Improved Sieving on Algebraic Curves

Autor: Vanessa Vitse, Alexandre Wallet

Publikováno v: Progress in Cryptology--LATINCRYPT 2015
LATINCRYPT 2015, 4th International Conference on Cryptology and Information Security in Latin America
LATINCRYPT 2015, 4th International Conference on Cryptology and Information Security in Latin America, Aug 2015, Guadalajara, Mexico. pp.295-307, ⟨10.1007/978-3-319-22174-8_16⟩
Progress in Cryptology--LATINCRYPT 2015 ISBN: 9783319221731
LATINCRYPT

International audience; The best algorithms for discrete logarithms in Jacobians of algebraic curves of small genus are based on index calculus methods coupled with large prime variations. For hyperelliptic curves, relations are obtained by looking f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::71226d1669541c442ea56a2eebe50d4a
https://hal.sorbonne-universite.fr/hal-01203086/file/SievingB.pdf

Elliptic Curve Discrete Logarithm Problem over Small Degree Extension Fields. Application to the Static Diffie-Hellman Problem on E(F q 5 )

Autor: Antoine Joux, Vanessa Vitse

Publikováno v: Journal of Cryptology
Journal of Cryptology, Springer Verlag, 2013, 26 (1), pp.119-143
HAL

International audience; In 2008 and 2009, Gaudry and Diem proposed an index calculus method for the resolution of the discrete logarithm on the group of points of an elliptic curve defined over a small degree extension field Fqn. In this paper, we st

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::36315099e59dc0aba7d3234108418201
https://hal.archives-ouvertes.fr/hal-01981543/document

Cover and Decomposition Index Calculus on Elliptic Curves Made Practical

Autor: Vanessa Vitse, Antoine Joux

Publikováno v: Advances in Cryptology – EUROCRYPT 2012 ISBN: 9783642290107
EUROCRYPT

We present a new "cover and decomposition" attack on the elliptic curve discrete logarithm problem, that combines Weil descent and decomposition-based index calculus into a single discrete logarithm algorithm. This attack applies, at least theoretica

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::15bed80e7835fb02359a391bb5c1f5bb
https://doi.org/10.1007/978-3-642-29011-4_3

A Crossbred Algorithm for Solving Boolean Polynomial Systems

Autor: Vanessa Vitse, Antoine Joux

Publikováno v: Lecture Notes in Computer Science
Lecture Notes in Computer Science-Number-Theoretic Methods in Cryptology
NuTMiC 2017
NuTMiC 2017, 2017, Varsovie, Poland. pp.3-21
HAL
Number-Theoretic Methods in Cryptology ISBN: 9783319766195
NuTMiC
Number-Theoretic Methods in Cryptology-First International Conference, NuTMiC 2017

International audience; We consider the problem of solving multivariate systems of Boolean polynomial equations: starting from a system of m polynomials of degree at most d in n variables, we want to find its solutions over F2. Except for d = 1, the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2bc759708015da0a67667f669ead8118

The point decomposition problem in Jacobian varieties

Autor: Wallet, Alexandre

Publikováno v: Data Structures and Algorithms [cs.DS]. Université Pierre et Marie Curie-Paris VI, 2016. English. ⟨NNT : 2016PA066438⟩

The discrete logarithm problem is a fundamental brick for several protocols for secured communications. Its instantiation over elliptic curves allows the deployment of efficient asymmetric primitives in embedded systems, because of the small size of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::4b43471de5e2a11d8708f650e0d07cb0
https://theses.hal.science/tel-01407675