Elliptic curve point multiplication is considered to be the most significant operation in all
elliptic curve cryptography systems, as it forms the basis of the elliptic curve discrete …

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 …

2's complement number system imposes a fundamental limitation on the power and
performance of arithmetic circuits, due to the fundamental need of cross-datapath carry …

We identify a canonical parameter in the Chinese Remainder Theorem (CRT) and call it the
“Reconstruction Coefficient”,(denoted by “RC”); and introduce the notions of “Partial” and …

In this paper we give a survey of a method combining the residue number system (RNS)
representation and the leak-resistant arithmetic on elliptic curves. These two techniques are …

The use of elliptic curve cryptosystems on embedded systems has been becoming
widespread for some years. Therefore the resistance of such cryptosystems to side-channel …

Recently, composite-order bilinear pairing has been shown to be useful in many
cryptographic constructions. However, it is time-costly to evaluate. This is because the …

In this work, we are interested in arithmetic on large prime field and their extensions of small
degree. We explain why it is very interesting to use RNS arithmetic for the base field 𝔽 p …

Modular arithmetic based processors are widely used in digital signal processing, image
processing, cryptography, etc. All major crypto-systems require the use of modular …

Lattice based cryptography is claimed as a serious candidate for post quantum
cryptography, it recently became an essential tool of modern cryptography. Nevertheless, if …