Members
Overall Objectives
Research Program
Application Domains
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography
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Bibliography

Major publications by the team in recent years
[1]
D. Augot, M. Finiasz.
Direct Construction of Recursive MDS Diffusion Layers using Shortened BCH Codes, in: 21st International Workshop on Fast Software Encryption, FSE 2014, London, United Kingdom, C. Cid, C. Rechberger (editors), springer, March 2014.
https://hal.inria.fr/hal-01044597
[2]
A. Couvreur.
Codes and the Cartier Operator, in: Proceedings of the American Mathematical Society, March 2014, vol. 142, pp. 1983-1996.
https://hal.inria.fr/hal-00710451
[3]
A. Couvreur, P. Gaborit, V. Gautier, A. Otmani, J.-P. Tillich.
Distinguisher-Based Attacks on Public-Key Cryptosystems Using Reed-Solomon Codes, in: WCC 2013 - International Workshop on Coding and Cryptography, Bergen, Norway, Selmer Center at the University of Bergen, Norway and Inria, Rocquencourt, France, April 2013, pp. 181-193.
https://hal.archives-ouvertes.fr/hal-00830594
[4]
A. Couvreur, A. Otmani, J.-P. Tillich.
Polynomial Time Attack on Wild McEliece Over Quadratic Extensions, in: EUROCRYPT 2014, Copenhagen, Denmark, May 2014, pp. 17-39.
https://hal.archives-ouvertes.fr/hal-00931774
[5]
F. Morain.
Implementing the asymptotically fast version of the elliptic curve primality proving algorithm, in: Math. Comp., 2007, vol. 76, pp. 493–505.
[6]
B. Smith.
Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves, in: J. of Cryptology, 2009, vol. 22, no 4, pp. 505-529.
[7]
B. Smith.
Families of fast elliptic curves from Q-curves, in: Advances in Cryptology - ASIACRYPT 2013, Bangalore, India, K. Sako, P. Sarkar (editors), Lecture Notes in Computer Science, Springer, December 2013, vol. 8269, pp. 61-78. [ DOI : 10.1007/978-3-642-42033-7_4 ]
https://hal.inria.fr/hal-00825287
Publications of the year

Articles in International Peer-Reviewed Journals

[8]
M. Borges-Quintana, M. A. Borges-Trenard, I. Márquez-Corbella, E. Martinez-Moro.
Computing coset leaders and leader codewords of binary codes, in: Journal of Algebra and Its Applications, November 2014, 19 p. [ DOI : 10.1142/S0219498815501285 ]
https://hal.archives-ouvertes.fr/hal-01088431
[9]
A. Couvreur.
Codes and the Cartier Operator, in: Proceedings of the American Mathematical Society, March 2014, vol. 142, pp. 1983-1996, A part of this work has been done when the author was a Post Doc researcher supported by the French ANR Defis program under contract ANR-08-EMER-003 (COCQ project).
https://hal.inria.fr/hal-00710451
[10]
A. Couvreur, P. Gaborit, V. Gauthier-Umana, A. Otmani, J.-P. Tillich.
Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes, in: Designs, Codes and Cryptography, 2014, vol. 73, no 2, pp. 641-666. [ DOI : 10.1007/s10623-014-9967-z ]
https://hal.archives-ouvertes.fr/hal-01096172
[11]
A. Couvreur, A. Otmani, J.-P. Tillich.
New identities relating wild Goppa codes, in: Finite Fields and Their Applications, September 2014, vol. 29, pp. 178-197. [ DOI : 10.1016/j.ffa.2014.04.007 ]
https://hal.archives-ouvertes.fr/hal-00880994
[12]
A. Enge, F. Morain.
Generalised Weber Functions, in: Acta Arithmetica, 2014, vol. 164, no 4, pp. 309-341. [ DOI : 10.4064/aa164-4-1 ]
https://hal.inria.fr/inria-00385608
[13]
I. Márquez-Corbella, E. Martinez-Moro, R. Pellikaan, R. Diego.
Computational aspects of retrieving a representation of an algebraic geometry code, in: Journal of Symbolic Computation, August 2014, vol. 64, pp. 67-87. [ DOI : 10.1016/j.jsc.2013.12.007 ]
https://hal.archives-ouvertes.fr/hal-01088430
[14]
J. S. R. Nielsen, A. Zeh.
Multi-Trial Guruswami–Sudan Decoding for Generalised Reed–Solomon Codes, in: Design Codes and Cryptography, March 2014, pp. 1-21. [ DOI : 10.1007/s10623-014-9951-7 ]
https://hal.inria.fr/hal-00975927
[15]
J. Pieltant, H. Randriam.
New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields, in: Mathematics of Computation, 2015, pp. S 0025-5718(2015)02921-4. [ DOI : 10.1090/S0025-5718-2015-02921-4 ]
https://hal.archives-ouvertes.fr/hal-00828153
[16]
A. Wachter-Zeh, A. Zeh, M. Bossert.
Decoding interleaved Reed-Solomon codes beyond their joint error-correcting capability, in: Designs, Codes and Cryptography, 2014, vol. 71, no 2, pp. 261-281. [ DOI : 10.1007/s10623-012-9728-9 ]
https://hal.archives-ouvertes.fr/hal-00957810

