Abstract
We instantiate the cryptosystem proposed by Boneh, Goh, and Nissim in TCC’05 [5] into an entity authentication scheme, in which an entity is authenticated by an interactive zero-knowledge proof on its private key. Completeness and soundness of our scheme is supported by the indistinguishability of BGN ciphertexts of sums and products, which essentially relies on the semantic security of the BGN cryptosystem. We further extend our scheme so that the authentication conveys Pedersen commitments on a message, while the BGN authentication serves the ‘proving you know how to open’ functionality for the commitment. Our message commitment scheme is both statistically hiding and computationally binding provided the subgroup decision problem is hard.
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References
Adida, B., Wikstrom, D.: Obfuscated ciphertext mixing. Cryptology ePrint Archive, Report 2005/394 (November 2005), http://eprint.iacr.org/
Vanstone, S.A., Menezes, A., van Oorschot, P.C.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
Beaver, D.: Adaptive zero knowledge and computational equivocation (extended abstract). In: STOC, pp. 629–638 (1996)
Blum, M.: Coin flipping by telephone. In: IEEE Spring COMPCOM, pp. 133–137 (1982)
Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-dnf formulas on ciphertexts. In: Theory of Cryptography Conference, TCC, Feburary 2005, pp. 325–341 (2005)
C.C.I.T.T.: Recommendation X.509. The Directory-Authentication (1988)
Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)
Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable zero-knowledge (extended abstract). In: STOC, pp. 235–244 (2000)
Chase, M., Healy, A., Lysyanskaya, A., Malkin, T., Reyzin, L.: Mercurial commitments with applications to zero-knowledge sets. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 422–439. Springer, Heidelberg (2005)
Courtois, N.: Efficient zero-knowledge authentication based on a linear algebra problem minRank. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 402–421. Springer, Heidelberg (2001)
Damgård, I., Nielsen, J.B.: Perfect hiding and perfect binding universally composable commitment schemes with constant expansion factor. Technical report, BRICS Report Series RS-01-41 (October 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)
Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000)
Feige, U., Fiat, A., Shamir, A.: Zero-knowledge proofs of identity. J. Cryptology 1(2), 77–94 (1988)
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)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)
The Open Group. Unix., http://www.unix.org/
Haller, N.M.: The s/key one-time password system. In: Symposium on Network and Distributed System Security, pp. 151–157 (1994)
International Organization for Standardization. ISO/IEC 9798-2 (July 1999)
Lamport, L.: Password authentification with insecure communication. Commun. ACM 24(11), 770–772 (1981)
Liskov, M., Lysyanskaya, A., Micali, S., Reyzin, L., Smith, A.: Mutually independent commitments. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 385–401. Springer, Heidelberg (2001)
Naor, M.: Bit commitment using pseudorandomness. J. Cryptology 4(2), 151–158 (1991)
Naor, M.: Deniable ring authentication. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 481–498. Springer, Heidelberg (2002)
Needham, R.M., Schroeder, M.D.: Using encryption for authentication in large networks of computers. Commun. ACM 21(12), 993–999 (1978)
Needham, R.M., Schroeder, M.D.: Authentication revisited. Operating Systems Review 21(1), 7 (1987)
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Schnorr, C.-P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)
Steiner, J.G., Neuman, B.C., Schiller, J.I.: Kerberos: An authentication service for open network systems. In: USENIX Winter, pp. 191–202 (1988)
Groth, J., et al.: Perfect non-interactive zero knowledge for np. Cryptology ePrint Archive, Report 2005/290 (August 2005), http://eprint.iacr.org/
Wei, V.K.: Signature from a new subgroup assumption. Cryptology ePrint Archive, Report 2005/429 (November 2005), http://eprint.iacr.org/
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Chan, YY., Li, J. (2006). BGN Authentication and Its Extension to Convey Message Commitments. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751595_40
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DOI: https://doi.org/10.1007/11751595_40
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