A New Identification Scheme Based on the Bilinear Diffie-Hellman Problem
We construct an interactive identification scheme based on the bilinear Diffie-Hellman problem and analyze its security. This scheme is practical in terms of key size, communication complexity, and availability of identity-variance provided that an algorithm of computing the Weil-pairing is feasible. We prove that this scheme is secure against active attacks as well as passive attacks if the bilinear Diffie-Hellman problem is intractable. Our proof is based on the fact that the computational Diffie-Hellman problem is hard in the additive group of points of an elliptic curve over a finite field, on the other hand, the decisional Diffie-Hellman problem is easy in the multiplicative group of the finite field mapped by a bilinear map. Finally, this scheme is compared with other identification schemes.
KeywordsGap-problems Identification scheme Bilinear Diffie-Hellman problem Weil-pairing
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- 1.M. Bellare and P. Rogaway, “Random Oracles are Practical: A Paradigm for Designing Efficient Protocols”, ACM Conference on Computer and Communications Security, pp. 62–73, 1993.Google Scholar
- 4.I. Blake, G. Seroussi and N. Smart, “Elliptic curves in cryptography”, Cambridge University Prress, LNS 265, 1999.Google Scholar
- 7.A. Fiat and A. Shamir, “How to prove yourself: pratical solutions to identification and signature problems”, Advances in Cryptology — Crypto’ 86, LNCS 263, Springer-Verlag, pp. 186–194, 1987.Google Scholar
- 8.O. Goldreich and H. Krawczyk, “On the composition of zero-knowledge proof systems”, In Proceedings of the 17th ICALP, LNCS 443, Springer-Verlag, pp. 268–282, 1990.Google Scholar
- 11.A. Joux and K. Nguyen, “Seperating decision Diffie-Hellman from Diffie-Hellman in cryptographic groups”, available from eprint.iacr.org.
- 12.A. J. Menezes, “Elliptic curve public key cryptosystems”, Kluwer Academic Publishers, 1993.Google Scholar
- 14.V. Miller, “Short programs for functions on curves”, unpublished manuscript, 1986.Google Scholar
- 15.T. Okamoto, “Provably secure and practical identification schemes and corresponding signature schemes”, Advances in Cryptology — Crypto’ 92, LNCS 740, Springer-Verlag, pp. 31–53, 1993.Google Scholar
- 16.T. Okamoto and D. Pointcheval, “The gap-problem: a new class of problems for the security of cryptographic schemes”, PKC 2001, LNCS 1992, Springer-Verlag, pp. 104–118, 2001.Google Scholar
- 17.K. Ohta and T. Okamoto, “A modification of the Fiat-Shamir scheme”, Advances in Cryptology-Crypto’ 88, LNCS 403, Springer-Verlag, pp. 232–243, 1990.Google Scholar
- 19.A.D. Santis, S. Micali, and G. Persiano, “Non-interactive zero-knowledge proof systems”, Advances in Cryptology — Crypto’ 87, LNCS 293, pp. 52–72, 1988.Google Scholar
- 22.J. H. Silverman, “The arithmetic of elliptic curves”, Springer-Verlag, GTM 106, 1986.Google Scholar
- 24.T. Yamanaka, R. Sakai, and M. Kasahara, “Fast computation of pairings over elliptic curves”, Proc. of SCIS 2002, pp. 709–714, Jan. 29–Feb. 1, 2002, Shirahama, Japan.Google Scholar