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Reducing elliptic curve logarithms to logarithms in a finite field
Open accessAbstract
Previously, no general-purpose algorithm was known for the elliptic curve logarithm problem that ran in better than exponential time.In this paper we demonstrate the reduction of the elliptic curve logarithm problem to the logarithm problem in the multiplicative group of an extension of the underlying hit e field.For the class of supersingular elliptic curves, the reduction takes probabilistic polynomial time, thus providing a probabilistic subexponential time algorithm for the former problem.The implications of our results to public key cryptography are discussed. , the subgroup of 2? generated by P, and the subgroup of nth roots of unity in Fqk, where n denot es the order of P. The isomorphism is given by the Weil pairing.Since the index-calculus methods for computing logarithms in a finite field have running times that are subexponential, the reduction is useful for the purpose of computing elliptic curve logarithms provided that k is small.This is indeed the case for special classes of elliptic curves, including the
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Elliptic curves over finite fields and the computation of square roots mod 𝑝
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Discrete logarithms in finite fields and their cryptographic significance
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Fast evaluation of logarithms in fields of characteristic two
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Nonsingular plane cubic curves over finite fields
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The Multiple Polynomial Quadratic Sieve
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Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357
Self-citationEfficient Elliptic Curve Exponentiation Using Mixed Coordinates
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Metadata
- Authors
- Menezes, A., Vanstone, S., & Okamoto, T.
- Venue
- Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91
- Publisher
- ACM Press
- Published
- 1991
- Pages
- 80-89
- OpenAlex
- W2028358228
- Cited by
- 337
- References
- 20
- FWCI
- 12.70
- Type
- conference paper
- Language
- en
- Open access
- bronze
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- Menezes, A., Vanstone, S., & Okamoto, T. (1991). Reducing elliptic curve logarithms to logarithms in a finite field. Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91. https://doi.org/10.1145/103418.103434
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