The strength of many security protocols lies on the computational intractability of the integer factorization and discrete logarithm problems. Currently, the best-known techniques employed are number field sieve (NFS) family of algorithms. They come under the class of sub-exponential time algorithms. This class of algorithms comprises of multiple steps. The relation collection (sieving step) is one of the computationally costly and highly memory-dependent phase of these algorithms. This paper discusses various ways to improve the efficiency of the relation collection phase by using parallelization techniques. Experiments have been carried out by using function field sieve, which is one of the NFS family algorithms, to show the computation efficiency of parallelization techniques along with the suitable sieving techniques and the key parameters. The result of our basic implementation is compared with the parallelized version of it. The result analysis depicts that the relation collection phase can be improved by using parallelization techniques up to fourfold.

中文翻译：

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使用 Pollard special-q 筛分的关系集合解决整数分解和离散对数问题

许多安全协议的优势在于整数分解和离散对数问题的计算难度。目前，采用的最著名的技术是数域筛 (NFS) 系列算法。它们属于次指数时间算法。这类算法包括多个步骤。关系收集（筛选步骤）是这些算法的计算成本高且高度依赖内存的阶段之一。本文讨论了通过使用并行化技术来提高关系收集阶段效率的各种方法。使用NFS家族算法之一的函数场筛进行了实验，以展示并行化技术的计算效率以及合适的筛分技术和关键参数。我们将基本实现的结果与其并行化版本进行比较。结果分析表明，关系收集阶段可以通过使用多达四倍的并行化技术进行改进。