Cryptology ePrint Archive: Report 2013/446

Weakness of F_{3^{6*509}} for Discrete Logarithm Cryptography

Gora Adj and Alfred Menezes and Thomaz Oliveira and Francisco Rodr\'iguez-Henr\'iquez

Abstract: In 2013, Joux, and then Barbulescu, Gaudry, Joux and Thom\'{e}, presented new algorithms for computing discrete logarithms in finite fields of small and medium characteristic. We show that these new algorithms render the finite field F_{3^{6*509}} = F_{3^{3054}} weak for discrete logarithm cryptography in the sense that discrete logarithms in this field can be computed significantly faster than with the previous fastest algorithms. Our concrete analysis shows that the supersingular elliptic curve over F_{3^{509}} with embedding degree 6 that had been considered for implementing pairing-based cryptosystems at the 128-bit security level in fact provides only a significantly lower level of security. Our work provides a convenient framework and tools for performing a concrete analysis of the new discrete logarithm algorithms and their variants.

Category / Keywords: public-key cryptography /

Date: received 15 Jul 2013, last revised 30 Nov 2013

Contact author: francisco at cs cinvestav mx

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Version: 20131201:015710 (All versions of this report)

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