Internet Research Task Force S.H. Shin Internet-Draft K. Kobara Intended status: Informational AIST Expires: January 16, 2017 July 15, 2016 Augmented Password-Authenticated Key Exchange (AugPAKE) draft-irtf-cfrg-augpake-06 Abstract This document describes a secure and highly-efficient augmented password-authenticated key exchange (AugPAKE) protocol where a user remembers a low-entropy password and its verifier is registered in the intended server. In general, the user password is chosen from a small set of dictionary whose space is within the off-line dictionary attacks. The AugPAKE protocol described here is secure against passive attacks, active attacks and off-line dictionary attacks (on the obtained messages with passive/active attacks). Also, this protocol provides resistance to server compromise in the context that an attacker, who obtained the password verifier from the server, must at least perform off-line dictionary attacks to gain any advantage in impersonating the user. The AugPAKE protocol is not only provably secure in the random oracle model but also the most efficient over the previous augmented PAKE protocols (SRP and AMP). Status of This Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://datatracker.ietf.org/drafts/current/. 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." This Internet-Draft will expire on January 16, 2017. Shin & Kobara Expires January 16, 2017 [Page 1] Internet-Draft Augmented PAKE (AugPAKE) July 2016 Copyright Notice Copyright (c) 2016 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 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. Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1. Keywords . . . . . . . . . . . . . . . . . . . . . . . . 3 2. AugPAKE Specification . . . . . . . . . . . . . . . . . . . . 4 2.1. Underlying Group . . . . . . . . . . . . . . . . . . . . 4 2.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1. Password Processing . . . . . . . . . . . . . . . . . 6 2.3. Protocol . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3.1. Initialization . . . . . . . . . . . . . . . . . . . 7 2.3.2. Actual Protocol Execution . . . . . . . . . . . . . . 7 3. Security Considerations . . . . . . . . . . . . . . . . . . . 9 3.1. General Assumptions . . . . . . . . . . . . . . . . . . . 9 3.2. Security against Passive Attacks . . . . . . . . . . . . 9 3.3. Security against Active Attacks . . . . . . . . . . . . . 10 3.3.1. Impersonation Attacks on User U . . . . . . . . . . . 10 3.3.2. Impersonation Attacks on Server S . . . . . . . . . . 10 3.3.3. Man-in-the-Middle Attacks . . . . . . . . . . . . . . 11 3.4. Security against Off-line Dictionary Attacks . . . . . . 11 3.5. Resistance to Server Compromise . . . . . . . . . . . . . 12 4. Implementation Consideration . . . . . . . . . . . . . . . . 13 5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 13 6. References . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.1. Normative References . . . . . . . . . . . . . . . . . . 13 6.2. Informative References . . . . . . . . . . . . . . . . . 14 Appendix A. Features of AugPAKE . . . . . . . . . . . . . . . . 15 Appendix B. Test Vector of AugPAKE . . . . . . . . . . . . . . . 16 Appendix C. AugPAKE over EC Groups . . . . . . . . . . . . . . . 18 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 20 1. Introduction Shin & Kobara Expires January 16, 2017 [Page 2] Internet-Draft Augmented PAKE (AugPAKE) July 2016 In the real world, many applications such as web mail, Internet banking/shopping/trade require secure channels between participating parties. Such secure channels can be established by using an authenticated key exchange (AKE) protocol, which allows the involving parties to authenticate each other and to generate a temporary session key. The temporary session key is used to protect the subsequent communications between the parties. Until now, password-only AKE (called, PAKE) protocols have attracted much attention because password-only authentication is very convenient to the users. However, it is not trivial to design a secure PAKE protocol due to the existence of off-line dictionary attacks on passwords. These attacks are possible since passwords are chosen from a relatively-small dictionary that allows for an attacker to perform the exhaustive searches. This problem was brought forth by Bellovin and Merritt [BM92], and many following works have been conducted in the literature (see some examples in [IEEEP1363.2]). A PAKE protocol is said to be secure if the best attack an active attacker can take