DHAES: An encryption scheme based on the Diffie-Hellman problem. Cryptology ePrint Archive, 1999. ,
The oracle Diffie-Hellman assumptions and an analysis of DHIES, Topics in Cryptology-CT-RSA, pp.143-158, 2001. ,
Elliptic curves and primality proving, Math. Comp, vol.61, issue.203, pp.29-68, 1993. ,
URL : https://hal.archives-ouvertes.fr/inria-00075302
, , 2017.
Security estimates for quadratic field based cryptosystems, pp.233-247, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00477949
Differential fault attacks on elliptic curve cryptosystems, Advances in Cryptology-CRYPTO 2000, pp.131-146, 2000. ,
Fast algorithms for computing isogenies between elliptic curves, Math. Comput, vol.77, issue.263, pp.1755-1778, 2008. ,
URL : https://hal.archives-ouvertes.fr/inria-00091441
Modular polynomials via isogeny volcanoes, Math. Comput, vol.81, issue.278, pp.1201-1231, 2012. ,
,
Class polynomials for nonholomorphic modular functions, Journal of Number Theory, vol.161, pp.204-229, 2016. ,
,
A key-exchange system based on imaginary quadratic fields, Journal of Cryptology, vol.1, issue.2, pp.107-118, 1988. ,
Analysis of Key-Exchange protocols and their use for building secure channels, Advances in Cryptology-EUROCRYPT 2001, vol.2045, 2001. ,
DOI : 10.1007/3-540-44987-6_28
URL : https://link.springer.com/content/pdf/10.1007%2F3-540-44987-6_28.pdf
CSIDH: An efficient post-quantum commutative group action. Cryptology ePrint Archive, vol.383, 2018. ,
Constructing elliptic curve isogenies in quantum subexponential time, Journal of Mathematical Cryptology, vol.8, issue.1, pp.1-29, 2014. ,
DOI : 10.1515/jmc-2012-0016
URL : http://arxiv.org/pdf/1012.4019
Elliptic curve cryptosystems in the presence of permanent and transient faults, Designs, Codes and Cryptography, vol.36, issue.1, pp.33-43, 2005. ,
DOI : 10.1007/s10623-003-1160-8
URL : http://eprint.iacr.org/2003/028.ps.gz
A Course in Computational Algebraic Number Theory, 1993. ,
, Heuristics on class groups of number fields, pp.33-62, 1983.
DOI : 10.1007/bfb0099440
URL : https://openaccess.leidenuniv.nl/bitstream/handle/1887/2137/346_069.pdf?sequence=1
A simple and compact algorithm for SIDH with arbitrary degree isogenies, Advances in Cryptology-ASIACRYPT 2017, pp.303-329, 2017. ,
DOI : 10.1007/978-3-319-70697-9_11
,
Montgomery curves and their arithmetic, Journal of Cryptographic Engineering, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01483768
Hard homogeneous spaces. Cryptology ePrint Archive, 2006. ,
Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack, SIAM Journal on Computing, vol.33, issue.1, pp.167-226, 2003. ,
Mathematics of isogeny based cryptography, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-02171952
Explicit isogenies in quadratic time in any characteristic, LMS Journal of Computation and Mathematics, vol.19, pp.267-282, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01320940
Computing isogenies between supersingular elliptic curves over Fp, Des. Codes Cryptography, vol.78, issue.2, pp.425-440, 2016. ,
,
Elliptic and modular curves over finite fields and related computational issues, Computational perspectives on number theory, vol.7, pp.21-76, 1995. ,
Nemo/Hecke: Computer algebra and number theory packages for the Julia programming language, Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, vol.17, pp.157-164, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01524140
Isogeny volcanoes and the SEA algorithm, Algorithmic Number Theory Symposium, vol.2369, pp.47-62, 2002. ,
Secure integration of asymmetric and symmetric encryption schemes, Advances in Cryptology-CRYPTO' 99, pp.537-554, 1999. ,
Improved algorithm for the isogeny problem for ordinary elliptic curves, Applicable Algebra in Engineering, Communication and Computing, vol.24, issue.2, pp.107-131, 2013. ,
Constructing isogenies between elliptic curves over finite fields, LMS Journal of Computation and Mathematics, vol.2, pp.118-138, 1999. ,
,
Mathematics of public key cryptography, 2012. ,
Extending the GHS Weil descent attack, Advances in cryptology-EUROCRYPT 2002 (Amsterdam), vol.2332, pp.29-44, 2002. ,
On the security of supersingular isogeny cryptosystems, Advances in Cryptology-ASIACRYPT 2016, pp.63-91, 2016. ,
Security of cryptosystems based on class groups of imaginary quadratic orders, Advances in Cryptology-ASIACRYPT 2000, pp.234-247, 2000. ,
A modular analysis of the FujisakiOkamoto transformation, Theory of Cryptography, pp.341-371, 2017. ,
Pairing the volcano, Mathematics of Computation, vol.82, issue.281, pp.581-603, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00448031
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies, Lecture Notes in Computer Science, vol.7071, pp.19-34, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00652846
Expander graphs based on GRH with an application to elliptic curve cryptography, Journal of Number Theory, vol.129, issue.6, pp.1491-1504, 2009. ,
A subexponential algorithm for evaluating large degree isogenies, ANTS IX: Proceedings of the Algorithmic Number Theory 9th International Symposium, vol.6197, pp.219-233, 2010. ,
,
Étude et accélération du protocole d'échange de clés de CouveignesRostovtsev-Stolbunov, 2017. ,
New public-key cryptosystem using braid groups, Advances in CryptologyCRYPTO, pp.166-183, 2000. ,
Endomorphism rings of elliptic curves over finite fields, 1996. ,
, Echidna databases, 2018.
