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Reducing elliptic curve logarithms to logarithms in a finite field
Abstract
Elliptic curve cryptosystems have the potential to provide relatively small block size, high-security public key schemes that can be efficiently implemented. As with other known public key schemes, such as RSA and discrete exponentiation in a finite field, some care must be exercised when selecting the parameters involved, in this case the elliptic curve and the underlying field. Specific classes of curves that give little or no advantage over previously known schemes are discussed. The main result of the paper is to demonstrate the reduction of the elliptic curve logarithm problem to the logarithm problem in the multiplicative group of an extension of the underlying finite 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.>
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Citations
Cites
The Arithmetic of Elliptic Curves
Silverman, J. H. (1986) · Graduate Texts in Mathematics · doi:10.1007/978-1-4757-1920-8 · Cited by 4,044
Cited by
A One Round Protocol for Tripartite Diffie–Hellman
Joux, A. (2000) · Lecture Notes in Computer Science · doi:10.1007/10722028_23 · Cited by 1,039
The State of Elliptic Curve Cryptography
Koblitz, N., Menezes, A., & Vanstone, S. (2000) · Designs, Codes and Cryptography · doi:10.1023/a:1008354106356 · Cited by 685
Self-citationThe Weil Pairing, and Its Efficient Calculation
Miller, V. S. (2004) · Journal of Cryptology · doi:10.1007/s00145-004-0315-8 · Cited by 578
Galbraith, S. D., Harrison, K., & Soldera, D. (2002) · Lecture Notes in Computer Science · doi:10.1007/3-540-45455-1_26 · Cited by 566
ID-Based Blind Signature and Ring Signature from Pairings
Zhang, F., & Kim, K. (2002) · Lecture Notes in Computer Science · doi:10.1007/3-540-36178-2_33 · Cited by 530
Metadata
- Authors
- Menezes, A. J., Okamoto, T., & Vanstone, S. A.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1993
- Volume
- 39
- Issue
- 5
- Pages
- 1639-1646
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2111310412
- Cited by
- 1,022
- References
- 1
- FWCI
- 15.03
- Type
- journal article
- Language
- en
- Open access
- closed
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- Menezes, A. J., Okamoto, T., & Vanstone, S. A. (1993). Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Transactions on Information Theory. https://doi.org/10.1109/18.259647
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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