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Evaluating logarithms in GF(2ⁿ)

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Don CoppersmithAuthors Info & Claims

STOC '84: Proceedings of the sixteenth annual ACM symposium on Theory of computing

Pages 201 - 207

https://doi.org/10.1145/800057.808682

Published: 01 December 1984 Publication History

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Abstract

We present a method for determining logarithms in GF(2ⁿ). Its asymptotic running time is O( exp (cn^1/3log^2/3n)) for a small constant c, while, by comparison, Adleman's scheme runs in time O( exp (c'n^1/2log^1/2n)). The ideas give a dramatic improvement even for moderate-sized fields such as GF(2¹²⁷), and make (barely) possible computations in fields of size around 2⁴⁰⁰. The method is not applicable to GF(q) for a large prime q.

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Barreto PLibert BMcCullagh NQuisquater J(2010)Signcryption Schemes Based on Bilinear MapsPractical Signcryption10.1007/978-3-540-89411-7_5(71-97)Online publication date: 4-Oct-2010
https://doi.org/10.1007/978-3-540-89411-7_5
Bertoni GBreveglieri LFragneto PPelosi GSportiello LGielen G(2006)Software implementation of Tate pairing over GF(2m)Proceedings of the conference on Design, automation and test in Europe: Designers' forum10.5555/1131355.1131358(7-11)Online publication date: 6-Mar-2006
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Granger RHolt APage DSmart NVercauteren F(2004)Function Field Sieve in Characteristic ThreeAlgorithmic Number Theory10.1007/978-3-540-24847-7_16(223-234)Online publication date: 2004
https://doi.org/10.1007/978-3-540-24847-7_16
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Index Terms

Evaluating logarithms in GF(2ⁿ)
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
      2. Computations on polynomials
2. Security and privacy
  1. Cryptography
  2. Systems security
    1. Operating systems security

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STOC '84: Proceedings of the sixteenth annual ACM symposium on Theory of computing

December 1984

547 pages

ISBN:0897911334

DOI:10.1145/800057

Chairman:
Richard DeMillo

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 December 1984

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Barreto PLibert BMcCullagh NQuisquater J(2010)Signcryption Schemes Based on Bilinear MapsPractical Signcryption10.1007/978-3-540-89411-7_5(71-97)Online publication date: 4-Oct-2010
https://doi.org/10.1007/978-3-540-89411-7_5
Bertoni GBreveglieri LFragneto PPelosi GSportiello LGielen G(2006)Software implementation of Tate pairing over GF(2m)Proceedings of the conference on Design, automation and test in Europe: Designers' forum10.5555/1131355.1131358(7-11)Online publication date: 6-Mar-2006
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Granger R(2003)Estimates for Discrete Logarithm Computations in Finite Fields of Small CharacteristicCryptography and Coding10.1007/978-3-540-40974-8_16(190-206)Online publication date: 2003
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Izu TTakagi T(2003)Efficient Computations of the Tate Pairing for the Large MOV DegreesInformation Security and Cryptology — ICISC 200210.1007/3-540-36552-4_20(283-297)Online publication date: 14-Mar-2003
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Izu TTakagi T(2002)Efficient computations of the Tate pairing for the large MOV degreesProceedings of the 5th international conference on Information security and cryptology10.5555/1765361.1765387(283-297)Online publication date: 28-Nov-2002
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Odlyzko A(2000)Discrete logarithms in finite fields and their cryptographic significanceAdvances in Cryptology10.1007/3-540-39757-4_20(224-314)Online publication date: 1-Dec-2000
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Recommendations

APN monomials over GF(2n ) for infinitely many n

On Cryptographically Significant Mappings over GF(2n)

Some results concerning cryptographically significant mappings over GF(2n)

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