Binary-Ternary Plus-Minus Modular Inversion in RNS

Karim Bigou (1) , Arnaud Tisserand (1)

1 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources

A fast RNS modular inversion for finite fields arithmetic has been published at CHES 2013 conference. It is based on the binary version of the plus-minus Euclidean algorithm. In the context of elliptic curve cryptography (i.e. 160–550 bits finite fields), it significantly speeds-up modular inversions. In this paper, we propose an improved version based on both radix 2 and radix 3. This new algorithm leads to 30 % speed-up for a maximal area overhead about 4 % on Virtex 5 FPGAs.

Mots clés: Residue Number System; Modular Arithmetic; Extended Euclidean Algorithm; ECC; FPGA

Domaines: Arithmétique des ordinateurs; Cryptographie et sécurité [cs.CR]; Micro et nanotechnologies/Microélectronique

Karim Bigou, Arnaud Tisserand. Binary-Ternary Plus-Minus Modular Inversion in RNS. IEEE Transactions on Computers, 2016, 65 (11), pp.3495-3501. ⟨10.1109/TC.2016.2529625⟩. ⟨hal-01314268⟩