Publication
Efficient SIMD Arithmetic Modulo a Mersenne Number
Publications associées (36)
Faster ECC over $\mathbb{F}_{2^{521}-1}$
In this paper we present a new multiplication algorithm for residues modulo the Mersenne prime . Using this approach, on an Intel Haswell Core i7-4770, constant-time variable-base scalar multiplication on NIST’s (and SECG’s) curve P-521 requires ...
Springer Berlin Heidelberg2015Generalised Mersenne Numbers Revisited
Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attrac ...
2013On the Cryptanalysis of Public-Key Cryptography
Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice is studied and techniques are presented to speed-up the ...
EPFL2012Solving 112-bit prime ECDLP on game consoles using sloppy reduction
Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Marcelo Kaihara
We describe a cell processor implementation of Pollard’s rho method to solve discrete logarithms in groups of elliptic curves over prime fields. The implementation was used on a cluster of PlayStation 3 game consoles to set a new record. We present in deta ...
2012Le foncteur de bi-ensembles des modules de p-permutation
Let k be an algebraically closed field of characteristic p, where p is a prime number or 0. Let G be a finite group and ppk(G) be the Grothendieck group of p-permutation kG-modules. If we tensor it with C, then Cppk becomes a C-linear biset functor. Recall ...
EPFL2012Erdos-Szekeres-type theorems for monotone paths and convex bodies
For any sequence of positive integers j(1)< j(2)= 2 and q >= 2, what is the s ...
London Math Soc2012Efficient SIMD arithmetic modulo a Mersenne number
Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung
This paper describes carry-less arithmetic operations modulo an integer 2^M − 1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implemen ...
IEEE Computer Soc Press2011Cryptographic Hash Functions in Groups and Provable Properties
We consider several "provably secure" hash functions that compute simple sums in a well chosen group (G,*). Security properties of such functions provably translate in a natural way to computational problems in G that are simple to define and possibly also ...
EPFL2011High-Performance Modular Multiplication on the Cell Processor
This paper presents software implementation speed records for modular multiplication arithmetic on the synergistic processing elements of the Cell broadband engine (Cell) architecture. The focus is on moduli which are of special interest in elliptic curve ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010High-Performance Modular Multiplication on the Cell Processor
This paper presents software implementation speed records for modular multiplication arithmetic on the synergistic processing elements of the Cell broadband engine (Cell) architecture. The focus is on moduli which are of special interest in elliptic curve ...
Springer Berlin Heidelberg2010