Residue Number System (RNS) is a non-weighted number system which was proposed by
Garner back in 1959 to achieve fast implementation of addition, subtraction and …

We present the first implementation of RSA in the residue number system (RNS) which does
not require any conversion, either from radix to RNS beforehand or RNS to radix afterward …

We present a new hardware architecture to compute scalar multiplications in the group of
rational points of elliptic curves defined over a prime field. We have made an implementation …

Cryptography plays a major role assuring security in computation and communication. In
particular, public-key cryptography enables the asymmetrical ciphering of data along with …

Side-channel attacks against implementations of elliptic-curve cryptography have been
extensively studied in the literature and a large tool-set of countermeasures is available to …

Dynamically reconfigurable systems are known to have many advantages such as area and
power reduction. The drawbacks of these systems are the reconfiguration delay and the …

The selection of the elements of the bases in an RNS modular multiplication method is
crucial and has a great impact in the overall performance. This work proposes specific sets …

Countermeasures to defeat most of side-channel attacks on exponentiations are based on
randomization of processed data. The exponent and the message blinding are particular …

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 …

The paper describes a new RNS modular multiplication algorithm for efficient
implementations of ECC over F _P FP. Thanks to the proposition of RNS-friendly Mersenne …