Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently
performing arithmetic operations such as addition, multiplication and division, and their …

Due to the increasing threats from possible large-scale quantum computers, post-quantum
cryptography (PQC) has drawn significant attention from various communities recently. In …

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 …

In this paper we investigate various arithmetic techniques which can be used to potentially
enhance the performance in the supersingular isogeny Diffie-Hellman (SIDH) key-exchange …

In this paper the authors present a new integrated symmetric-key cryptographic method,
named SJA, which is the combination of advanced Caesar Cipher method, TTJSA method …

Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography,
and error correcting codes. Although recent microprocessors typically offer a wide range of …

Modular multiplication (MM) is a fundamental operation in many cryptographic and
arithmetic applications. In this article, we present an improved Barrett modular multiplication …

We give a systematic overview of techniques to compute arithmetic modulo 2 xpy±1 and
propose improvements. This is useful for computations in the supersingular isogeny Diffie …

Barrett's algorithm is the most commonly known method of performing a modular
multiplication, which is the core of many modern encryption algorithms such as RSA …

The usual formulation of efficient division uses Newton iteration to compute an inverse in a
related domain where multiplicative inverses exist. On one hand, Newton iteration allows …