Computing discrete logarithms in F 3 6·137 and F 3 6·163 using Magma, Arithmetic of Finite Fields, pp.3-22, 2014. ,
Weakness of F 3 6·509 for discrete logarithm cryptography, PAIRING 2013, pp.20-44, 2014. ,
The function field sieve, Algorithmic Number Theory (ANTS-I), pp.141-154, 1994. ,
DOI : 10.1007/3-540-58691-1_48
Function Field Sieve Method for Discrete Logarithms over Finite Fields, Information and Computation, vol.151, issue.1-2, pp.5-16, 1999. ,
DOI : 10.1006/inco.1998.2761
Algorithmes de logarithmes discrets dans les corps finis, 2013. ,
URL : https://hal.archives-ouvertes.fr/tel-00925228
An appendix for a recent paper of Kim, Cryptology ePrint Archive, 1076. ,
Discrete logarithm in GF(2 809 ) with FFS, LNCS, vol.8383, pp.221-238, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00818124
Improving NFS for the Discrete Logarithm Problem in Non-prime Finite Fields, EUROCRYPT 2015, pp.129-155, 2015. ,
DOI : 10.1007/978-3-662-46800-5_6
URL : https://hal.archives-ouvertes.fr/hal-01112879
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
The Tower Number Field Sieve, ASIACRYPT 2015, pp.31-55, 2015. ,
DOI : 10.1007/978-3-662-48800-3_2
URL : https://hal.archives-ouvertes.fr/hal-01155635
Efficient Algorithms for Pairing-Based Cryptosystems, LNCS, vol.2442, pp.354-368, 2002. ,
DOI : 10.1007/3-540-45708-9_23
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
Computing logarithms in GF(2 n ), LNCS, vol.84, issue.196, pp.73-82, 1984. ,
Discrete logarithms in GF(p) ? 180 digits. NM- BRTHRY archives, item 004703, 2014. ,
An Algorithm to Solve the Discrete Logarithm Problem with the Number Field Sieve, LNCS, vol.3958, pp.174-190, 2006. ,
DOI : 10.1007/11745853_12
Fast evaluation of logarithms in fields of characteristic two, IEEE Transactions on Information Theory, vol.30, issue.4, pp.587-594, 1984. ,
DOI : 10.1109/TIT.1984.1056941
Discrete logarithms inGF(p), Algorithmica, vol.13, issue.1-4, pp.1-15, 1986. ,
DOI : 10.1007/BF01840433
New directions in cryptography, IEEE Transactions on Information Theory, vol.22, issue.6, pp.644-654, 1976. ,
DOI : 10.1109/TIT.1976.1055638
A rigorous proof of the Waterloo algorithm for the discrete logarithm problem, Designs, Codes and Cryptography, vol.26, issue.1/3, pp.229-241, 2002. ,
DOI : 10.1023/A:1016521712726
Handbook of finite fields, chapter Computational linear algebra over finite fields, pp.520-535, 2013. ,
The Complete Analysis of a Polynomial Factorization Algorithm over Finite Fields, Journal of Algorithms, vol.40, issue.1, pp.37-81, 2001. ,
DOI : 10.1006/jagm.2001.1158
URL : https://hal.archives-ouvertes.fr/inria-00073319
Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve, SIAM Journal on Discrete Mathematics, vol.6, issue.1, pp.124-138, 1993. ,
DOI : 10.1137/0406010
Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption, Cryptology ePrint Archive, 2015. ,
DOI : 10.1007/978-3-662-49890-3_11
Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption, Advances in Cryptology - EUROCRYPT 2016 -35th Annual International Conference on the Theory and Applications of Cryptographic Techniques Proceedings, Part I, volume 9665 of Lecture Notes in Computer Science, pp.263-293, 2016. ,
DOI : 10.1007/978-3-662-49890-3_11
Breaking '128-bit secure' supersingular binary curves -(or how to solve discrete logarithms in F 2 4·1223 and F 2 12·367 ), CRYPTO 2014, Part II, pp.126-145, 2014. ,
