Most public key crypto systems use finite field modulo arithmetic. This modulo arithmetic is applied on real numbers, binary values and polynomial functions. The computation cost ...
We provide a modular method for computing the splitting field Kf of an integral polynomial f by suitable use of the byproduct of computation of its Galois group Gf by p-adic Staudu...
We consider the problem of solving a linear system Ax = b over a cyclotomic field. What makes cyclotomic fields of special interest is that we can easily find a prime p that sp...
We utilize effective algorithms for computing in the cohomology of a Shimura curve together with the Jacquet-Langlands correspondence to compute systems of Hecke eigenvalues assoc...
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit ...
Marc Baboulin, Alfredo Buttari, Jack Dongarra, Jak...