Abstract
We analyze the security of an interactive identification scheme. The scheme is the obvious extension of the original square root scheme of Goldwasser, Micali and Rackoff to 2mth roots. This scheme is quite practical, especially in terms of storage and communication complexity. Although this scheme is certainly not new, its security was apparently not fully understood. We prove that this scheme is secure if factoring integers is hard, even against active attacks where the adversary is first allowed to pose as a verifier before attempting impersonation.
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References
M. Bellare, J. Kilian, and P. Rogaway. Entity authentication and key distribution. In Advances in Cryptology — Crypto’ 93, pages 232–233, 1993.
U. Feige, A. Fiat, and A. Shamir. Zero-knowledge proofs of identity. J. Cryptology, 1:77–94, 1988.
A. Fiat and A. Shamir. How to prove yourself: practical solutions to identification and signature problems. In Advances in Cryptology—Crypto’ 86, pages 186–194, 1986.
S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM J. Comput., 18:186–208, 1989.
S. Goldwasser, S. Micali, and R. Rivest. A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput., 17:281–308, 1988.
L. Guillou and J. Quisquater. A “paradoxical” identity-based signature scheme resulting from zero-knowledge. In Advances in Cryptology—Crypto’ 88, pages 216–231, 1988.
L. Guillou and J. Quisquater. A practical zero-knowledge protocol fitted to security microprocesors minimizing both transmission and memory. In Advances in Cryptology-Eurocrypt’ 88, pages 123–128, 1988.
K. Ohta and T. Okamoto. A modification of the Fiat-Shamir Scheme. In Advances in Cryptology-Crypto’ 88, pages 232–243, 1988.
T. Okamoto. Provably secure and practical identification schemes and corresponding signature schemes. In Advances in Cryptology-Crypto’ 92, pages 31–53, 1992.
H. Ong and C. Schnorr. Fast signature generation with a Fiat Shamir-like scheme. In Eurocrypt, pages 432–440, 1990.
C. Schnorr. Efficient signature generation by smart cards. J. Cryptology, 4:161–174, 1991.
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© 1996 Springer-Verlag Berlin Heidelberg
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Shoup, V. (1996). On the Security of a Practical Identification Scheme. In: Maurer, U. (eds) Advances in Cryptology — EUROCRYPT ’96. EUROCRYPT 1996. Lecture Notes in Computer Science, vol 1070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68339-9_30
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DOI: https://doi.org/10.1007/3-540-68339-9_30
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