Computing Individual Discrete Logarithms Faster in $${{\mathrm{GF}}}(p^n)$$ with the NFS-DL Algorithm, ASIACRYPT 2015, pp.149-173, 2015. ,
DOI : 10.1007/978-3-662-48797-6_7
Extended tower number field sieve with application to finite fields of arbitrary composite extension degree, Cryptology ePrint Archive, vol.526, 2016. ,
The Function Field Sieve Is Quite Special, Algorithmic Number Theory, pp.431-445, 2002. ,
DOI : 10.1007/3-540-45455-1_34
URL : https://hal.archives-ouvertes.fr/hal-01102040
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
The Number Field Sieve in the Medium Prime Case, LNCS, vol.4117, pp.326-344, 2006. ,
DOI : 10.1007/11818175_19
URL : https://hal.archives-ouvertes.fr/hal-01102034
Discrete logarithm record in characteristic 3, GF(3 5·479 ) a 3796-bit field. Number Theory list, item 004745, 2014. ,
Improving the polynomial time precomputation of frobenius representation discrete logarithm algorithms -simplified setting for small characteristic finite fields, ASIACRYPT 2014, Part I, pp.378-397, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01213649
The special number field sieve in Fpn -application to pairing-friendly constructions, PAIRING 2013, pp.45-61, 2014. ,
An upper bound on the number of monomials in determinants of sparse matrices with symbolic entries, Mathematica Pannonica, vol.8, pp.73-82, 1997. ,
Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case, Cryptology ePrint Archive, vol.32, issue.1, 1027. ,
DOI : 10.1007/978-3-662-49890-3_17
URL : https://hal.archives-ouvertes.fr/hal-01281966
Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case, CRYPTO 2016, 2016. ,
DOI : 10.1007/978-3-662-49890-3_17
URL : https://hal.archives-ouvertes.fr/hal-01281966
Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case, 2016. ,
DOI : 10.1007/978-3-662-49890-3_17
URL : https://hal.archives-ouvertes.fr/hal-01281966
Discrete logarithms in GF(2 1279 ) Number Theory list, item 004751, 2014. ,
Discrete logarithms in GF(p) ? 768 bits, NMBRTHRY archives, vol.004917, 2016. ,
Computation of discrete logarithms in prime fields, Designs, Codes and Cryptography, vol.8, issue.1, pp.47-62, 1991. ,
DOI : 10.1007/BF00123958
Factoring polynomials with rational coefficients, Mathematische Annalen, vol.32, issue.4, pp.515-534, 1982. ,
DOI : 10.1007/BF01457454
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. ,
A method of factoring and the factorization of F7, Math. Comp, vol.29, issue.129, pp.183-205, 1975. ,
Discrete logarithms in finite fields and their cryptographic significance, LNCS, vol.84, issue.209, pp.224-314, 1985. ,
DOI : 10.1007/3-540-39757-4_20
Analysis and comparison of some integer factoring algorithms Computational methods in number theory, part I, Mathematical Centre Tracts Mathematisch Centrum, vol.154, pp.89-139, 1982. ,
Discrete logarithms in the jacobian of a genus 2 supersingular curve over GF(2 367 ) Number Theory list, item 004665 4404 )), https, DL in GF, 2014. ,
A simple method for obtaining relations among factor basis elements for special hyperelliptic curves. Cryptology ePrint Archive, 2015. ,
A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm, Cryptology ePrint Archive, vol.69, issue.231, 2016. ,
DOI : 10.1007/978-3-662-49890-3_17
A generalisation of the conjugation method for polynomial selection for the extended tower number field sieve algorithm, Cryptology ePrint Archive, vol.537, 2016. ,
Tower number field sieve variant of a recent polynomial selection method. Cryptology ePrint Archive, 2016. ,