Abstract
We present new results in the framework of secure multiparty computation based on homomorphic threshold cryptosystems. We introduce the conditional gate as a special type of multiplication gate that can be realized in a surprisingly simple and efficient way using just standard homomorphic threshold ElGamal encryption. As addition gates are essentially for free, the conditional gate not only allows for building a circuit for any function, but actually yields efficient circuits for a wide range of tasks.
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References
Algesheimer, J., Camenisch, J., Shoup, V.: Efficient computation modulo a shared secret with application to the generation of shared safe-prime products. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)
Boudot, F., Schoenmakers, B., Traoré, J.: A fair and effcient solution to the socialist millionaires’ problem. Discrete Applied Mathematics 111(1–2), 23–36 (2001); Special issue on Coding and Cryptology
Cachin, C.: Efficient private bidding and auctions with an oblivious third party. In: 6th ACM Conference on Computer and Communications Security, pp. 120–127. ACM Press, New York (1999)
Cramer, R., Damgård, I., Nielsen, J.B.: Multiparty computation from threshold homomorphic encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280–300. Springer, Heidelberg (2001)
Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)
Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002)
Damgård, I., Jurik, M.: A length-flexible threshold cryptosystem with applications. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 350–364. Springer, Heidelberg (2003)
Damgård, I., Nielsen, J.B.: Universally composable efficient multiparty computation from threshold homomorphic encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 247–264. Springer, Heidelberg (2003)
Franklin, M., Haber, S.: Joint encryption and message-efficient secure computation. Journal of Cryptology 9(4), 217–232 (1996)
Fischlin, M.: A cost-effective pay-per-multiplication comparison method for millionaires. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 457–471. Springer, Heidelberg (2001)
Gilboa, N.: Two party RSA key generation. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 116–129. Springer, Heidelberg (1999)
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 295–310. Springer, Heidelberg (1999)
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure applications of Pedersen’s distributed key generation protocol. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 373–390. Springer, Heidelberg (2003)
Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)
Garay, G., MacKenzie, P., Yang, K.: Efficient and universally composable committed oblivious transfer and applications. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 297–316. Springer, Heidelberg (2004)
Garay, J., MacKenzie, P., Yang, K.: Efficient and secure multi-party computation with faulty majority and complete fairness (2004) (submitted), Available at http://eprint.iacr.org/2004/009/
Groth, J.: A verifable secret shuffle of homomorphic encryptions. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 145–160. Springer, Heidelberg (2003)
Ioannidis, I., Grama, A.: An efficient protocol for Yao’s millionaires’ problem. In: Proceedings of the 36th Annual Hawaii International Conference on System Sciences (HICSS 2003), 6 pages. IEEE, Los Alamitos (2003)
Juels, A., Jakobsson, M.: Mix and match: Secure function evaluation via ciphertexts. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 162–177. Springer, Heidelberg (2000)
Jakobsson, M., Yung, M.: Proving without knowing: On oblivious, agnostic and blindfolded provers. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 186–200. Springer, Heidelberg (1996)
Katz, J., Myers, S., Ostrovsky, R.: Cryptographic counters and applications to electronic voting. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 78–92. Springer, Heidelberg (2001)
Kurosawa, K., Ogata, W.: Bit-slice auction circuit. In: Gollmann, D., Karjoth, G., Waidner, M. (eds.) ESORICS 2002. LNCS, vol. 2502, pp. 24–38. Springer, Heidelberg (2002)
Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay—a secure two-party computation system. In: Proceedings of Usenix Security 2004, August 9–13 (2004) (to appear)
Naor, M., Nissim, K.: Communication complexity and secure function evaluation. In: Mixer II, NEC Research Institute, Princeton, New Jersey. DIMACS Mixer Series, October 9 (2001)
Pedersen, T.: A threshold cryptosystem without a trusted party. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991)
Pinkas, B.: Fair secure two-party computation. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 87–105. Springer, Heidelberg (2003)
Yao, A.: Protocols for secure computations. In: Proc. 23rd IEEE Symposium on Foundations of Computer Science (FOCS 1982), pp. 160–164. IEEE Computer Society, Los Alamitos (1982)
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Schoenmakers, B., Tuyls, P. (2004). Practical Two-Party Computation Based on the Conditional Gate. In: Lee, P.J. (eds) Advances in Cryptology - ASIACRYPT 2004. ASIACRYPT 2004. Lecture Notes in Computer Science, vol 3329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30539-2_10
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