A subexponential-time quantum algorithm for the dihedral hidden subgroup problem, SIAM Journal of Computing, vol.35, issue.1, pp.170-188, 2005. ,
, Another Subexponential-time Quantum Algorithm for the Dihedral Hidden Subgroup Problem, vol.22, pp.20-34, 2013.
Elliptic Functions, Graduate texts in mathematics, vol.112, 1987. ,
A key recovery attack on discrete log-based schemes using a prime order subgroup, Advances in Cryptology-CRYPTO '97, pp.249-263, 1997. ,
On the class-number of the corpus p( ? k), Proceedings of the ,
, London Mathematical Society, vol.2, issue.1, pp.358-372, 1928.
Public key cryptography based on semigroup actions, Advances in Mathematics of Communications, vol.1, issue.4, pp.489-507, 2007. ,
, La méthode des graphes. exemples et applications. In: Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata), pp.217-242, 1986.
An algorithm to compute volcanoes of 2-isogenies of elliptic curves over finite fields, Applied Mathematics and Computation, vol.176, issue.2, pp.739-750, 2006. ,
Speeding the Pollard and elliptic curve methods of factorization, Mathematics of computation, vol.48, issue.177, pp.243-264, 1987. ,
Calcul du nombre de points sur une courbe elliptique dans un corps fini: aspects algorithmiques, les Dixhuitièmes Journées Arithmétiques, vol.7, pp.255-282, 1993. ,
, Announcing request for nominations for public-key post-quantum cryptographic algorithms, 2016.
Elliptic curves with the Montgomeryform and their cryptographic applications, Public Key Cryptography-PKC 2000, vol.1751, pp.238-257, 2000. ,
A subexponential time algorithm for the dihedral hidden subgroup problem with polynomial space, 2004. ,
Computing isogenies between Montgomery curves using the action of (0, 0), Post-Quantum Cryptography, pp.229-247, 2018. ,
Public-key cryptosystem based on isogenies, Cryptology ePrint Archive, issue.145, 2006. ,
Counting points on elliptic curves over finite fields, Journal de Théorie des Nombres de Bordeaux, vol.7, issue.1, pp.219-254, 1995. ,
The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol.106, 1992. ,
Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, vol.151, 1994. ,
Reductionist security arguments for public-key cryptographic schemes based on group action, 2009. ,
Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves, Adv. Math. Commun, vol.4, issue.2, 2010. ,
, Cryptographic schemes based on isogenies, 2012.
Accelerating the CM method, LMS J. Comput. Math, vol.15, pp.172-204, 2012. ,
Constructing elliptic curves over finite fields with prescribed torsion, Mathematics of Computation, vol.81, pp.1131-1147, 2012. ,
, Modular polynomials, 2018.
An elliptic curve trapdoor system, Journal of Cryptology, vol.19, issue.1, pp.115-133, 2006. ,
SoK: The problem landscape of SIDH. Cryptology ePrint Archive, p.336, 2018. ,
Isogénies entre courbes elliptiques, C. R. Acad. Sci. Paris Sér. A-B, vol.273, pp.238-241, 1971. ,
, Algorithmic Number Theory, 7th International Symposium, vol.4076, pp.525-542, 2006.
, GMP-ECM software, 2018.