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Fast evaluation of logarithms in fields of characteristic two

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D. CoppersmithAuthors Info & Claims

IEEE Transactions on Information Theory, Volume 30, Issue 4

Pages 587 - 594

https://doi.org/10.1109/TIT.1984.1056941

Published: 01 September 2006 Publication History

Abstract

A method for determining logarithms in GF (2^{n}) is presented. Its asymptotic running time is O(exp (cn^{1/3} log^{2/3} n)) for a small constant c, while, by comparison, Adleman's scheme runs in time O(exp (c^{'}n^{1/2} log^{1/2} n )) . The ideas give a dramatic improvement even for moderate-sized fields such as GF (2^{127}), and make (barely) possible computations in fields of size around 2^{400} . The method is not applicable to GF (q) for a large prime q .

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IEEE Transactions on Information Theory Volume 30, Issue 4

July 1984

129 pages

ISSN:0018-9448

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IEEE Press

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Published: 01 September 2006

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De Micheli GGaudry PPierrot C(2020)Asymptotic Complexities of Discrete Logarithm Algorithms in Pairing-Relevant Finite FieldsAdvances in Cryptology – CRYPTO 202010.1007/978-3-030-56880-1_2(32-61)Online publication date: 17-Aug-2020
Oliveira TLópez JCervantes-Vázquez DRodríguez-Henríquez F(2019)Koblitz Curves over Quadratic FieldsJournal of Cryptology10.1007/s00145-018-9294-z32:3(867-894)Online publication date: 1-Jul-2019
Shim K(2016)A Survey of Public-Key Cryptographic Primitives in Wireless Sensor NetworksIEEE Communications Surveys & Tutorials10.1109/COMST.2015.245969118:1(577-601)Online publication date: 27-Jan-2016
Joux APierrot C(2016)Technical history of discrete logarithms in small characteristic finite fieldsDesigns, Codes and Cryptography10.1007/s10623-015-0147-678:1(73-85)Online publication date: 1-Jan-2016
Adj GMenezes AOliveira TRodríguez-Henríquez F(2015)Weakness of F 3 6 ⋅ 1429 and F 2 4 ⋅ 3041 for discrete logarithm cryptographyFinite Fields and Their Applications10.1016/j.ffa.2014.10.00932:C(148-170)Online publication date: 1-Mar-2015
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Rigorous, subexponential algorithms for discrete logarithms over finite fields

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