4-Round Resettably-Sound Zero Knowledge
Conference paper
Abstract
While 4-round constructions of zero-knowledge arguments are known based on the existence of one-way functions, constuctions of resettably-sound zero-knowledge arguments require either stronger assumptions (the existence of a fully-homomorphic encryption scheme), or more communication rounds. We close this gap by demonstrating a 4- round resettably-sound zero-knowledge argument for NP based on the existence of one-way functions.
Keywords
Signature Scheme Commitment Scheme Auxiliary Input Partial Transcript Signing Oracle
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References
- 1.Barak, B., Goldreich, O.: Universal arguments and their applications. In: Computational Complexity, pp. 162–171 (2002)Google Scholar
- 2.Barak, B., Goldreich, O., Goldwasser, S., Lindell, Y.: Resettably-sound zero-knowledge and its applications. In: FOCS 2002, pp. 116–125 (2001)Google Scholar
- 3.Bellare, M., Goldreich, O.: On defining proofs of knowledge. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 390–420. Springer, Heidelberg (1993)CrossRefGoogle Scholar
- 4.Bellare, M., Jakobsson, M., Yung, M.: Round-optimal zero-knowledge arguments based on any one-way function. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 280–305. Springer, Heidelberg (1997)CrossRefGoogle Scholar
- 5.Bitansky, N., Paneth, O.: From the impossibility of obfuscation to a new non-black-box simulation technique. In: FOCS (2012)Google Scholar
- 6.Bitansky, N., Paneth, O.: On the impossibility of approximate obfuscation and applications to resettable cryptography. In: STOC (2013)Google Scholar
- 7.Blum, M.: How to prove a theorem so no one else can claim it. In: Proc. of the International Congress of Mathematicians, pp. 1444–1451 (1986)Google Scholar
- 8.Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. In: ITCS, pp. 309–325. ACM (2012)Google Scholar
- 9.Chung, K.M., Ostrovsky, R., Pass, R., Visconti, I.: Simultaneous resettability from one-way functions. In: 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, pp. 60–69. IEEE Computer Society (2013)Google Scholar
- 10.Chung, K.M., Pass, R., Seth, K.: Non-black-box simulation from one-way functions and applications to resettable security. In: STOC. ACM (2013)Google Scholar
- 11.Di Crescenzo, G., Persiano, G., Visconti, I.: Improved setup assumptions for 3-round resettable zero knowledge. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 530–544. Springer, Heidelberg (2004)CrossRefGoogle Scholar
- 12.Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: STOC 1990, pp. 416–426 (1990)Google Scholar
- 13.Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178. ACM (2009)Google Scholar
- 14.Goldreich, O.: Foundations of Cryptography — Basic Tools. Cambridge University Press (2001)Google Scholar
- 15.Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for NP. Journal of Cryptology 9(3), 167–190 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
- 16.Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
- 17.Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems. In: STOC 1985, pp. 291–304. ACM (1985), http://doi.acm.org/10.1145/22145.22178
- 18.Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
- 19.Goyal, V., Jain, A., Ostrovsky, R., Richelson, S., Visconti, I.: Constant-round concurrent zero knowledge in the bounded player model. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 21–40. Springer, Heidelberg (2013)CrossRefGoogle Scholar
- 20.Lin, H., Pass, R.: Constant-round non-malleable commitments from any one-way function. In: STOC, pp. 705–714 (2011)Google Scholar
- 21.Merkle, R.C.: A digital signature based on a conventional encryption function. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 369–378. Springer, Heidelberg (1988)Google Scholar
- 22.Micali, S.: Computationally sound proofs. SIAM Journal on Computing 30(4), 1253–1298 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
- 23.Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: STOC 1989, pp. 33–43 (1989)Google Scholar
- 24.Ostrovsky, R., Visconti, I.: Simultaneous resettability from collision resistance. Electronic Colloquium on Computational Complexity (ECCC) 19, 164 (2012)Google Scholar
- 25.Ostrovsky, R., Wigderson, A.: One-way fuctions are essential for non-trivial zero-knowledge. In: ISTCS, pp. 3–17 (1993)Google Scholar
- 26.Pass, R., Rosen, A.: New and improved constructions of non-malleable cryptographic protocols. In: STOC 2005, pp. 533–542 (2005)Google Scholar
- 27.Pass, R., Tseng, W.L.D., Wikström, D.: On the composition of public-coin zero-knowledge protocols. SIAM J. Comput. 40(6), 1529–1553 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
- 28.Rompel, J.: One-way functions are necessary and sufficient for secure signatures (1990)Google Scholar
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