1,228 research outputs found
Discrete logarithms in curves over finite fields
A survey on algorithms for computing discrete logarithms in Jacobians of
curves over finite fields
Solving discrete logarithms on a 170-bit MNT curve by pairing reduction
Pairing based cryptography is in a dangerous position following the
breakthroughs on discrete logarithms computations in finite fields of small
characteristic. Remaining instances are built over finite fields of large
characteristic and their security relies on the fact that the embedding field
of the underlying curve is relatively large. How large is debatable. The aim of
our work is to sustain the claim that the combination of degree 3 embedding and
too small finite fields obviously does not provide enough security. As a
computational example, we solve the DLP on a 170-bit MNT curve, by exploiting
the pairing embedding to a 508-bit, degree-3 extension of the base field.Comment: to appear in the Lecture Notes in Computer Science (LNCS
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