IACR News item: 22 July 2013
Gora Adj, Alfred Menezes, Thomaz Oliveira, Francisco Rodr\\\'iguez-Henr\\\'iquez
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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