is restricted to the on-line dictionary attacks, which allow to check a guessed password only by interacting with the honest party. An augmented PAKE protocol (e.g., [BM93], [RFC2945], [ISOIEC11770-4], [IEEEP1363.2]) provides extra protection for server compromise in the sense that an attacker, who obtained a password verifier from a server, cannot impersonate the corresponding user without performing off-line dictionary attacks on the password verifier. This additional security is known as "resistance to server compromise". The AugPAKE protocol described in this document is an augmented PAKE which also achieves highly efficiency over the previous works (SRP [RFC2945], [ISOIEC11770-4], and AMP [ISOIEC11770-4]). In summary, 1) The AugPAKE protocol is secure against passive attacks, active attacks and off-line dictionary attacks on the obtained messages with passive/active attacks (see [SKI10] for the formal security proof), and 2) It provides resistance to server compromise. At the same time, the AugPAKE protocol has similar computational efficiency to the plain Diffie-Hellman key exchange [DH76] that does not provide authentication by itself. Specifically, the user and the server need to compute 2 and 2.17 modular exponentiations, respectively, in the AugPAKE protocol. After excluding pre-computable costs, the user and the server are required to compute only 1 and 1.17 modular exponentiations, respectively. Compared with SRP [RFC2945], [ISOIEC11770-4], and AMP [ISOIEC11770-4], the AugPAKE protocol is more efficient 1) than SRP in terms of the user's computational costs and 2) than AMP in terms of the server's computational costs. 1.1. Keywords Shin & Kobara Expires January 16, 2017 [Page 3] Internet-Draft Augmented PAKE (AugPAKE) July 2016 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 [RFC2119]. 2. AugPAKE Specification 2.1. Underlying Group The AugPAKE protocol can be implemented over the following group. o Let p and q be sufficiently large primes such that q is a divisor of ((p - 1) / 2) and every factors of ((p - 1) / 2) are also primes comparable to q in size. This p is called a "secure" prime. We denote by G a multiplicative subgroup of prime order q over the field GF(p), the integers modulo p. Let g be a generator for the subgroup G so that all the subgroup elements are generated by g. The group operation is denoted multiplicatively (in modulo p). By using a secure prime p, the AugPAKE protocol has computational efficiency gains. Specifically, it does not require the order check of elements, received from the counterpart party. Note that the groups, defined in Discrete Logarithm Cryptography [SP800-56A] and RFC 5114 [RFC5114], are not necessarily the above secure prime groups. Alternatively, one can implement the AugPAKE protocol over the following groups. o Let p and q be sufficiently large primes such that p = (2 * q) + 1. This p is called a "safe" prime. We denote by G a multiplicative subgroup of prime order q over the field GF(p), the integers modulo p. Let g be any element of G other than 1. For example, g = h^2 mod p where h is a primitive element. The group operation is denoted multiplicatively (in modulo p). o Let p and q be sufficiently large primes such that q is a divisor of ((p - 1) / 2). We denote by G a multiplicative subgroup of prime order q over the field GF(p), the integers modulo p. Let g be a generator for the subgroup G so that all the subgroup elements are generated by g. The group operation is denoted multiplicatively (in modulo p). If p is not a "secure" prime, the AugPAKE protocol MUST perform the order check of received elements. 2.2. Notation Shin & Kobara Expires January 16, 2017 [Page 4] Internet-Draft Augmented PAKE (AugPAKE) July 2016 The AugPAKE protocol is a two-party protocol where a user and a server authenticate each other and generate a session key. The following notation is used in this document: U The user's identity (e.g., defined in [RFC4282]). It is a string in {0,1}^* where {0,1}^* indicates a set of finite binary strings. S The server's identity. It is a string in {0,1}^*. b = H(a) A binary string a is given as input to a secure one-way hash function H (e.g., SHA-2 family [FIPS180-3]) which produces a fixed-length output b. The hash function H maps {0,1}^* to {0,1}^k where {0,1}^k indicates a set of binary strings of length k and k is a security parameter. b = H'(a) A binary string a is given as input to a secure one-way hash function H' which maps the input a in {0,1}^* to the output b in Z_q^* where Z_q^* is a set of positive integers modulo prime q. a | b It denotes a concatenation of binary strings a and b in {0,1}^*. 