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##### GRACE - 2017

Overall Objectives
New Software and Platforms
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography

## Section: New Results

### Discrete Logarithm computations in finite fields with the NFS algorithm

The best discrete logarithm record computations in prime fields and large characteristic finite fields are obtained with Number Field Sieve algorithm (NFS) at the moment.

#### Computing discrete logarithms in $GF\left({p}^{6}\right)$

A. Guillevic, L. Grémy, F. Morain and E. Thomé (from CARAMBA EPC in LORIA) computed a discrete log on a curve of embedding degree 6 and cryptographic size. This clearly showed that curves with small embedding degrees are indeed weak. The article [23] was presented by L. Grémy during the SAC 2017 conference in Ottawa.

#### Identity management on Bitcoin's blockchain

D. Augot and W. George in collaboration with Hervé Chabanne (Safran Identity and Security, ex Morpho, now Idemia) designed two schemes to allow users to authenticate using so-called anonymous credentials, issues by an identity provider. We used Brands anonymous credentials with selective disclosure each time, first for a finely tuned, user managed, identity scheme [12], second for a more classical high throughput scheme [13], inspired by CONIKS https://coniks.cs.princeton.edu.

#### Law and Blokchain smart contracts

D. Augot, with Célia Zolynski, is co-advising Hanna-Mae Bisserier, a PhD student law, on the impact of blockchains on legal systems. The PhD is in law, and D. Augot only gives scientific and technological explanations, while the direction of the thesis is done by Célia Zolynski.