Abstract Modern Graphics Processing Units (GPU) have reached a dimension with respect
to performance and gate count exceeding conventional Central Processing Units (CPU) by …

We describe a cell processor implementation of Pollard's rho method to solve discrete
logarithms in groups of elliptic curves over prime fields. The implementation was used on a …

Acceleration of cryptographic applications on massive parallel computing platforms, such as
Graphic Processing Units (GPUs), becomes a real challenge concerning practical …

Homomorphic Encryption (HE) enables secure cloud offload processing on encrypted data.
HE schemes are limited in the complexity and type of operations they can perform …

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 modular exponentiation on large numbers is computationally intensive. An effective way
for performing this operation consists in using Montgomery exponentiation in the Residue …

This brief presents a residue-to-binary converter for the moduli set {2 n-1, 2 n+ 1, 2 2n+ 1, 2
2n+ p}, where n is a positive integer and 0≤ p≤ n-2. The converter consists of three …

Privacy guarantees are still insufficient for outsourced data processing in the cloud. While
employing encryption is feasible for data at rest or in transit, it is not for computation without …

In earlier publications, many researchers have addressed the problem of residue-to-binary
conversion for the popular moduli set (2 n, 2 n− 1, 2 n+ 1), where n is a positive integer …

The paper suggests an algorithm for finding Residue Number Systems (RNS) with six
modules (6-tuples) with the Sum of Quotients SQ= 2 k for some positive integer k. It is shown …