Zero-Knowledge Proofs and String Commitments Withstanding Quantum Attacks

The concept of zero-knowledge (ZK) has become of fundamental importance in cryptography. However, in a setting where entities are modeled by quantum computers, classical arguments for proving ZK fail to hold since, in the quantum setting, the concept of rewinding is not generally applicable. Moreover, known classical techniques that avoid rewinding have various shortcomings in the quantum setting.

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

[2]  Ran Canetti,et al.  Universally Composable Commitments , 2001, CRYPTO.

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

[4]  Ivan Damgård,et al.  Perfect Hiding and Perfect Binding Universally Composable Commitment Schemes with Constant Expansion Factor , 2001, CRYPTO.

[5]  Moni Naor,et al.  Bit commitment using pseudorandomness , 1989, Journal of Cryptology.

[6]  Maassen,et al.  Generalized entropic uncertainty relations. , 1988, Physical review letters.

[7]  Daniele Micciancio,et al.  Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More , 2003, CRYPTO.

[8]  Erez Petrank,et al.  Is code equivalence easy to decide? , 1997, IEEE Trans. Inf. Theory.

[9]  Igor E. Shparlinski,et al.  On reducing a system of equations to a single equation , 2004, ISSAC '04.

[10]  Alexei Y. Kitaev,et al.  Parallelization, amplification, and exponential time simulation of quantum interactive proof systems , 2000, STOC '00.

[11]  Olivier Danvy,et al.  From Interpreter to Logic Engine by Defunctionalization , 2003, LOPSTR.

[12]  Moni Naor,et al.  Concurrent zero-knowledge , 1998, STOC '98.

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

[14]  Olivier Danvy,et al.  A functional correspondence between call-by-need evaluators and lazy abstract machines , 2003, Inf. Process. Lett..

[15]  Ran Canetti,et al.  Universal Composition with Joint State , 2003, CRYPTO.

[16]  David Chaum,et al.  Minimum Disclosure Proofs of Knowledge , 1988, J. Comput. Syst. Sci..

[17]  Manuel Blum,et al.  Non-interactive zero-knowledge and its applications , 1988, STOC '88.

[18]  Daniele Micciancio.  Improved cryptographic hash functions with worst-case/average-case connection , 2002, STOC '02.

[19]  John Watrous,et al.  Succinct quantum proofs for properties of finite groups , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[20]  Ivan Damgård,et al.  Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols , 1994, CRYPTO.

[21]  Miklós Ajtai,et al.  Generating Hard Instances of Lattice Problems , 1996, Electron. Colloquium Comput. Complex..

[22]  Oded Regev,et al.  Quantum computation and lattice problems , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[23]  Jeroen van de Graaf,et al.  Towards a formal definition of security for quantum protocols , 1998 .

[24]  Gilles Brassard,et al.  Zero-Knowledge Simulation of Boolean Circuits , 1986, CRYPTO.

[25]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[26]  Bas Luttik,et al.  Split-2 bisimilarity has a finite axiomatization over CCS with Hennessy's merge , 2004, Log. Methods Comput. Sci..

[27]  Louis Salvail,et al.  Perfectly Concealing Quantum Bit Commitment from any Quantum One-Way Permutation , 2000, EUROCRYPT.

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

[29]  Louis Salvail,et al.  Computational Collapse of Quantum State with Application to Oblivious Transfer , 2003, TCC.

[30]  NaorMoni,et al.  Perfect Zero-Knowledge Arguments for NP Using Any One-Way Permutation , 1998 .

[31]  John Watrous,et al.  PSPACE has constant-round quantum interactive proof systems , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[32]  Jirí Srba,et al.  Highly Undecidable Questions for Process Algebras , 2004, IFIP TCS.

[33]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[34]  Ulrich Meyer,et al.  Cache-Oblivious Data Structures and Algorithms for Undirected Breadth-First Search and Shortest Paths , 2004, SWAT.

[35]  Boaz Barak,et al.  How to go beyond the black-box simulation barrier , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[36]  Juan A. Garay,et al.  Strengthening Zero-Knowledge Protocols Using Signatures , 2003, Journal of Cryptology.

[37]  I. Damgård,et al.  Zero-Knowledge Proofs and String Commitments Withstanding Quantum Attacks , 2004, CRYPTO.

[38]  Rafail Ostrovsky,et al.  Perfect Zero-Knowledge Arguments for NP Using Any One-Way Permutation , 1998, Journal of Cryptology.

[39]  Kim G. Larsen,et al.  Optimal Strategies in Priced Timed Game Automata , 2004, FSTTCS.

[40]  Ivan Damgård,et al.  Efficient Concurrent Zero-Knowledge in the Auxiliary String Model , 2000, EUROCRYPT.

[41]  Joe Kilian,et al.  On the Concurrent Composition of Zero-Knowledge Proofs , 1999, EUROCRYPT.