On the Function Field Sieve and the Impact of Higher Splitting Probabilities

Faruk Göloğlu; Robert Granger; Gary McGuire; Jens Zumbrägel

doi:10.1007/978-3-642-40084-1_7

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On the Function Field Sieve and the Impact of Higher Splitting Probabilities

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On the Function Field Sieve and the Impact of Higher Splitting Probabilities

Faruk Göloğlu, Robert Granger, Gary McGuire and Jens Zumbrägel

Advances in Cryptology – CRYPTO 2013, Vol.8043, pp.109-128

Springer, Berlin, Heidelberg

The 33rd Annual Cryptology Conference - Advances in Cryptology - CRYPTO 2013 (Santa Barbara, CA, USA, 18/08/2013–22/08/2013)

18/08/2013

DOI: https://doi.org/10.1007/978-3-642-40084-1_7

Abstract

Discrete logarithm problem; Function field sieve

In this paper we propose a binary field variant of the JouxLercier medium-sized Function Field Sieve, which results not only in complexities as low as L_qⁿ (1/3,(4/9)^1/3) for computing arbitrary logarithms, but also in an heuristic polynomial time algorithm for finding the discrete logarithms of degree one and two elements when the field has a subfield of an appropriate size. To illustrate the efficiency of the method, we have successfully solved the DLP in the finite fields with 2¹⁹⁷¹ and 2³¹⁶⁴ elements, setting a record for binary fields.

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Title: On the Function Field Sieve and the Impact of Higher Splitting Probabilities
Creators: Faruk Göloğlu
Robert Granger
Gary McGuire
Jens Zumbrägel
Publication Details: Advances in Cryptology – CRYPTO 2013, Vol.8043, pp.109-128
Conference: The 33rd Annual Cryptology Conference - Advances in Cryptology - CRYPTO 2013 (Santa Barbara, CA, USA, 18/08/2013–22/08/2013)
Publisher: Springer, Berlin, Heidelberg
Publication Date: 18/08/2013
Identifiers: 99515604102346
Academic Unit: Department of Computer Science
Resource Type: Conference presentation

On the Function Field Sieve and the Impact of Higher Splitting Probabilities

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