Transfering Proofs of Zero-Knowledge Systems with Quantum Correlations

The use of quantum correlations to attack security protocols is an important research line deserving growing attention. An important class of cryptographic protocols used as building blocks for several other more complex protocols is zero-knowledge proof systems. One of the properties that zero-knowledge proof systems are assumed to satisfy is that it is impossible for the verifier to show to a third party that he has interacted with the prover (impossibility of transferring proofs). Herein, it is shown how Bell pairs, together with tamper-proofing, can be used to break the impossibility of transferring proofs for an important class of zero-knowledge proof systems.

[1]  James P. Crutchfield,et al.  Quantum automata and quantum grammars , 2000, Theor. Comput. Sci..

[2]  Cynthia Dwork,et al.  Finite state verifiers I: the power of interaction , 1992, JACM.

[3]  John Watrous.  Zero-Knowledge against Quantum Attacks , 2009, SIAM J. Comput..

[4]  Shafi Goldwasser,et al.  Multi party computations: past and present , 1997, PODC '97.

[5]  Birgit Pfitzmann,et al.  Composition and integrity preservation of secure reactive systems , 2000, CCS.

[6]  Yuval Ishai,et al.  On Adaptive vs. Non-adaptive Security of Multiparty Protocols , 2001, EUROCRYPT.

[7]  Eric Allender,et al.  Complexity Theory , 1997, Encyclopedia of Cryptography and Security.

[8]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[9]  Ronald Cramer,et al.  A secure and optimally efficient multi-authority election scheme , 1997, Eur. Trans. Telecommun..

[10]  Ingo Wegener,et al.  Complexity Theory , 2005 .

[11]  Dan Suciu,et al.  Journal of the ACM , 2006 .

[12]  Alexander Russell,et al.  The symmetric group defies strong Fourier sampling , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[13]  Silvio Micali,et al.  Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems , 1991, JACM.

[14]  Amos Fiat,et al.  Untraceable Electronic Cash , 1990, CRYPTO.

[15]  John C. Mitchell,et al.  A Probabilistic Polynomial-time Calculus For Analysis of Cryptographic Protocols (Preliminary Report) , 2001, MFPS.

[16]  John C. Mitchell,et al.  Composition of Cryptographic Protocols in a Probabilistic Polynomial-Time Process Calculus , 2003, CONCUR.

[17]  Amos Fiat,et al.  How to Prove Yourself: Practical Solutions to Identification and Signature Problems , 1986, CRYPTO.

[18]  Ran Canetti,et al.  Security and Composition of Multiparty Cryptographic Protocols , 2000, Journal of Cryptology.

[19]  Adi Shamir,et al.  IP = PSPACE , 1992, JACM.