0x A hexadecimal value is shown preceded by "0x". X * Y mod p It indicates a multiplication of X and Y modulo prime p. X = g^x mod p The g^x indicates a multiplication computation of g by x times. The resultant value modulo prime p is assigned to X. The discrete logarithm problem says that it is computationally hard to compute the discrete logarithm x from X, g and p. w The password remembered by the user. This password may be used as an effective password (instead of itself) in the form of H'(0x00 | U | S | w). W Shin & Kobara Expires January 16, 2017 [Page 5] Internet-Draft Augmented PAKE (AugPAKE) July 2016 The password verifier registered in the server. This password verifier is computed as follows: W = g^w mod p where the user's password w is used itself, or W = g^w' mod p where the effective password w' = H'(0x00 | U | S | w) is used. bn2bin(X) It indicates a conversion of a multiple precision integer X to the corresponding binary string. If X is an element over GF(p), its binary representation MUST have the same bit length as the binary representation of prime p. U -> S: msg It indicates a message transmission that the user U sends a message msg to the server S. U: It indicates a local computation of user U (without any out-going messages). 2.2.1. Password Processing The input password MUST be processed according to the rules of the [RFC4013] profile of [RFC3454]. The password SHALL be considered a "stored string" per [RFC3454] and unassigned code points are therefore prohibited. The output SHALL be the binary representation of the processed UTF-8 character string. Prohibited output and unassigned code points encountered in SASLprep pre-processing SHALL cause a failure of pre-processing and the output SHALL NOT be used with the AugPAKE protocol. The following table shows examples of how various character data is transformed by the rules of the [RFC4013] profile. # Input Output Comments - ----- ------ -------- 1 IX IX SOFT HYPHEN mapped to nothing 2 user user no transformation 3 USER USER case preserved, will not match #2 4 a output is NFKC, input in ISO 8859-1 5 IX output is NFKC, will match #1 6 Error - prohibited character 7 Error - bidirectional check 2.3. Protocol The AugPAKE protocol consists of two phases: initialization and actual protocol execution. The initialization phase SHOULD be Shin & Kobara Expires January 16, 2017 [Page 6] Internet-Draft Augmented PAKE (AugPAKE) July 2016 finished in a secure manner between the user and the server, and it is performed all at once. Whenever the user and the server need to establish a secure channel, they can run the actual protocol execution through an open network (i.e., the Internet) in which an active attacker exists. 2.3.1. Initialization U -> S: (U, W) The user U computes W = g^w mod p (instead of w, the effective password w' may be used), and transmits W to the server S. The W is registered in the server as the password verifier of user U. Of course, user U just remembers the password w only. If resistance to server compromise is not necessary, the server can store w' instead of W. In either case, server S SHOULD NOT store any plaintext passwords. As noted above, this phase SHOULD be performed securely and all at once. 2.3.2. Actual Protocol Execution The actual protocol execution of the AugPAKE protocol allows the user and the server to share an authenticated session key through an open network (see Figure 1). +-----------------+ +------------------+ | User U | | Server S (U,W) | | | (U, X) | | | |----------------------------->| | | | | | | | (S, Y) | | | |<-----------------------------| | | | | | | | V_U | | | |----------------------------->| | | | | | | | V_S | | | |<-----------------------------| | | | | | +-----------------+ +------------------+ Figure 1: Actual Protocol Execution of AugPAKE U -> S: (U, X) Shin & Kobara Expires January 16, 2017 [Page 7] Internet-Draft Augmented PAKE (AugPAKE) July 2016 The user U chooses a random element x from Z_q^* and computes its Diffie-Hellman public value X = g^x mod p. The user sends the first message (U, X) to the server S. S -> U: (S, Y) If the received X from user U is 0, 1 or -1 (mod p), server S MUST terminate the protocol execution. Otherwise, the server chooses a random element y from Z_q^* and computes Y = (X * (W^r))^y mod p where r = H'(0x01 | U | S | bn2bin(X)). Note that X^y * g^(w * r * y) mod p can be computed from y and (w * r * y) efficiently using Shamir's