Applying Sieving to the Computation of Quadraticclass

Applying sieving to the computation of quadratic class groups

We present a new algorithm for computing the ideal class group of an imaginary quadratic order which is based on the multiple polynomial version of the quadratic sieve factoring algorithm. Although no formal analysis is given, we conjecture that our algorithm has sub-exponential complexity, and computational experience shows that it is significantly faster in practice than existing algorithms.

Computation of Slip analysis to detect adhesion for protection of rail vehicle and derailment

Adhesion level for the proper running of rail wheelset on track has remained a significant problem for researchers in detecting slippage to avoid accidents. In this paper, the slippage of rail wheels has been observed applying forward and lateral motions to slip velocity and torsion motion. The longitudinal and lateral forces behavior is watched with respect to traction force to note correlatio...

Sieving Methods for Class Group Computation

Use of SIMD-based data parallelism to speed up sieving in integer-factoring algorithms

Many cryptographic protocols derive their security from the apparent computational intractability of the integer factorization problem. Currently, the best known integer-factoring algorithms run in subexponential time. Efficient parallel implementations of these algorithms constitute an important area of practical research. Most reported implementations use multi-core and/or distributed paralle...

SIMD-Based Implementations of Sieving in Integer-Factoring Algorithms

The best known integer-factoring algorithms consist of two stages: the sieving stage and the linear-algebra stage. Efficient parallel implementations of both these stages have been reported in the literature. All these implementations are based on multi-core or distributed parallelization. In this paper, we experimentally demonstrate that SIMD instructions available in many modern processors ca...