R. Barbulescu and C. Pierrot, Abstract, LMS Journal of Computation and Mathematics, vol.17, issue.A, pp.230-246, 2014.
DOI : 10.1017/CBO9781139856065

R. Barbulescu, Algorithmes de logarithmes discrets dans les corps finis, 2013.
URL : https://hal.archives-ouvertes.fr/tel-00925228

R. Barbulescu, P. Gaudry, A. Guillevic, and F. Morain, Improvements to the number field sieve for non-prime finite fields
URL : https://hal.archives-ouvertes.fr/hal-01052449

R. Barbulescu, P. Gaudry, A. Joux, and E. Thomé, A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic, EUROCRYPT 2014, pp.1-16, 2014.
DOI : 10.1007/978-3-642-55220-5_1

URL : https://hal.archives-ouvertes.fr/hal-00835446

E. R. Canfield, P. Erdös, and C. Pomerance, On a problem of Oppenheim concerning ???factorisatio numerorum???, Journal of Number Theory, vol.17, issue.1, pp.1-28, 1983.
DOI : 10.1016/0022-314X(83)90002-1

G. E. Collins and M. J. Encarnación, Efficient Rational Number Reconstruction, Journal of Symbolic Computation, vol.20, issue.3, pp.287-297, 1995.
DOI : 10.1006/jsco.1995.1051

D. Coppersmith, Solving Homogeneous Linear Equations Over GF(2) via Block Wiedemann Algorithm, Mathematics of Computation, vol.62, issue.205, pp.333-350, 1994.
DOI : 10.2307/2153413

D. Coppersmith, Modifications to the Number Field Sieve, Journal of Cryptology, vol.6, issue.3, pp.169-180, 1993.
DOI : 10.1007/BF00198464

K. Foster, HT90 and " simplest " number fields, Illinois J. Math, vol.55, issue.4, pp.1621-1655, 2011.

D. Freeman, M. Scott, and E. Teske, 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

H. Jeljeli, Accelerating Iterative SpMV for the Discrete Logarithm Problem Using GPUs, GPUs, 2014.
DOI : 10.1007/978-3-319-16277-5_2

H. Jeljeli, An implementation of the Block-Wiedemann algorithm on NVIDIA-GPUs using the Residue Number System (RNS) arithmetic, 2014.

A. Joux and R. Lercier, Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method, Mathematics of Computation, vol.72, issue.242, pp.953-967, 2003.
DOI : 10.1090/S0025-5718-02-01482-5

URL : https://hal.archives-ouvertes.fr/hal-01102016

A. Joux and R. Lercier, Algorithmes pour résoudre leprobì eme du logarithme discret dans les corps finis, Nouvelles Méthodes Mathématiques en Cryptographie, volume Fascicule Journées Annuelles p, p.23, 2007.

A. Joux, R. Lercier, N. Smart, and F. Vercauteren, The Number Field Sieve in the Medium Prime Case, CRYPTO 2006, pp.326-344, 2006.
DOI : 10.1007/11818175_19

URL : https://hal.archives-ouvertes.fr/hal-01102034

A. Joux and C. Pierrot, The special number field sieve in Fpn -application to pairing-friendly constructions, PAIRING 2013, pp.45-61, 2014.

M. Kalkbrener, An upper bound on the number of monomials in determinants of sparse matrices with symbolic entries, Mathematica Pannonica, vol.73, p.82, 1997.

T. Kleinjung, 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

A. K. Lenstra and E. R. Verheul, The XTR Public Key System, CRYPTO 2000, pp.1-19, 2000.
DOI : 10.1007/3-540-44598-6_1

A. K. Lenstra, H. W. Lenstra, and L. Lovász, Factoring polynomials with rational coefficients, Mathematische Annalen, vol.32, issue.4, pp.515-534, 1982.
DOI : 10.1007/BF01457454

D. Matyukhin, Effective version of the number field sieve for discrete logarithms in the field GF(p k ) (in Russian), Trudy po Discretnoi Matematike, vol.9, pp.121-151, 2006.

D. V. Matyukhin, 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

B. A. Murphy, Polynomial selection for the number field sieve integer factorisation algorithm, Australian National Univers, 1999.

C. Pierrot, The multiple number field sieve with conjugation method, p.641, 2014.

S. Pohlig and M. Hellman, An improved algorithm for computing logarithms over GF(p) and his cryptographic significance, IEEE Trans. Inform. Theory, vol.241, pp.106-110, 1978.

J. M. Pollard, Monte Carlo methods for index computation (mod p), Math. Comp, vol.32, issue.143, pp.918-924, 1978.

K. Rubin and A. Silverberg, Torus-Based Cryptography, CRYPTO 2003, pp.349-365, 2003.
DOI : 10.1007/978-3-540-45146-4_21

O. Schirokauer, 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

O. Schirokauer, Virtual logarithms, Journal of Algorithms, vol.57, issue.2, pp.140-147, 2005.
DOI : 10.1016/j.jalgor.2004.11.004

P. Smith and C. Skinner, A public-key cryptosystem and a digital signature system based on the Lucas function analogue to discrete logarithms, ASIACRYPT'94, pp.357-364, 1995.
DOI : 10.1007/BFb0000447

D. Wiedemann, Solving sparse linear equations over finite fields, IEEE Transactions on Information Theory, vol.32, issue.1, pp.54-62, 1986.
DOI : 10.1109/TIT.1986.1057137