trick [MOV97]. Then, server S sends the second message (S, Y) to the user U. U -> S: V_U If the received Y from server S is 0, 1 or -1 (mod p), user U MUST terminate the protocol execution. Otherwise, the user computes K = Y^z mod p where z = 1 / (x + (w * r)) mod q and r = H'(0x01 | U | S | bn2bin(X)). Also, user U generates an authenticator V_U = H(0x02 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)). Then, the user sends the third message V_U to the server S. S -> U: V_S If the received V_U from user U is not equal to H(0x02 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)) where K = g^y mod p, server S MUST terminate the protocol execution. Otherwise, the server generates an authenticator V_S = H(0x03 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)) and a session key SK = H(0x04 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)). Then, server S sends the fourth message V_S to the user U. U: If the received V_S from server S is not equal to H(0x03 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)), user U MUST terminate the protocol execution. Otherwise, the user generates a session key SK = H(0x04 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)). In the actual protocol execution, the sequential order of message exchanges is very important in order to avoid any possible attacks. For example, if the server S sends the second message (S, Y) and the fourth message V_S together, any attacker can easily derive the correct password w with off-line dictionary attacks. Shin & Kobara Expires January 16, 2017 [Page 8] Internet-Draft Augmented PAKE (AugPAKE) July 2016 The session key SK, shared only if the user and the server authenticate each other successfully, MAY be generated by using a key derivation function (KDF) [SP800-108]. After generating SK, the user and the server MUST delete all the internal states (e.g., Diffie- Hellman exponents x and y) from memory. For the formal proof [SKI10] of the AugPAKE protocol, we need to change slightly the computation of Y (in the above S -> U: (S, Y)) and K (in the above S -> U: V_S) as follows: Y = (X * (W^r))^y' and K = g^y' where y' = H'(0x05 | bn2bin(y)). 3. Security Considerations This section shows why the AugPAKE protocol (i.e., the actual protocol execution) is secure against passive attacks, active attacks and off-line dictionary attacks, and also provides resistance to server compromise. 3.1. General Assumptions o An attacker is computationally-bounded. o Any hash functions, used in the AugPAKE protocol, are secure in terms of pre-image resistance (one-wayness), second pre-image resistance and collision resistance. 3.2. Security against Passive Attacks An augmented PAKE protocol is said to be secure against passive attacks in the sense that an attacker, who eavesdrops the exchanged messages, cannot compute an authenticated session key (shared between the honest parties in the protocol). In the AugPAKE protocol, an attacker can get the messages (U, X), (S, Y), V_U, V_S by eavesdropping, and then wants to compute the session key SK. That is, the attacker's goal is to derive the correct K from the obtained messages X and Y because the hash functions are secure and the only secret in the computation of SK is K = g^y mod p. Note that X = g^x mod p and Y = (X * (W^r))^y = X^y * W^(r * y) = X^y * (g^y)^t = X^y * K^t hold where t = w * r mod q. Though t is determined from possible password candidates and X, the only way for the attacker to extract K from X and Y is to compute X^y. However, the probability for the attacker to compute X^y is negligible in the security parameter for Shin & Kobara Expires January 16, 2017 [Page 9] Internet-Draft Augmented PAKE (AugPAKE) July 2016 the underlying groups since both x and y are random elements chosen from Z_q^*. Therefore, the AugPAKE protocol is secure against passive attacks. 3.3. Security against Active Attacks An augmented PAKE protocol is said to be secure against active attacks in the sense that an attacker, who completely controls the exchanged messages, cannot compute an authenticated session key (shared with the honest party in the protocol) with the probability better than that of on-line dictionary attacks. In other words, the probability for an active attacker to compute the session key is restricted by the on-line dictioinary attacks where it grows linearly to the number of interactions with the honest party. In the AugPAKE protocol, the user (resp., the server) computes the session key SK only if the received authenticator V_S (resp., V_U) is valid. There are three cases to be considered in the active attacks. 