Abstract
We study the problem of secure function evaluation in the so called commodity based cryptography model as proposed by Beaver in his STOC 97 paper. We propose very efficient protocols for implementing addition and multiplication over GF(q). Differently than in previous works, in our protocol each step of the computation is verifiable. Moreover, no copying of commitments is necessary, because commitments are not destroyed during the computation. Also, no error correcting techniques are necessary here yielding simpler protocols. The protocol is based on novel verifiable primitives (one time multiplication proofs, multiplication gates and pre-distributed commitments) in the commodity based model which allow two players to perform secure multiplication of shares over GF(q) with round-complexity equal to one.
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References
Asokan, N., Shoup, V., Waidner, M.: Optimistic Fair Exchange of Digital Signatures. IEEE Journal on Selected Areas in Communications 18(4), 593–610 (2000)
Beaver, D.: Foundations of Secure Interactive Computing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 377–391. Springer, Heidelberg (1991)
Beaver, D.: Efficient Multiparty Protocols Using Circuit Randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1991)
Beaver, D.: Commodity-Based Cryptography (Extended Abstract). In: STOC 1997, pp. 446–455 (1997)
Beaver, D.: One-Time Tables for Two-Party Computation. In: Hsu, W.-L., Kao, M.-Y. (eds.) COCOON 1998. LNCS, vol. 1449, pp. 361–370. Springer, Heidelberg (1998)
Blundo, C., Masucci, B., Stinson, D.R., Wei, R.: Constructions and Bounds for Unconditionally Secure Non-Interactive Commitment Schemes. Designs, Codes, and Cryptography, Special Issue in Honour of Ron Mullin 26(1-3), 97–110 (2002)
Chaum, D., Crepeau, C., Damgard, I.: Multiparty Unconditionally Secure Protocols (extended abstract). In: STOC 1988, pp. 11–19 (1988)
Cleve, R.: Controlled Gradual Disclosure Schemes for Random Bits and Their Applications. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 573–588. Springer, Heidelberg (1989)
Crepeau, C., van de Graaf, J., Tapp, A.: Committed Oblivious Transfer and Private Multi-Party Computations. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 110–123. Springer, Heidelberg (1995)
Goldreich, O.: Secure Multi-Party Computation, lecture notes, Available from http://www.wisdom.weizmann.ac.il/~oded/pp.html
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non- Cryptographic Fault-Tolerant Distributed Computation. In: 20th STOC, pp. 1–10 (1988)
Goldwasser, S., Levin, L.A.: Fair Computation of General Functions in Presence of Immoral Majority. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 77–93. Springer, Heidelberg (1990)
Hanaoka, G., Shikata, J., Zheng, Y., Imai, H.: Unconditionally Secure Digital Signature Schemes Admitting Transferability. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 130–142. Springer, Heidelberg (2000)
Kilian, J.: Founding Cryptography on Oblivious Transfer. In: STOC 1988, pp. 20–31 (1988)
Matsumoto, T., Imai, H.: On the Key Predistribution Systems: A Practical Solution to the Key Distribution Problem. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 185–193. Springer, Heidelberg (1988)
Micali, S., Rogaway, P.: Secure Computation (Abstract). In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 392–404. Springer, Heidelberg (1991)
Nascimento, A.C.A., Mueller-Quade, J., Otsuka, A., Imai, H.: Unconditionally Secure Homomorphic Commitments. In: Fossorier, M.P.C., Høholdt, T., Poli, A. (eds.) AAECC 2003. LNCS, vol. 2643, pp. 87–97. Springer, Heidelberg (2003)
Rabin, T.: Robust Sharing of Secrets When the Dealer Is Honest or Cheating. JACM 41(6), 1089–1109 (1994)
Rivest, R.L.: Unconditionally Secure Commitment and Oblivious Transfer Schemes Using Concealing Channels and a Trusted Initializer, Available from http://theory.lcs.mit.edu/~rivest/Rivest-commitment.pdf (preprint)
Yao, A.C.: Protocols for Secure Computations. In: FOCS 1982, pp. 160–164 (1982)
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Nascimento, A.C.A., Mueller-Quade, J., Otsuka, A., Hanaoka, G., Imai, H. (2003). Unconditionally Secure Homomorphic Pre-distributed Bit Commitment and Secure Two-Party Computations. In: Boyd, C., Mao, W. (eds) Information Security. ISC 2003. Lecture Notes in Computer Science, vol 2851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10958513_12
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DOI: https://doi.org/10.1007/10958513_12
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