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Computer Science CSC 774Dr. Peng Ning CSC 774 Advanced Network Security Topic 2.5 Secret Handshake Slides by Tong Zhou
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Computer Science CSC 774Dr. Peng Ning Goals Authenticate without revealing credentials –Consider two groups G 1 and G 2, two parties A G 1 and B G 2. A and B wants to authenticate each other. –If G 1 ≠ G 2 : A and B only know they are not in the same group. –If G 1 = G 2 : A and B can authenticate to each other. –A third party learns nothing by observing conversations between A and B.
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Computer Science CSC 774Dr. Peng Ning Preliminaries: Pairing-based Cryptography Bilinear Maps: –Two cyclic groups of large prime order q: G 1 and G 2 – is a bilinear map if ê should be computable, non-degenerate and satisfies Bilinear Diffie-Hellman assumption, i.e., given P, aP, bP, cP, it is hard to compute
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Computer Science CSC 774Dr. Peng Ning Protocol Sketch Equipped with bilinear map ê and one-way hash function H 1 CA has a master key t. Assume a drivers and cops scenario.
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Computer Science CSC 774Dr. Peng Ning Protocol Sketch Driver’s Licence: “p65748392a”,T A T A = tH 1 (“p65748392a-driver”) Traffic cop credential: “xy6542678d”,T B T B = tH 1 (“xy6542678d-cop”) Driver’s licence, please. Please show me your pseudonym. xy6542678d p65748392a
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Computer Science CSC 774Dr. Peng Ning Protocol Sketch – Attacker Igor Driver’s Licence: “p65748392a”,T A T A = tH 1 (“p65748392a-driver”) Obtains Bob’s pseudonym “xy6542678d” I am a cop. Driver’s licence, please. Please show me your pseudonym. xy6542678d p65748392a ??? This guy is not a cop.
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Computer Science CSC 774Dr. Peng Ning Secret-Handshake Scheme (SHS) SHS.CreateGroup(G): executed by an administrator, generates the group secret GroupSecret G for G. SHS.AddUser(U,G,GroupSecret G ): creates user secret UserSecret U,G for new user U. SHS.HandShake(A,B): Users A and B authenticates each other. B discovers A G if and only if A discovers B G. SHS.TraceUser: Administrator tells the user from a transcript T generated during conversation between A and B. SHS.RemoveUser: Administrator revokes user U
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Computer Science CSC 774Dr. Peng Ning Pairing-Based Handshake (PBH) PBH.CreateGroup: Administrator sets GroupSecret G as a random number PBH.AddUser: Administrator generates pseudonyms for users: and then generates the corresponding secret points: where H 1 is a one-way hash function.
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Computer Science CSC 774Dr. Peng Ning Pairing-Based Handshake (PBH) PBH.Handshake: AB AB AB
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Computer Science CSC 774Dr. Peng Ning Pairing-Based Handshake (PBH) PBH.TraceUser: Since the conversations of handshaking include the pseudonyms, administrator can easily figure out the users. PBH.RemoveUser: Administrator removes user U by broadcasting its pseudonyms to all the other users, so that other users won’t accept pseudonyms of U.
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Computer Science CSC 774Dr. Peng Ning Computational Diffie-Hellman Instead of Bilinear Diffie-Hellman CreateGroup: Administrator picks (p,q,g). p and q are primes, g is a generator of a subgroup in of order q. Also, picks up a private key x, and computes the public key y=g x mod p AddUser: For user U, administrator generates id U, then generates a pair so that id U, w, t will be given to the user.
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Computer Science CSC 774Dr. Peng Ning Computational Diffie-Hellman Instead of Bilinear Diffie-Hellman AddUser: For user U, administrator generates id U, then generates a pair so that id U, w, t will be given to the user. –How to generate the pair (w,t)? Randomly pick r, compute
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Computer Science CSC 774Dr. Peng Ning Computational Diffie-Hellman Instead of Bilinear Diffie-Hellman Handshake: Assume user A has (id A, w A, t A ) and user B has (id B, w B, t B ). Define several marks (ElGamal Encryption): –
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Computer Science CSC 774Dr. Peng Ning Computational Diffie-Hellman Instead of Bilinear Diffie-Hellman AB Handshake: AB randomly picks computes AB randomly picks computes verifies resp b AB verifies resp a
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