3.3.1. Impersonation Attacks on User U When an attacker impersonates the user U, the attacker can compute the same SK (to be shared with the server S) only if the authenticator V_U is valid. For a valid authenticator V_U, the attacker has to compute the correct K from X and Y because the hash functions are secure. In this impersonation attack, the attacker of course knows the discrete logarithm x of X and guesses a password w'' from the password dictionary. So, the probability for the attacker to compute the correct K is bounded by the probability of w = w''. That is, this impersonation attack is restricted by the on-line dictionary attacks where the attacker can try a guessed password communicating with the honest server S. Therefore, the AugPAKE protocol is secure against impersonation attacks on user U. 3.3.2. Impersonation Attacks on Server S When an attacker impersonates the server S, the attacker can compute the same SK (to be shared with the user U) only if the authenticator V_S is valid. For a valid authenticator V_S, the attacker has to compute the correct K from X and Y because the hash functions are secure. In this impersonation attack, the attacker chooses a random element y and guesses a password w'' from the password dictionary so that Y = (X * (W'^r))^y = X^y * W'^(r * y) = X^y * (g^y)^t' where t' = w'' * r mod q. The probability for the attacker to compute the correct K is bounded by the probability of w = w''. Shin & Kobara Expires January 16, 2017 [Page 10] Internet-Draft Augmented PAKE (AugPAKE) July 2016 Also, the attacker knows whether the guessed password is equal to w or not by seeing the received authenticator V_U. However, when w is not equal to w'', the probability for the attacker to compute the correct K is negligible in the security parameter for the underlying groups since the attacker has to guess the discrete logarithm x (chosen by user U) as well. That is, this impersonation attack is restricted by the on-line dictionary attacks where the attacker can try a guessed password communicating with the honest user U. Therefore, the AugPAKE protocol is secure against impersonation attacks on server S. 3.3.3. Man-in-the-Middle Attacks When an attacker performs the man-in-the-middle attack, the attacker can compute the same SK (to be shared with the user U or the server S) only if one of the authenticators V_U, V_S is valid. Note that if the attacker relays the exchanged messages honestly, it corresponds to the passive attacks. In order to generate a valid authenticator V_U or V_S, the attacker has to compute the correct K from X and Y because the hash functions are secure. So, the attacker is in the same situation as discussed above. Though the attacker can test two passwords (one with user U and the other with server S), it does not change the fact that this attack is restricted by the on-line dictionary attacks where the attacker can try a guessed password communicating with the honest party. Therefore, the AugPAKE protocol is also secure against man-in-the-middle attacks. 3.4. Security against Off-line Dictionary Attacks An augmented PAKE protocol is said to be secure against off-line dictionary attacks in the sense that an attacker, who completely controls the exchanged messages, cannot reduce the possible password candidates better than on-line dictionary attacks. Note that, in the on-line dictionary attacks, an attacker can test one guessed password by running the protocol execution (i.e., communicating with the honest party). As discussed in Section 3.2, an attacker in the passive attacks does not compute X^y (and the correct K = g^y mod p) from the obtained messages X, Y. This security analysis also indicates that, even if the attacker can guess a password, the K is derived independently from the guessed password. Next, we consider an active attacker whose main goal is to perform the off-line dictionary attacks in the AugPAKE protocol. As in Section 3.3, the attacker can 1) test one guessed password by impersonating the user U or the server S, or 2) test two guessed passwords by impersonating the server S (to the honest user U) and impersonating the user U (to the honest server S) in the man-in-the-middle attacks. Whenever the honest party receives Shin & Kobara Expires January 16, 2017 [Page 11] Internet-Draft Augmented PAKE (AugPAKE) July 2016 an invalid authenticator, the party terminates the actual protocol execution without sending any message. In fact, this is important to prevent an attacker from testing more than one password in the active attacks. Since passive attacks and active attacks cannot remove the possible password candidates efficiently than on-line dictionary attacks, the AugPAKE protocol is secure against off-line dictionary attacks. 