Abstract
Bellare and Micali have shown how to build strong signature schemes from the mere assumption that trapdoor permutation generators exist. Subsequently, Naor and Yung have shown how to weaken the assumption under which a strong signature scheme can be built: it is enough to start from permutations that are one-way rather than trapdoor. In this paper, which is independent from and orthogonal to the work of Naor and Yung, we weaken in a different way the assumption under which a strong signature scheme can be built: it is enough to start from what we call a weak signature scheme (defined below). Weak signature schemes are trapdoor in nature, but they need not be based on permutations. As an application, the Guillou-Quisquater-Simmons signature scheme (a variant on Williams’ and Rabin’s schemes, also defined below) can be used to build a strong signature scheme, whereas it is not clear that it gives rise directly to an efficient trapdoor (or even one-way) permutation generator.
Supported in part by Canada NSERC grant A4107.
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Bellare, M. and Micali, M., “How to sign given any trapdoor function”, Proceedings of the 20th ACM Symposium on Theory of Computing, 1988, pp. 32–42. (Also presented at CRYPTO’ 88.)
Diffie, W. and Hellman, M. E., “New directions in cryptography”, IEEE Transactions on Information Theory, vol. IT-22, 1976, pp. 644–654.
Goldwasser, S., Micali, S. and Rivest, R.L., “A digital signature scheme secure against adaptive chosen-message attacks”, SIAM Journal on Computing, vol. 17, no. 2, April 1988, pp. 281–308.
Guillou, L. and Quisquater, J.-J., “Efficient digital public-key signatures with shadow”, Advances in Cryptology-CRYPTO’ 87 Proceedings, Springer-Verlag, 1988, p. 223.
Naor, M. and Yung, M., “Universal one-way hash functions and their cryptographic applications”, Proceedings of the 21st ACM Symposium on Theory of Computing, 1989, pp. 33–43.
Rabin, M. O., “Digital signatures and public-key functions as intractable as factorization”, Technical Report mit/lcs/tr-212, M.I.T., 1979.
Rivest, R. L., Shamir, A. and Adleman, L. M., “A method for obtaining digital signatures and public-key cryptosystems”, Communications of the ACM, vol. 21, 1978, pp. 120–126.
Simmons, G. J., “A protocol to provide verifiable proof of identity and unforgeable transaction receipts”, IEEE Journal on Selected Areas of Communications, vol. 7, no. 4, May 1989, pp. 435–447.
Simmons, G. J. and Purdy, G. B., “Zero-knowledge proofs of identity and veracity of transactions receipts”, Advances in Cryptology-EUROCRYPT’ 88 Proceedings, Springer-Verlag, 1988, pp. 35–49.
Williams, H. C., “A modification of the RSA public-key encryption procedure”, IEEE Transactions on Information Theory, vol.IT-26, 1980, pp. 726–729.
Yao, A. C.-C., “Theory and applications of trapdoor functions”, Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science, 1982, pp. 80–91.
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© 1990 Springer-Verlag Berlin Heidelberg
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Brassard, G. (1990). How to improve signature schemes. In: Quisquater, JJ., Vandewalle, J. (eds) Advances in Cryptology — EUROCRYPT ’89. EUROCRYPT 1989. Lecture Notes in Computer Science, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46885-4_3
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DOI: https://doi.org/10.1007/3-540-46885-4_3
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