Abstract
We present the first private information retrieval (PIR) scheme which is both, deterministically correct and has poly-logarithmic communication complexity. Our PIR protocol is symmetrically secure, and improves by a few orders of magnitude the known probabilistically correct poly-logarithmic scheme. This result is achieved as an application of our methodology which introduces a broad family of games, called Secure Games with Polynomial Expressions (SGPEs), that involve two interacting players: Alice and Bob. The objective of these games is the secure “interactive computation” of the value of a polynomial expression which is made up of polynomials and field elements that both players distributedly contribute to the game. The players wish to keep some or all the data (field elements and polynomials) they contribute to the game, secret and independently secure. We show that any SGPE can be played much more efficiently than by using generic methods, and so that no party reveals more than what it intends to. Besides the above mentioned PIR application, we present additional applications such as the “lists’ intersection predicate” which is useful for secure conduct of e-commerce procedures, such as negotiation methods known as “settlement escrows” in the legal/ economics/ business literature.
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References
Elwyn R. Berlekamp, Algebraic Coding Theory. McGraw-Hill, 1968.
Elwyn R. Berlekamp and L. Welch, Error Correction of Algebraic Block Codes. U.S. Patent, Number 4,633,470 1986.
Daniel Bleichenbacher and Phong Nguyen, Noisy Polynomial Interpolation and Noisy Chinese Remaindering. In the Proceedings of EURO-CRYPT2000, Lecture Notes in Computer Science, Springer, 2000.
Adam M. Brandeburger and Barry J. Nalebuff, Co-opetition, Doubleday Publications, 1996.
Christian Cachin, Silvio Micali, and Markus Stadler, Computationally Private Information Retrieval with Polylogarithmic Communication, In the Proceedings of EUROCRYPT’ 99, Lecture Notes in Computer Science, Springer, 1999.
Benny Chor and Niv Gilboa, Computationally Private Information Retrieval, In the Proceedings of the 29th ACM Symposium on the Theory of Computing, 1997.
Benny Chor, Oded Goldreich, Eyal Kushilevitz, and Madhu Sudan, Private Information Retrieval, In the Proceedings of the 36th Annual Symposium on Foundations of Computer Science, 1995.
Yael Gertner, Yuval Ishai, Eyal Kushilevitz, and Tal Malkin, Protecting Data Privacy in Private Information Retrieval Schemes, In the Proceedings of the 30th ACM Symposium on the Theory of Computing, 1998.
Robert H. Gertner and Geoffrey P. Miller, Settlement Escrows, Journal of Legal Studies, Vol. 24, pp.87–122, 1995.
S. Goldwasser, Multi-party computations: Past and present. In PODC’97, pages 1–6. invited talk.
Venkatesan Guruswami and Madhu Sudan, Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes. In the Proceedings of the 39th Annual Symposium on Foundations of Computer Science, 1998.
Oded Goldreich, Silvio Micali and Avi Wigderson, How to Play any Mental Game — A Completeness Theorem for Protocols with Honest Majority. In the Proceedings of the 19th ACMSymposium on the Theory of Computing, 1987.
Oded Goldreich, Madhu Sudan and Ronitt Rubinfeld, Learning Polynomials with Queries: The Highly Noisy Case. In the Proceedings of the 36th Annual Symposium on Foundations of Computer Science, 1995.
Aggelos Kiayias and Moti Yung, Computationally Perfect Symmetric Encryption based on Polynomial Reconstruction, manuscript, 2001.
Joe Kilian, Use of Randomness in Algorithms and Protocols. MIT Press, Cambridge, Massachusetts 1990.
Eyal Kushilevitz amd Rafail Ostrovsky, Replication is not Needed: Single Database, Computationally-Private Information Retrieval, In the Proceedings of the 38th Annual Symposium on Foundations of Computer Science, 1997.
F. J. MacWilliams and N. Sloane, The Theory of Error Correcting Codes. North Holland, Amsterdam, 1977.
Moni Naor and Benny Pinkas, Oblivious Transfer and Polynomial Evaluation. In the Proceedings of the 31th ACM Symposium on the Theory of Computing, 1999.
Madhu Sudan, Decoding of Reed Solomon Codes beyond the Error-Correction Bound. Journal of Complexity 13(1), pp. 180–193, 1997.
Andrew C. Yao, How to Generate and Exchange Secrets. In the Proceedings of the 27th Annual Symposium on Foundations of Computer Science, 1986.
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Kiayias, A., Yung, M. (2001). Secure Games with Polynomial Expressions. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_76
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DOI: https://doi.org/10.1007/3-540-48224-5_76
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