman exchange ensures Forward Secrecy. Brusilovsky [Page 1] Internet Draft draft-brusilovsky-pak-03.txt October 2006 Table of Contents 1. Introduction 2. Password Authendicated Key exchange 3. Diffie-Hellman parameters 4. IANA considerations 5. Security Considerations 6. Acknowledgments 7. References Authors' and Contributors' Addresses 1. Introduction When we propose PAK, we adhere to the following set of requirements: a. Mutual authentication based on just a pre-shared, human-memorizable password. b. Fulfillment of the need to guard against a man-in-the-middle and against offline dictionary attack. c. Simplicity and openness, to promote widespread adoption and to minimize flaws. PAK (Password Authenticated Key exchange) satisfies all of the above. PAK was presented at the sacred WG meeting at the IETF63 in Paris, where it was proposed as a new work item for the sacred WG. PAK advantages are listed here: - Provides strong key exchange with weak passwords - Foils the man-in-the-middle attack - Provides explicit mutual authentication - Ensures Forward Secrecy The PAK protocol [BMP00, MP05] has been proved to be as secure as the Diffie-Hellman [DH76] problem in the random oracle model [BR93]. That is, PAK retains its security when used with low-entropy passwords, hence, it can be seamlessly integrated into existing applications, which require secure authentication. Brusilovsky [Page 2] Internet Draft draft-brusilovsky-pak-02.txt October 2006 2. Password Authendicated Key exchange We briefly describe PAK in this section. Details of the protocol are omitted for simplicity. Diffie-Hellman key agreement requires that both the sender and recipient of a message create their own secret random numbers and exchange the exponentiation of their respective numbers. By raising the exchanged value with its secret random number both parties can compute the same shared secret Diffie-Hellman key. PAK has two parties, Alice and Bob, sharing a secret password PW. The global Diffie-Hellman publicly known constants, a prime p and a generator g are carefully selected so that 1. A safe prime p is large enough to make the computation of discrete logarithm infeasible and 2. Powers of g modulo p cover the entire range of p-1 integers from 1 to p-1. (References demonstrate working example of selections). Conventions in this I-D: - a mod b denotes the least non-negative remainder when a is divided by b; - Hi(u) denotes an agreed-on hash function (e.g., based on SHA-1) computed over a string u; The various H() act as independent random functions. - s|t denotes concatenation of the strings s and t; - ^ denotes exponentiation. Initially, Alice selects a secret random exponent x and computes g^x mod p; Bob selects a secret random exponent y and computes g^y mod p. For efficiency purposes, short exponents could be used for x and y provided they have a certain minimum size. Then: 1. Alice initiates the exchange by picking a random x and sending Za = H1(A|B|PW)*(g^x mod p) to Bob; 2. Bob, upon receiving that quantity, verifies that Za is not a zero and then divides it by H1(A|B|PW) to recover g^x mod p. Then Bob picks a random y and computes S1 = H3(A|B|PW|Za/H1(A|B|PW)|g^y mod p|(Za/H1(A|B|PW))^y mod p), and Zb = H2(A|B|PW)*(g^y mod p). Alice sends Zb and S1 to Bob. 3. Upon receiving that message, Alice checks that Zb is not zero. Now Alice can authenticate Bob by recovering what should be g^y mod p using H2(A|B|PW), and computing S1 itself. If the calculated S1 is equal to the received value, Alice computes the key: K = H5(A|B|PW|g^x mod p|Zb/H2(A|B|PW) mod p|(Zb/H2(A|B|PW))^x mod p) To authenticate herself and to complete the exchange, Alice also computes the quantity Brusilovsky [Page 4] Internet Draft draft-brusilovsky-pak-02.txt October 2006 S2 = H4(A|B|PW|g^x mod p|Zb/H2(A|B|PW) mod p|(Zb/H2(A|B|PW))^x mod p) and sends it to Bob. 4. Bob authenticates Alice by computing S2 himself and checking it against the value received from Alice. If both are the same, Bob also computes the key K = H5(A|B|PW|Za/H1(A|B|PW) mod p|g^y mod p|(Za/H1(A|B|PW))^y mod p) If any of the above verifications fails, the protocol halts; otherwise, both parties have authenticated each other and established the key. COMMENT TO ALEC: Aren't we repeating what we just described below??? A --> B: Za = H1(A|B|PW)*(g^x mod p), Bob checks that Za does not equal zero and calculates S1 and Zb: S1 = H3(A|B|PW|Za/H1(A|B|PW) mod p|g^y mod p|(Za/H1(A|B|PW))^y mod p) Zb = H2(A|B|PW)*(g^y mod p) A <-- B: Zb, S1 Alice checks that Zb does not equal zero,verifies S1 and calculates S2 and K: S2 = H4(A|B|PW|g^x mod p|Zb/H2(A|B|PW) mod p|(Zb/H2(A|B|PW))^x mod p) K = H5(A|B|PW|g^x mod p|Zb/H2(A|B|PW) mod p|(Zb/H2(A|B|PW))^x mod p) A --> B: S2 Bob verifies S2 calculates K = H5(A|B|PW|Za/H1(A|B|PW) mod p|g^y mod p|(Za/H1(A|B|PW))^y mod p) 3. Diffie-Hellman parameters: [OTASP] and [WLAN] pre-sets public parameters p and g to their "published" values. This is necessary to protect against an attacker sending bogus p and g values tricking the legitimate user to engage in improper Diffie-Hellman exponentiation and leaking some information about the password. In addition, if short exponents [MP05]are used for Diffi-Hellman parameters x and y, then they should have a minimum size of 384 bits as also required in [OTASP] and [WLAN]. The independent random functions H1 and H2 should each output 1152 bits assuming prime p is 1024 bits long and session keys K are 128 bits long. H3, H4, and H5 each output 128 bits. More information on instantiating random functions using hash functions can be found in [BR93]. We use the FIPS 180 SHA-1 hashing function to instantiate the random function as done in [WLAN]: H1(z): SHA-1(1,1,z) mod 2^128, SHA-1(1,2,z) mod 2^128,. . ., SHA-1(1,9,z) mod 2^128 H2(z): SHA-1(2,1,z) mod 2^128, SHA-1(2,2,z) mod 2^128,. . ., SHA-1(2,9,z) mod 2^128 H3(z): SHA(3,len(z),z,z) mod 2^128 H4(z): SHA(4,len(z),z,z) mod 2^128 Brusilovsky [Page 5] Internet Draft draft-brusilovsky-pak-03.txt October 2006 H5(z): SHA(5,len(z),z,z) mod 2^128 In order to create 1152 output bits for H1 and H2, nine calls to SHA-1 are made and 128 lsbs of each output are used. The input payload of each call to SHA-1 consists of a) 32 bits of function type which for H1 is set to 1 and for H2 is set to 2; b) a counter value which is incremented from 1 to 9 for each call of SHA-1; c) and finally the argument z to the function which in our application is (A|B|PW). The functions H3, H4, and H5 require only one call to the SHA-1 hashing function and its payload consists of a) 32 bits of function type (e.g. 3 for H3); b) a 32 bit value for the length of the argument z; c) the actual argument repeated twice. Finally, the 128 least significant bits of the output are used. 4. IANA considerations No IANA considerations at this time 5. Security Considerations PAK involves the use of shared keys. Protection the shared values and managing (limiting) their exposure over time is of outmost importance. 6. Acknowledgments The authors are grateful for the thoughtful comments received from Shehryar Qutub and Yaron Sheffer. 7. References [BMP00] V. Boyko, P. MacKenzie, S. Patel, Provably secure password authentication and key exchange using Diffie-Hellman, Proc. of Eurocrypt 2000. [BR93] M. Bellare and P. Rogaway, Random Oracles are Practical: A Paradigm for Designing Efficient Protocols, Proc. Of the fifth annual conference on computer and communications security, 1993. Brusilovsky [Page 6] Internet Draft draft-brusilovsky-pak-03.txt October 2006 [DH76] W. Diffie and M.E. Hellman, New directions in cryptography, IEEE Transactions on Information Theory 22 (1976), 644-654. [MP05] P. MacKenzie, S. Patel, Hard Bits of the Discrete Log with Applications to Password Authentication, CT-RSA 2005. [RFC2631] IETF RFC 2631, E. Rescorla, Diffie-Hellman Key Agreement Method, Standards track,1999 [SHA1] National Institute of Standards and Technology (NIST), "Announcing the Secure Hash Standard", FIPS 180-1, U.S. Department of Commerce, April 1995. [OTASP] Over-the-Air Service Provisioning of Mobile Stations in Spread Spectrum Standards, 3GPP2 C.S0016-C v. 1.0 5, 3GPP2, 10/2004. [WLAN] Wireless Local Area Network (WLAN) Interworking, 3GPP2 X.S0028-0, v.1.0, 3GPP2, 4/2005 [WLAN-PP2] 3GPP2 X.S0028-0, v.1.0 (2005), Wireless Local Area Network (WLAN) Interworking. [X.800] ITU-T Recommendation X.805 (2003), Security Architecture for Systems Providing End to end Communications. Authors' and Contributors' Addresses Alec Brusilovsky Lucent Technologies 1960 Lucent Lane, Naperville, IL 60564 USA Tel: +1 630 979 5490 Email: abrusilovsky@lucent.com Igor Faynberg Lucent Technologies Tel: +1 732 949 0137 Email: faynberg@lucent.com Sarvar Patel Lucent Technologies Tel: +1 973 386 6558 Email: sarvar@lucent.com Brusilovsky [Page 7] Internet Draft draft-brusilovsky-pak-03.txt October 2006 Zachary Zeltsan Lucent Technologies Tel: +1 732 949 4187 Email: zeltsan@lucent.com Intellectual Property Statement The IETF takes no position regarding the validity or scope of any Intellectual Property Rights or other rights that might be claimed to pertain 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; nor does it represent that it has made any independent effort to identify any such rights. 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