About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
IEEE Trans. Inf. Theory
Paper
Fast Evaluation of Logarithms in Fields of Characteristic Two
Abstract
A method for determining logarithms in GF (2<sup>n</sup>) is presented. Its asymptotic running time is O(exp(cn<sup>1/3</sup> log<sup>2/3</sup> n)) for a small constant c, while, by comparison, Adleman's scheme runs in time O(exp(c′n<sup>1/2</sup> 1og<sup>1/2</sup> n)). The ideas give a dramatic improvement even for moderate-sized fields such as GF (2<sup>127</sup>), and make (barely) possible computations in fields of size around 2<sup>400</sup>. The method is not applicable to GF (q) for a large prime q. © 1984 IEEE.