Computations of small discrete logarithms are feasible even in “secure” groups, and are
used as subroutines in several cryptographic protocols in the literature. For example, the …

Asymmetric cryptographic algorithms (eg, RSA and ECC) have been implemented on
Graphics Processing Units (GPUs) for several years. These implementations mainly exploit …

A major cryptanalytic computation is currently underway on multiple platforms, including
standard CPUs, FPGAs, PlayStations and Graphics Processing Units (GPUs), to break the …

Asymmetric cryptographic algorithm (eg, RSA and Elliptic Curve Cryptography)
implementations on Graphics Processing Units (GPUs) have been researched for over a …

Software implementations of discrete logarithm based cryptosystems over finite fields
typically make the assumption that any domain parameters they encounter define cyclic …

This work presents a GPU implementation of the Montgomery multiplication algorithm that is
heavily optimized for the GPU's SEVID architecture, as well as the field sizes and constraints …

Outsourcing helps relocate data from the cyber-physical system (CPS) for efficient storage at
low cost. Current server-based outsourcing mainly focuses on the benefits of servers. This …

In traditional multiple precision large integer multiplication algorithm, the required number of
additions approximates the number of multiplications needed. In some platforms, the great …

This introductory chapter describes briefly the evolution of cryptography over the past
thousand years until present. After that, we present lattice-based cryptography, a promising …

Multiple precision (MP) arithmetic is a core building block of a wide variety of algorithms in
computational mathematics and computer science. In mathematics MP is used in …