International Conferences with Proceedings

[17]
Best Paper
D. Augot, M. Finiasz.
Direct Construction of Recursive MDS Diffusion Layers using Shortened BCH Codes, in: 21st International Workshop on Fast Software Encryption, FSE 2014, London, United Kingdom, C. Cid, C. Rechberger (editors), Lecture Notes in Computer Science, Springer, March 2014, Best paper award.
https://hal.inria.fr/hal-01044597
[18]
D. Augot, P.-A. Fouque, P. Karpman.
Diffusion Matrices from Algebraic-Geometry Codes with Efficient SIMD Implementation, in: Selected Areas in Cryptology - SAC 2014, Montreal, Canada, A. Joux, A. Youssef (editors), Lecture Notes in Computer Science, Springer, August 2014, vol. 8781, pp. 243-260. [ DOI : 10.1007/978-3-319-13051-4_15 ]
https://hal.inria.fr/hal-01094085
[19]
D. Augot, F. Levy-Dit-Vehel, A. Shikfa.
A Storage-Efficient and Robust Private Information Retrieval Scheme Allowing Few Servers, in: 13th International Conference, Cryptology and Network Security (CANS 2014) Proceedings, Heraklion, Greece, D. Gritzalis, A. Kiayias, I. Askoxylakis (editors), Lecture notes in computer science, Springer, October 2014, vol. 8813, pp. 222 - 239. [ DOI : 10.1007/978-3-319-12280-9_15 ]
https://hal.inria.fr/hal-01094807
[20]
R. Barbulescu, P. Gaudry, A. Guillevic, F. Morain.
Improving NFS for the discrete logarithm problem in non-prime finite fields, in: Eurocrypt 2015, Sofia, Bulgaria, M. Fischlin, E. Oswald (editors), Eurocrypt 2015, 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, April 2015, 27 p.
https://hal.inria.fr/hal-01112879
[21]
C. Costello, H. Hisil, B. Smith.
Faster Compact Diffie-Hellman: Endomorphisms on the x-line, in: EUROCRYPT 2014, Copenhagen, Denmark, P. Q. Nguyen, E. Oswald (editors), Lecture Notes in Computer Science, Springer, May 2014, vol. 8441, pp. 183-200. [ DOI : 10.1007/978-3-642-55220-5_11 ]
https://hal.inria.fr/hal-00932952
[22]
A. Couvreur, I. Márquez-Corbella, R. Pellikaan.
A Polynomial Time Attack against Algebraic Geometry Code Based Public Key Cryptosystems, in: IEEE International Symposium onInformation Theory (ISIT), Honolulu, United States, IEEE, June 2014, pp. 1446-1450. [ DOI : 10.1109/ISIT.2014.6875072 ]
https://hal.archives-ouvertes.fr/hal-00937476
[23]
A. Couvreur, A. Otmani, J.-P. Tillich.
Polynomial Time Attack on Wild McEliece Over Quadratic Extensions, in: Advances in Cryptology - Eurocrypt 2014, Copenhagen, Denmark, P. Q. Nguyen, E. Oswald (editors), LNCS, Springer, May 2014, vol. 8441, pp. 17-39. [ DOI : 10.1007/978-3-642-55220-5_2 ]
https://hal.archives-ouvertes.fr/hal-00931774
[24]
A. Couvreur, A. Otmani, J.-P. Tillich, V. Gauthier-Umana.
A Polynomial-Time Attack on the BBCRS Scheme, in: Practice and Theory in Public-Key Cryptography - PKC 2015, Washington, United States, LNCS, March 2015.
https://hal.archives-ouvertes.fr/hal-01104078