3.5. Resistance to Server Compromise We consider an attacker who has obtained a (user's) password verifier from a server. In the (augmented) PAKE protocols, there are two limitations [BJKMRSW00]: 1) the attacker can find out the correct password from the password verifier with the off-line dictionary attacks because the verifier has the same entropy as the password; and 2) if the attacker impersonates the server with the password verifier, this attack is always possible because the attacker has enough information to simulate the server. An augmented PAKE protocol is said to provide resistance to server compromise in the sense that the attacker cannot impersonate the user without performing off-line dictionary attacks on the password verifier. In order to show resistance to server compromise in the AugPAKE protocol, we consider an attacker who has obtained the password verifier W and then tries to impersonate the user U without off-line dictionary attacks on W. As a general attack, the attacker chooses two random elements c and d from Z_q^*, and computes X = (g^c) * (W^d) mod p and sends the first message (U, X) to the server S. In order to impersonate user U successfully, the attacker has to compute the correct K = g^y mod p where y is randomly chosen by server S. After receiving Y from the server, the attacker's goal is to find out a value e satisfying Y^e = K mod p. That is, log_g (Y^e) = log_g K mod q (c + (w * d) + (w * r)) * y * e = y mod q (c + w * (d + r)) * e = 1 mod q where log_g K indicates the logarithm of K to the base g. Since there is no off-line dictionary attacks on W, the above solution is that e = 1 / c mod q and d = -r mod q. However, the latter is not possible since r is determined by X (i.e., r = H'(0x01 | U | S | bn2bin(X))) and H' is a secure hash function. Therefore, the AugPAKE protocol provides resistance to server compromise. Shin & Kobara Expires January 16, 2017 [Page 12] Internet-Draft Augmented PAKE (AugPAKE) July 2016 4. Implementation Consideration As discussed in Section 3, the AugPAKE protocol is secure against passive attacks, active attacks and off-line dictionary attacks, and provides resistance to server compromise. However, an attacker in the on-line dictionary attacks can check whether one password (guessed from the password dictionary) is correct or not by interacting with the honest party. Let N be a dictionary size of passwords. Certainly, the attacker's success probability grows with the probability of (I / N) where I is the number of interactions with the honest party. In order to provide a reasonable security margin, implementation SHOULD take a countermeasure to the on-line dictionary attacks. For example, it would take about 90 years to test 2^(25.5) passwords with one minute lock-out for 3 failed password guesses (see Appendix A in [SP800-63]). 5. IANA Considerations This document has no request to IANA. 6. References 6.1. Normative References [FIPS180-3] Information Technology Laboratory, , "Secure Hash Standard (SHS)", NIST FIPS Publication 180-3, October 2008, . [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. [RFC3454] Hoffman, P. and M. Blanchet, "Preparation of Internationalized Strings ("stringprep")", RFC 3454, December 2002. [RFC4013] Zeilenga, K., "SASLprep: Stringprep Profile for User Names and Passwords", RFC 4013, February 2005. [RFC4282] Aboba, B., Beadles, M., Arkko, J., and P. Eronen, "The Network Access Identifier", RFC 4282, December 2005. [SP800-108] Chen, L., "Recommendation for Key Derivation Using Pseudorandom Functions (Revised)", NIST Special Publication 800-108, October 2009, . Shin & Kobara Expires January 16, 2017 [Page 13] Internet-Draft Augmented PAKE (AugPAKE) July 2016 6.2. Informative References [BJKMRSW00] Bellare, M., Jablon, D., Krawczyk, H., MacKenzie, P., Rogaway, P., Swaminathan, R., and T. Wu, "Proposal for P1363 Study Group on Password-Based Authenticated-Key- Exchange Methods", IEEE P1363.2: Password-Based Public-Key Cryptography , Submissions to IEEE P1363.2 , February 2000, . [BM92] Bellovin, S. M. and M. Merritt, "Encrypted Key Exchange: Password-based Protocols Secure against Dictionary Attacks", Proceedings of the IEEE Symposium on Security and Privacy , IEEE Computer Society , 1992. [BM93] Bellovin, S. M. and