89 citations · 134 across the 7 of their papers we have counts for
9 papers
Deterministic factoring with oracles
Fran{\c c}ois Morain, Gu{é}na{ë}l Renault, Benjamin Smith
We revisit the problem of integer factorization with number-theoretic oracles, including a well-known problem: can we factor an integer unconditionally, in deterministic polyno…
Computing cardinalities of Q-curve reductions over finite fields
François Morain, Charlotte Scribot, Benjamin Smith
We present a specialized point-counting algorithm for a class of elliptic curves over F\_{p^2} that includes reductions of quadratic Q-curves modulo inert primes and, more generall…
Solving discrete logarithms on a 170-bit MNT curve by pairing reduction
Aurore Guillevic, François Morain, Emmanuel Thomé
Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances…
Factoring Safe Semiprimes with a Single Quantum Query
Frédéric Grosshans, Thomas Lawson, François Morain +1
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order…
Improvements to the number field sieve for non-prime finite fields
Razvan Barbulescu, Pierrick Gaudry, Aurore Guillevic +1
We propose various strategies for improving the computation of discrete logarithms in non-prime fields of medium to large characteristic using the Number Field Sieve. This includes…
Discrete logarithm computations over finite fields using Reed-Solomon codes
Daniel Augot, François Morain
Cheng and Wan have related the decoding of Reed-Solomon codes to the computation of discrete logarithms over finite fields, with the aim of proving the hardness of their decoding.…