Finding ECM-friendly curves through a study of Galois properties, ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium, vol.1, pp.63-86, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00671948
Twisted Edwards curves, Progress in Cryptology -AFRICACRYPT, vol.5023, pp.389-405, 2008. ,
Starfish on strike, Progress in Cryptology -LATINCRYPT 2010, vol.6212, pp.61-80, 2010. ,
, ECM using Edwards curves. Mathematics of Computation, vol.82, pp.1139-1179, 2013.
, EECM-MPFQ: ECM using Edwards curves
Double-base scalar multiplication revisited. Cryptology ePrint Archive, 2017. ,
Explicit-formulas database ,
A complete set of addition laws for incomplete Edwards curves, Cryptology ePrint Archive, 2009. ,
ECM at work, Advances in Cryptology -ASI-ACRYPT 2012, pp.467-484, 2012. ,
Efficient arithmetic on elliptic curves using a mixed Edwards-Montgomery representation, Cryptology ePrint Archive, vol.218, 2008. ,
Efficient and secure elliptic curve point multiplication using double-base chains, Advances in Cryptology, ASIACRYPT 2005, vol.3788, pp.59-78, 2005. ,
URL : https://hal.archives-ouvertes.fr/lirmm-00106030
Massively parallel elliptic curve factoring, Advances in Cryptology -EUROCRYPT' 92, vol.658, pp.183-193, 1992. ,
A normal form for elliptic curves, Bulletin of the American Mathematical Society, vol.44, pp.393-422, 2007. ,
Twisted Edwards curves revisited, International Conference on the Theory and Application of Cryptology and Information Security, pp.326-343, 2008. ,
Fast Modular Arithmetic on the Kalray MPPA-256 Processor for an Energy-Efficient Implementation of ECM, IEEE Transactions on Computers, vol.66, issue.12, pp.2019-2030 ,
URL : https://hal.archives-ouvertes.fr/hal-01299697
, , 2017.
Factorization of a 768-bit rsa modulus, Advances in Cryptology -CRYPTO 2010, vol.6223, pp.333-350, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00444693
, The development of the number field sieve, vol.1554, 1993.
Factoring integers with elliptic curves, Annals of Mathematics, vol.126, issue.3, pp.679-673, 1987. ,
On hybrid SIDH schemes using Edwards and Montgomery curve arithmetic. Cryptology ePrint Archive, 1213. ,
On the Analysis of Public-Key Cryptologic Algorithms, 2015. ,
Evaluating recurrences of form Xm+n = f (Xm, Xn, Xm?n) via Lucas chains, 1983. ,
Speeding the Pollard and elliptic curve methods of factorization, Mathematics of Computation, vol.48, issue.177, pp.243-264, 1987. ,
Elliptic curve scalar multiplication combining Yao's algorithm and double bases, Cryptographic Hardware and Embedded Systems, CHES 2009, vol.5747, pp.304-316, 2009. ,
, CADO-NFS, An Implementation of the Number Field Sieve Algorithm, 2017.
On the evaluation of powers, SIAM Journal of Computing, vol.5, issue.1, pp.100-103, 1976. ,
50 largest factors found by ECM ,
years of ECM, Algorithmic Number Theory. ANTS, vol.4076, pp.525-542, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00070192
GMP-ECM (elliptic curve method for integer factorization ,