M. Merritt, "Augmented Encrypted Key Exchange: A Password-based Protocol Secure against Dictionary Attacks and Password File Compromise", Proceedings of the 1st ACM Conference on Computer and Communication Security , ACM Press , 1993. [DH76] Diffie, W. and M. Hellman, "New Directions in Cryptography", IEEE Transactions on Information Theory Volume IT-22, Number 6, 1976. [IEEE1363.2] IEEE 1363.2, , "IEEE Standard Specifications for Password- Based Public-Key Cryptographic Techniques", IEEE Std 1363.2, IEEE Computer Society , January 2009. [IEEEP1363.2] IEEE P1363.2, , "Password-Based Public-Key Cryptography", Submissions to IEEE P1363.2 , , . [ISOIEC11770-4] ISO/IEC 11770-4, , "Information technology -- Security techniques -- Key management -- Part 4: Mechanisms based on weak secrets", International Standard ISO/IEC 11770-4:2006, May 2006, . [MOV97] Menezes, A. J., Oorschot, P. C., and S. A. Vanstone, "Simultaneous Multiple Exponentiation", in Handbook of Applied Cryptography , CRC Press , 1997. Shin & Kobara Expires January 16, 2017 [Page 14] Internet-Draft Augmented PAKE (AugPAKE) July 2016 [RFC2945] Wu, T., "The SRP Authentication and Key Exchange System", RFC 2945, September 2000. [RFC5114] Lepinski, M. and S. Kent, "Additional Diffie-Hellman Groups for Use with IETF Standards", RFC 5114, January 2008. [SKI10] Shin, S. H., Kobara, K., and H. Imai, "Security Proof of AugPAKE", Cryptology ePrint Archive: Report 2010/334, June 2010, . [SP800-56A] Barker, E., Johnson, D., and M. Smid, "Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography (Revised)", NIST Special Publication 800-56A, March 2007, . [SP800-63] Burr, W. E., Dodson, D. F., and W. T. Polk, "Electronic Authentication Guideline", NIST Special Publication 800-63 Version 1.0.2, April 2006, . Appendix A. Features of AugPAKE Below are some features of the AugPAKE protocol. Security: o AugPAKE is zero knowledge (password) proof. It is secure against passive/active/off-line dictionary attacks. It is also resistant to server-compromise impersonation attacks. o AugPAKE provides Perfect Forward Secrecy (PFS) and is secure against Denning-Sacco attack. o Any cryptographically secure Diffie-Hellman groups can be used. o The formal security proof of AugPAKE can be found at [SKI10]. o AugPAKE can be easily used with strong credentials. o In the case of server compromise, an attacker has to perform off- line dictionary attacks while computing modular exponentiation with a password candidate. Shin & Kobara Expires January 16, 2017 [Page 15] Internet-Draft Augmented PAKE (AugPAKE) July 2016 Intellectual Property: o AugPAKE was publicly disclosed on Oct. 2008. o AIST applied for a patent in Japan on July 10, 2008. AIST would provide royal-free license of AugPAKE. o IPR disclosure (see https://datatracker.ietf.org/ipr/2037/) Miscellaneous: o The user needs to compute only 2 modular exponentiation computations while the server needs to compute 2.17 modular exponentiation computations. AugPAKE needs to exchange 2 group elements and 2 hash values. This is almost the same computation/ communication costs as the plain Diffie-Hellman key exchange. If we use a large (e.g., 2048/3072-bits) parent group, the hash size would be relatively small. o AugPAKE can be easily converted to 'balanced' PAKE. o AugPAKE has the same performance for any type of secret. o Internationalization of character-based passwords can be supported. o AugPAKE can be implemented over any ECP (Elliptic Curve Group over GF[P]), EC2N (Elliptic Curve Group over GF[2^N]), and MODP (Modular Exponentiation Group) groups. o AugPAKE has request/response nature. o No Trusted Third Party (TTP) and clock synchronization o No additional primitive (e.g., Full Domain Hash (FDH) and/or ideal cipher) is needed. o Easy implementation. We already implemented AugPAKE and have been testing in AIST. Appendix B. Test Vector of AugPAKE Here is a test vector of the AugPAKE protocol. p = 0x FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF 43000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000 Shin & Kobara Expires January 16, 2017 [Page 16] Internet-Draft Augmented PAKE (AugPAKE) July 2016 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000 0000000000000000330A0DFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFDA5193AB q = 0x FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF 43 g = 0x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augpakeuser@aist.go.jp S = augpakeserver@aist.go.jp X = 0x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x 