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This paper presents parallel point-multiplication on conic curves based on standard NAF algorithm and Chinese Remainder Theorem. All analysis of parallel methodologies should take advantage of the basic parallel algorithms of conic curves cryptosystem in our previous works. We employ standard NAF algorithm to parallel the point-multiplication over finite field Fp by adopting the pipeline technique to compute point-addition and point-double respectively. The expression of point-addition over ring Zn is deduced to declare that the parallel methodology over finite field Fp could be used over ring Zn. The operation of pointmultiplication over ring Zn is paralleled by partitioning the operation into two different finite fields based on Chinese Remainder Theorem and then combining the two temporary parameters to get the final result. After that, a quantitative performance contrast is made between sequential algorithm and parallel algorithm to show our approaches allow speeding up the point-multiplication on conic curves and reduce the time complexity. Additionally, the parallel method of paralleling point-multiplication over ring Zn introduced in this paper is also more efficient than an old parallel algorithm we proposed before.

Point-to-point latency is one of the most important metrics for high performance computer networks and is used widely in communication performance modeling, link-failure detection, and application optimization. However, it is often hard to determine the full-scale point-to-point latency of large scale HPC networks since it often requires measurements to the square of the number of terminal nodes. In this paper, we propose an efficient method to generate measurement plans for arbitrary indirect HPC networks and reduces the measurement requirements from O(n 2 ) to m, which is often O(n) in modern indirect networks containing n nodes and m links, thus significantly reduces the latency measure overhead. Both analysis and experiments show that the proposed method can reduce the overhead of large-scale fat-tree networks by orders of magnitudes.

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