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- Thorsten Kleinjung, Kazumaro Aoki, +10 authors Paul Zimmermann
- CRYPTO
- 2010

This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.

- David Adrian, Karthikeyan Bhargavan, +11 authors Paul Zimmermann
- ACM Conference on Computer and Communications…
- 2015

We investigate the security of Diffie-Hellman key exchange as used in popular Internet protocols and find it to be less secure than widely believed. First, we present Logjam, a novel flaw in TLS that… (More)

- Pierrick Gaudry, Emmanuel Thomé, Nicolas Thériault, Claus Diem
- Math. Comput.
- 2004

In this article, we examine how the index calculus approach for computing discrete logarithms in small genus hyperelliptic curves can be improved by introducing a double large prime variation. Two… (More)

- Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé
- EUROCRYPT
- 2014

The difficulty of computing discrete logarithms in fields Fqk depends on the relative sizes of k and q. Until recently all the cases had a sub-exponential complexity of type L(1/3), similar to the… (More)

- Emmanuel Thomé
- J. Symb. Comput.
- 2002

This paper describes a new algorithm for computing linear generators (vector generating polynomials) for matrix sequences, running in subquadratic time. This algorithm applies in particular to the… (More)

- Claus Diem, Emmanuel Thomé
- Journal of Cryptology
- 2007

We study an index calculus algorithm to solve the discrete logarithm problem (DLP) in degree 0 class groups of non-hyperelliptic curves of genus 3 over finite fields. We present a heuristic analysis… (More)

- Razvan Barbulescu, Cyril Bouvier, +5 authors Paul Zimmermann
- 2013

We give details on solving the discrete logarithm problem in the 202-bit prime order subgroup of F2809 using the Function Field Sieve algorithm (FFS). To our knowledge, this computation is the… (More)

In this paper, we discuss an implementation of various algorithms for multiplying polynomials in GF(2)[x]: variants of the window methods, Karatsuba’s, Toom-Cook’s, Schönhage’s and Cantor’s… (More)

- Razvan Barbulescu, Cyril Bouvier, +5 authors Paul Zimmermann
- Public Key Cryptography
- 2013

- Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé
- IACR Cryptology ePrint Archive
- 2013

The difficulty of computing discrete logarithms in fields Fqk depends on the relative sizes of k and q. Until recently all the cases had a sub-exponential complexity of type L(1/3), similar to the… (More)