# Emmanuel Thomé

## Computations

I have taken part to the following cryptographic record calculations.

- 2014. Discrete logarithm record over prime fields: 180 decimal
digits.
- Original text announcement on NMBRTHRY mailing list.
- Software.
- Some more software (linear algebra on GPUs, H. Jeljeli).

- 2013, 2014. Igusa class polynomial computation. We computed the triple
*H*parametrizing principally polarized abelian varieties having complex multiplication by the maximal order of a quartic CM field with class number h=20016. Previous state of the art was around h=500. This has been announced in 2014, together with a genus 2 Jacobian having the corresponding complex multiplication ring._{1}, Ĥ_{2}, Ĥ_{3}- Paper.
- Software.
- Original text announcement on NMBRTHRY mailing list.

- 2013. Discrete logarithm record over binary fields: GF(2^809).
- eprint report
- Original text announcement on NMBRTHRY mailing list.
- Software.

- 2012. Discrete logarithm record over binary fields: GF(2^619).
We broke an old record by almost the smallest possible increment,
but did this in a day.
- ECC 2012 rump session. slides.
- Software.
- Some more software (linear algebra on GPUs, H. Jeljeli).

- 2012: Factorization of RSA-704. This is the largest factorization achieved so far with publicly available software, namely Cado-NFS (part of the software used to factor RSA-768 is not published). Report on IACR eprint.
- 2010: Factorization of RSA-768. This is the largest publicly
announced RSA modulus factorization known.
- Report on IACR eprint.
- Paper.
- Original text announcement on NMBRTHRY mailing list.
- An attempt at collecting some of the press articles. We've been outnumbered.

- 2007: Discrete logarithm record over non-hyperelliptic curves of
genus 3: a
*C*curve over GF(2_{3,4}^{31}), with a 93-bit group order (see the paper). - 2006: Discrete logarithm record over hyperelliptic curves of genus 3: a curve over GF(p) with a 27-bit prime p, having a 81-bit group order (see the paper).
- 2002: Discrete logarithms in GF(2^607).
- Paper.
- Original text announcement on NMBRTHRY mailing list.

Last modification: Fri 30 Sep 2016 12:13:01 PM CEST

© 2006– Emmanuel Thomé ; valid XHTML 1.0, valid CSS

© 2006– Emmanuel Thomé ; valid XHTML 1.0, valid CSS