Montgomery reduction within the context of residue number system arithmetic

Jean-Claude Bajard (1) , Julien Eynard (2) , Nabil Merkiche (3)

1 ALMASTY - ALgorithms for coMmunicAtion SecuriTY
2 ECE - Department of Electrical and Computer Engineering [Waterloo]
3 DGA_IP - DGA/Ingénierie des Projets

This paper is a survey of Montgomery reduction in the context of residue number system arithmetic. We present the main variants of RNS Montgomery reduction, some efficient embedded hardware implementations, applications in asymmetric cryptography (RSA, ECC, pairing, lattices), to end with the use of RNS against side-channel analysis and fault attacks.

Domaines: Informatique [cs]

Jean-Claude Bajard, Julien Eynard, Nabil Merkiche. Montgomery reduction within the context of residue number system arithmetic. Journal of Cryptographic Engineering, 2018, 8 (3), pp.189-200. ⟨10.1007/s13389-017-0154-9⟩. ⟨hal-01494547⟩