Fast Modular Arithmetic on the Kalray MPPA-256 Processor for an Energy-Efficient Implementation of ECM

Masahiro Ishii (1) , Jérémie Detrey (2) , Pierrick Gaudry (2) , Atsuo Inomata (3) , Kazutoshi Fujikawa (3)

1 Nara Institute of Science and Technology
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
3 ITC - Information iniTiative Center

The Kalray MPPA-256 processor is based on a recent low-energy manycore architecture. In this article, we investigate its performance in multiprecision arithmetic for number-theoretic applications. We have developed a library for modular arithmetic that takes full advantage of the particularities of this architecture. This is in turn used in an implementation of the ECM, an algorithm for integer factorization using elliptic curves. For parameters corresponding to a cryptanalytic context, our implementation compares well to state-of-the-art implementations on GPU, while using much less energy.

Mots clés: Kalray MPPA-256 manycore processor; Multiprecision modular arithmetic; Integer factorization; Elliptic curve method

Domaines: Cryptographie et sécurité [cs.CR]; Arithmétique des ordinateurs

Masahiro Ishii, Jérémie Detrey, Pierrick Gaudry, Atsuo Inomata, Kazutoshi Fujikawa. Fast Modular Arithmetic on the Kalray MPPA-256 Processor for an Energy-Efficient Implementation of ECM. IEEE Transactions on Computers, 2017, 66 (12), pp.2019-2030. ⟨10.1109/TC.2017.2704082⟩. ⟨hal-01299697v2⟩