Abstract
In this paper, we describe a new algorithm for discrete logarithms in small characteristic. This algorithm is based on index calculus and includes two new contributions. The first is a new method for generating multiplicative relations among elements of a small smoothness basis. The second is a new descent strategy that allows us to express the logarithm of an arbitrary finite field element in terms of the logarithm of elements from the smoothness basis. For a small characteristic finite field of size Q = pn, this algorithm achieves heuristic complexity LQ(1/4 + o(1)). For technical reasons, unless is already a composite with factors of the right size, this is done by embedding double-struck FQ in a small extension with double-struck FQe with e ≤ 2⌈logpn⌉. © 2014 Springer-Verlag.
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CITATION STYLE
Joux, A. (2014). A new index calculus algorithm with complexity L(1/4 + o(1)) in small characteristic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8282 LNCS, pp. 355–379). Springer Verlag. https://doi.org/10.1007/978-3-662-43414-7_18
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