Abstract
We propose a distributed key generation protocol for the threshold Paillier cryptosystem. Often in the multiparty computation based on the threshold Paillier cryptosystem, the existence of a trusted dealer is assumed to distribute secret key shares, but it can be a single point of attack, so it is not preferable. Building on the threshold Paillier cryptosystem with a trusted dealer, we show how to eliminate the trusted dealer by robust distributed key generation without using safe primes.
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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: CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)
Bangerter, E., Camenisch, J., Krenn, S.: Efficiency limitations for Sigma-protocols for group homomorphisms. In: Micciancio, D. (ed.) Theory of Cryptography. LNCS, vol. 5978, pp. 553–571. Springer, Heidelberg (2010)
Baudron, O., Fouque, P.-A., Pointcheval, D., Poupard, G., Stern, J.: Practical multi-candidate election system. In: Proc. 20th ACM PODC, pp. 274–283 (2001)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorem for non-cryptographic fault-tolerant distributed computation. In: Proc. 20th Annual ACM Symposium on Theory of Computing (STOC), pp. 1–10 (1988)
Boneh, D., Franklin, M.: Efficient generation of shared RSA keys. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 425–439. Springer, Heidelberg (1997)
Boneh, D., Franklin, M.: Efficient generation of shared RSA keys. J. ACM 48(4), 702–722 (2001)
Brickell, E., Chaum, D., Damgård, I., Graaf, J.: Gradual and verifiable release of a secret. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 156–166. Springer, Heidelberg (1988)
Cachin, C.: An asynchronous protocol for distributed computation of RSA inverses and its applications. In: Proc. ACM PODC, pp. 153–162 (2003)
Camenisch, J., Michels, M.: Proving in zero-knowledge that a number is the product of two safe primes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 107–122. Springer, Heidelberg (1999)
Catalano, D., Gennaro, R., Halevi, S.: Computing inverses over a shared secret modulus. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 190–207. Springer, Heidelberg (2000)
Chan, A., Frankel, Y., Tsiounis, Y.: Easy come - easy go divisible cash. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 561–575. Springer, Heidelberg (1998); Updated version with corrections, GTE Tech. Report available at http://www.ccs.neu.edu/home/yiannis/
Cramer, R., Damgård, I.: Zero-knowledge proofs for finite field arithmetic or: Can zero-knowledge be for free? In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 424–441. Springer, Heidelberg (1998)
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)
Damgård, I., Dupont, K.: Efficient threshold RSA signatures with general moduli and no extra assumptions. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 346–361. Springer, Heidelberg (2005)
Damgård, I., Fujisaki, E.: An integer commitment scheme based on groups with hidden order. Cryptology ePrint Archive 2001/064 (2001)
Damgård, I., Fujisaki, E.: A statistically-hiding integer commitment scheme based on groups with hidden order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 125–142. Springer, Heidelberg (2002)
Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)
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., Koprowski, M.: Practical threshold RSA signatures without a trusted dealer. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 152–165. Springer, Heidelberg (2001)
Damgård, I., Mikkelsen, G.L.: Efficient robust and constant-round distributed RSA key generation. In: Micciancio, D. (ed.) Theory of Cryptography. LNCS, vol. 5978, pp. 183–200. Springer, Heidelberg (2010)
Damgård, I., Thorbek, R.: Linear integer secret sharing and distributed exponentiation. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 75–90. Springer, Heidelberg (2006)
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Fouque, P.-A., Poupard, G., Stern, J.: Sharing decryption in the context of voting or lotteries. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 90–104. Springer, Heidelberg (2001)
Fouque, P.A., Stern, J.: Fully distributed threshold RSA under standard assumptions. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 310–330. Springer, Heidelberg (2001)
Frankel, Y., MacKenzie, P.D., Yung, M.: Robust efficient distributed RSA-key generation. In: Proc. 30th ACM STOC, pp. 663–672 (1998)
Franklin, M.K., Gondree, M., Mohassel, P.: Improved efficiency for private stable matching. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 163–177. Springer, Heidelberg (2006)
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. J. Cryptology 20(1), 51–83 (2007)
Hirt, M., Nielsen, J.B.: Robust multiparty computation with linear communication complexity. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 463–482. Springer, Heidelberg (2006)
Malkin, M., Wu, T., Boneh, D.: Experimenting with shared RSA key generation. In: Proc. Internet Society’s 1999 Symposium on Network and Distributed System Security (SNDSS 1999), pp. 43–56 (1999)
Okamoto, T.: An efficient divisible electronic cash scheme. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 438–451. Springer, Heidelberg (1995)
Ong, E., Kubiatowicz, J.: Optimizing robustness while generating shared secret safe primes. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 120–137. Springer, Heidelberg (2005)
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
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)
Pedersen, T.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Rabin, T.: A simplified approach to threshold and proactive RSA. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 89–104. Springer, Heidelberg (1998)
Schoenmakers, B., Tuyls, P.: Efficient binary conversion for Paillier encrypted values. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 522–537. Springer, Heidelberg (2006)
Shamir, A.: How to share a secret. Communications of ACM 22(11), 612–613 (1979)
Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)
SecureSCM Project. Secure computation models and frameworks. Technical Report D9.1, D9.1_SecureSCM_V1.0.pdf (2008), http://www.securescm.org/
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Nishide, T., Sakurai, K. (2011). Distributed Paillier Cryptosystem without Trusted Dealer. In: Chung, Y., Yung, M. (eds) Information Security Applications. WISA 2010. Lecture Notes in Computer Science, vol 6513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17955-6_4
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DOI: https://doi.org/10.1007/978-3-642-17955-6_4
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