The radius-stepping algorithm is an efficient, parallelixable algorithm for finding the shortest paths in graphs. It solved the problem in Δ-Stepping algorithm, which has no known theoretical bounds fur general graphs. 1" this paper, we describe a parallel privacy-preserving method for finding SingleSource Shortest Paths (SSSP). Our optimized method is based on the Radius-Stepping algorithm. The method is implemented on iop of the Secure Multiparty Computation (SMC) Sharemiiid platform. We have reshaped the radius-stepping algorithm to work on vectors representing the graph in a SIMD manner, in order to enable a fast execution using the secret-sharing based SMC protocol set of Sharemind. The results of the real implementation show an efficient method that reduced the execution time hundreds of times iii comparison with a standard case of the privacy-preserving radius-stepping and Δ-Stepping algorithms.

The aim of Elliptic Curve Cryptosystems (ECC) is to achieve the same security level as RSA but with shorter key size. The basic operation in the ECC is scalar multiplication which is an expensive operation. In this paper, we focus on optimizing ECC scalar multiplication based on Non-Adjacent Form (NAF). A new algorithm is introduced that combines an Add-Subtract Scalar Multiplication Algorithm with NAF representation to accelerate the performance of the ECC calculation. Parallelizing the new algorithm shows an efficient method to calculate ECC. The proposed method has speed up the calculation up to 60% compared with the standard method.