Abstract
If p is a prime and g and x integers, then computation of y such that
is referred to as discrere exponentiarion. Using the successive squaring method, it is very fast (polynomial in the number of bits of ∣p∣ + ∣g∣ + ∣x∣). On the other hand, the inverse problem, namely, given p, g, and y, to compute some z such that Equation 1.1 holds, which is referred to as the discrete logarithm problem, appears to be quite hard in general. Many of the most widely used public key cryptosystems are based on the assumption that discrete logarithms are indeed hard to compute, at least for carefully chosen primes.
Full text of this paper to appear in Designs, Codes, and Cryptography 1 (1991).
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References
D. Coppersmith, A. Odlyzko, and R. Schroeppel, Discrete logarithms in GF (p), Algorithmica 1 (1986), 1–15.
B. A. LaMacchia and A. M. Odlyzko, Solving large sparse linear systems over finite fields, Advances in Cryptology: Proceedings of Crypto’ 90, A. Menezes, S. Vanstone, eds., to be published.
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A. M. Odlyzko, Discrete logarithms in finite fields and their cryptographic significance, Advances in Cryptology: Proceedings of Eurocrypt’ 84, T. Beth, N. Cot, I. Ingemarsson, eds., Lecture Notes in Computer Science 209, Springer-Verlag, NY (1985), 224–314.
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© 1991 Springer-Verlag Berlin Heidelberg
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LaMacchia, B.A., Odlyzko, A.M. (1991). Computation of Discrete Logarithms in Prime Fields. In: Menezes, A.J., Vanstone, S.A. (eds) Advances in Cryptology-CRYPTO’ 90. CRYPTO 1990. Lecture Notes in Computer Science, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-38424-3_43
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