Conferences without Proceedings

[25]
D. Augot.
Generalization of Gabidulin Codes over Fields of Rational Functions, in: 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen, Netherlands, July 2014.
https://hal.inria.fr/hal-01094843
[26]
A. Couvreur, I. Márquez-Corbella, R. Pellikaan.
Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes, in: 4th ICMCTA - Fourth International Castle Meeting on Coding Theory and Applications, Palmela, Portugal, September 2014.
https://hal.inria.fr/hal-01069272
[27]
N. Dück, I. Márquez-Corbella, E. Martínez-Moro.
On the fan associated to a linear code *, in: 4th ICMCTA - Fourth International Castle Meeting on Coding Theory and Applications, Palmela, Portugal, September 2014, forthcoming.
https://hal.archives-ouvertes.fr/hal-01088432
[28]
I. Márquez-Corbella, R. Pellikaan.
Error-correcting pairs: a new approach to code-based cryptography, in: 20th Conference on Applications of Computer Algebra (ACA 2014), New York, United States, July 2014.
https://hal.archives-ouvertes.fr/hal-01088433

Patents

[29]
D. Augot, F. Levy-Dit-Vehel, A. Shikfa.
Storage efficient and unconditionnally secure private information retrieval, September 2014, no 14305549.9.
https://hal.inria.fr/hal-01111694

Other Publications

[30]
S. Ballet, J. Pieltant.
Tower of algebraic function fields with maximal Hasse-Witt invariant and tensor rank of multiplication in any extension of 𝔽2 and 𝔽3, September 2014.
https://hal.archives-ouvertes.fr/hal-01063511
[31]
R. Barbulescu, P. Gaudry, A. Guillevic, F. Morain.
Improvements to the number field sieve for non-prime finite fields, November 2014.
https://hal.inria.fr/hal-01052449
[32]
A. Couvreur.
An upper bound on the number of rational points of arbitrary projective varieties over finite fields, September 2014.
https://hal.archives-ouvertes.fr/hal-01069510
[33]
C. Gonçalves.
A Point Counting Algorithm for Cyclic Covers of the Projective Line, August 2014.
https://hal.archives-ouvertes.fr/hal-01054645
[34]
B. Smith.
The Q-curve construction for endomorphism-accelerated elliptic curves, September 2014.
https://hal.inria.fr/hal-01064255
References in notes
[35]
S. Ballet, J. Chaumine, J. Pieltant.
Shimura modular curves and asymptotic symmetric tensor rank of multiplication in any finite field, in: Conference on Algebraic Informatics, Porquerolles Island, France, T. Muntean, D. Poulakis, R. Rolland (editors), Lecture notes in computer science / Theoretical Computer Science and General Issues, Springer-Verlag Berlin Heidelberg, September 2013, vol. 8080, pp. 160-172. [ DOI : 10.1007/978-3-642-40663-8_16 ]
https://hal.archives-ouvertes.fr/hal-00828070
[36]
H. Cohn, N. Heninger.
Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding, in: Innovations in Computer Science - ICS 2010, Tsinghua University, Beijing, China, January 7-9, 2011. Proceedings, B. Chazelle (editor), Tsinghua University Press, 2011, pp. 298-308.
[37]
I. M. Duursma.
Weight distributions of geometric Goppa codes, in: Trans. Amer. Math. Soc., 1999, vol. 351, no 9, pp. 3609–3639.
http://dx.doi.org/10.1090/S0002-9947-99-02179-0
[38]
S. R. Ghorpade, G. Lachaud.
Étale Cohomology, Lefschetz Theorems and number of points of singular varieties over finite fields, in: Mosc. Math. J., 2002, vol. 2, no 3, pp. 589–631.
[39]
R. J. McEliece.
A Public-Key System Based on Algebraic Coding Theory, Jet Propulsion Lab, 1978, pp. 114–116, DSN Progress Report 44.
[40]
V. Sidelnikov, S. Shestakov.
On the insecurity of cryptosystems based on generalized Reed-Solomon codes, in: Discrete Math. Appl., 1992, vol. 1, no 4, pp. 439-444.