Finding irreducible polynomials over finite fields, Proceedings of the eighteenth annual ACM symposium on Theory of computing, pp.350-355, 1986. ,
A Kilobit Special Number Field Sieve Factorization, Advances in Cryptology?ASIACRYPT 2007, pp.1-12, 2007. ,
DOI : 10.1007/978-3-540-76900-2_1
Polynomial selection for the number field sieve, 2011. ,
Better polynomials for GNFS, Mathematics of Computation, vol.85, issue.298, 2014. ,
DOI : 10.1090/mcom3048
URL : https://hal.archives-ouvertes.fr/hal-01089507
Algorithmes de logarithmes discrets dans les corps finis, 2013. ,
URL : https://hal.archives-ouvertes.fr/tel-00925228
Algebraic ) improvements to the number field sieve for non-prime finite fields, Aurore Guillevic, and François Morain ,
Improving NFS for the Discrete Logarithm Problem in Non-prime Finite Fields, Advances in Cryptology -EUROCRYPT 2015, pp.129-155, 2015. ,
DOI : 10.1007/978-3-662-46800-5_6
URL : https://hal.archives-ouvertes.fr/hal-01112879
Abstract, LMS Journal of Computation and Mathematics, vol.17, issue.A, pp.230-246 ,
DOI : 10.1017/CBO9781139856065
Pairing-friendly elliptic curves of prime order, Selected areas in cryptography, pp.319-331, 2006. ,
Bounds for resultants of univariate and bivariate polynomials, Linear Algebra and its Applications, vol.432, issue.8, pp.1995-2005, 2010. ,
DOI : 10.1016/j.laa.2009.08.012
Computing Logarithms in Finite Fields of Characteristic Two, SIAM Journal on Algebraic Discrete Methods, vol.5, issue.2, pp.276-285, 1984. ,
DOI : 10.1137/0605029
Elliptic curves suitable for pairing based cryptography. Designs, Codes and Cryptography, pp.133-141, 2005. ,
DOI : 10.1007/s10623-004-3808-4
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.3813
Factoring integers with the number field sieve, Lecture Notes in Math, vol.32, issue.107, pp.50-94, 1993. ,
DOI : 10.1109/TIT.1986.1057137
Advanced topics in computational number theory, volume 193 of Graduate Texts in Mathematics, 2000. ,
An Algorithm to Solve the Discrete Logarithm Problem with the Number Field Sieve, Public Key Cryptology?PKC 2006, pp.174-190, 2006. ,
DOI : 10.1007/11745853_12
Modifications to the Number Field Sieve, Journal of Cryptology, vol.6, issue.3, pp.169-180, 1993. ,
DOI : 10.1007/BF00198464
HT90 and " simplest " number fields, Illinois J. Math, vol.55, issue.4, pp.1621-1655, 2011. ,
A Taxonomy of Pairing-Friendly Elliptic Curves, Journal of Cryptology, vol.2, issue.5, pp.224-280, 2010. ,
DOI : 10.1007/s00145-009-9048-z
Discrete logarithms in GF(p) using the number field sieve, SIAM Journal on Discrete Mathematics, vol.6, issue.1, pp.124-138, 1993. ,
The Function Field Sieve Is Quite Special, Algorithmic Number Theory?ANTS V, pp.431-445, 2002. ,
DOI : 10.1007/3-540-45455-1_34
URL : https://hal.archives-ouvertes.fr/hal-01102040
The Number Field Sieve in the Medium Prime Case, Advances in Cryptology?CRYPTO 2006, pp.326-344, 2006. ,
DOI : 10.1007/11818175_19
URL : https://hal.archives-ouvertes.fr/hal-01102034
The Special Number Field Sieve in $\mathbb{F}_{p^{n}}$, Pairing-Based Cryptography ? Pairing 2013, pp.45-61, 2013. ,
DOI : 10.1007/978-3-319-04873-4_3
On polynomial selection for the general number field sieve, Mathematics of Computation, vol.75, issue.256, pp.2037-2047, 2006. ,
DOI : 10.1090/S0025-5718-06-01870-9
Polynomial selection Slides at CADO workshop, 2008. ,
Factorization of a 768-Bit RSA Modulus, Advances in Cryptology?CRYPTO 2010, pp.333-350, 2010. ,
DOI : 10.1007/978-3-642-14623-7_18
URL : https://hal.archives-ouvertes.fr/inria-00444693
Mersenne Factorization Factory, Advances in Cryptology?ASIACRYPT 2014, pp.358-377, 2014. ,
DOI : 10.1007/978-3-662-45611-8_19
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.567.8915
The number field sieve, The development of the number field sieve, pp.11-42, 1993. ,
DOI : 10.1109/TIT.1986.1057137
URL : https://hal.archives-ouvertes.fr/inria-00108061
On asymptotic complexity of computing discrete logarithms over GF(p), Discrete Mathematics and Applications, vol.13, issue.1, pp.27-50, 2003. ,
DOI : 10.1515/156939203321669546
New explicit conditions of elliptic curve traces for FR-reduction, IEICE Trans. on Fundamentals of Electronics, Communic. and Computer Sci, vol.84, issue.5, pp.1234-1243, 2001. ,
Elliptic curves for pairing applications Cryptology ePrint Archive, Report, vol.302, 2005. ,
The Multiple Number Field Sieve with Conjugation and Generalized Joux-Lercier Methods, Advances in Cryptology -EUROCRYPT 2015, pp.156-170, 2015. ,
DOI : 10.1007/978-3-662-46800-5_7
URL : https://hal.archives-ouvertes.fr/hal-01056205
The lattice sieve, Lecture Notes in Math, vol.1554, pp.43-49, 1993. ,
DOI : 10.1090/psapm/042/1095550
Discrete Logarithms and Local Units, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.345, issue.1676, pp.409-423, 1676. ,
DOI : 10.1098/rsta.1993.0139
Using number fields to compute logarithms in finite fields, Mathematics of Computation, vol.69, issue.231, pp.1267-1283, 2000. ,
DOI : 10.1090/S0025-5718-99-01137-0
Special prime numbers and discrete logs in finite prime fields, Mathematics of Computation, vol.71, issue.237, pp.363-377, 2002. ,
DOI : 10.1090/S0025-5718-00-01308-9
Solving sparse linear equations over finite fields, IEEE Trans. Inform. Theory, vol.32, issue.1, pp.54-62, 1986. ,