39033C00E1C30FF1A945DD699C516D3BB194FABBB46ADF54A2ED0820FEE0A4 DE52128E2126A4393E3040E07D90432B8C19433EC920274E5A7C165DC89AA2 C6D77E801A0C7676BC71955A52E74775C57C63B97304C73211C2035BD7B6D1 Shin & Kobara Expires January 16, 2017 [Page 17] Internet-Draft Augmented PAKE (AugPAKE) July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x 490C7CE33DCC3EBE8D0406EEB97CA154882DCBBA0A728F3B870263BCA36 9DB6 V_S = 0x D70D2CAA821B9D84E29D75EB5E9B2DB038BA1256ECFC35C553832743A6E 36F Appendix C. AugPAKE over EC Groups The AugPAKE protocol can be implemented over any elliptic curve groups. The following is such an example. Let p and q be sufficiently large primes, and let m be some positive integer. An elliptic curve E is defined by one of the following two curve equations y^2 = x^3 + a * x + b over the prime field GF(p) or y^2 + x * y = x^3 + a * x^2 + b over the binary field GF(2^m) together with the point at infinity 0_E where x, y, and two coefficients a and b are elements of GF(p) or GF(2^m). Let #E be the number of points on E, and prime q be the order of the desired group. The cofactor k is the value (#E / q) satisfying k = 2^n * q_1 * q_2 ... q_t where n = {0,1,2} and every primes q_i > q for i = 1, 2, ..., t. Optionally, k = 2^n. Also, n can be 3 for good performance and security. Let G be a generator for a subgroup of q points on E so that all the subgroup elements are generated by G. The group operation is denoted additively. For example, (X = [x] * G) indicates that an addition computation of G by x times and the resultant value is assigned to X. By using the above elliptic curve groups, the AugPAKE protocol has computational efficiency gains. Specifically, it does not require the order check of elements, received from the counterpart party. The AugPAKE protocol consists of two phases: initialization and actual protocol execution. The initialization phase SHOULD be Shin & Kobara Expires January 16, 2017 [Page 18] Internet-Draft Augmented PAKE (AugPAKE) July 2016 finished in a secure manner between the user and the server, and it is performed all at once. Whenever the user and the server need to establish a secure channel, they can run the actual protocol execution through an open network (i.e., the Internet) in which an active attacker exists. Initialization U -> S: (U, W) The user U computes W = [w] * G (instead of w, the effective password w' may be used), and transmits W to the server S. The W is registered in the server as the password verifier of user U. Of course, user U just remembers the password w only. Actual Protocol Execution U -> S: (U, X) The user U chooses a random element x from Z_q^* and computes its elliptic curve Diffie-Hellman public value X = [x] * G. The user sends the first message (U, X) to the server S. S -> U: (S, Y) If the received X from user U is not a point on E or [2^n] * X = 0_E, server S MUST terminate the protocol execution. Otherwise, the server chooses a random element y from Z_q^* and computes Y = [y] * (X + ([r] * W)) where r = H'(0x01 | U | S | bn2bin(X)). Then, server S sends the second message (S, Y) to the user U. U -> S: V_U If the received Y from server S is not a point on E or [2^n] * Y = 0_E, user U MUST terminate the protocol execution. Otherwise, the user computes K = [z] * Y where z = 1 / (x + (w * r)) mod q and r = H'(0x01 | U | S | bn2bin(X)). Also, user U generates an authenticator V_U = H(0x02 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)). Then, the user sends the third message V_U to the server S. S -> U: V_S If the received V_U from user U is not equal to H(0x02 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)) where K = [y] * G, server S MUST terminate the protocol execution. Otherwise, the server generates an authenticator V_S = H(0x03 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)) and a session key SK = H(0x04 | U | S | bn2bin(X) | bn2bin(Y) | Shin & Kobara Expires January 16, 2017 [Page 19] Internet-Draft Augmented PAKE (AugPAKE) July 2016 bn2bin(K)). Then, server S sends the fourth message V_S to the user U. U: If the received V_S from server S is not equal to H(0x03 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)), user U MUST terminate the protocol execution. Otherwise, the user generates a session key SK = H(0x04 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)). Authors' Addresses SeongHan Shin AIST 2-4-7 Aomi, Koto-ku Tokyo, Tokyo 135-0064 JP Phone: +81-3-3599-8001 Email: seonghan.shin@aist.go.jp Kazukuni Kobara AIST Email: kobara_conf-ml@aist.go.jp Shin & Kobara Expires January 16, 2017 [Page 20]