International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 22 July 2013

Gora Adj, Alfred Menezes, Thomaz Oliveira, Francisco Rodr\\\'iguez-Henr\\\'iquez
ePrint Report ePrint Report
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 $\\Fmain = \\FF_{3^{3054}}$ 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 $\\FF_{3^{509}}$ 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.

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