The Universal Block Lanczos–Padé Method for Linear Systems Over Large Prime Fields

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• 作者：M. A. Cherepniov ; N. L. Zamarashkin
• 刊名：Journal of Mathematical Sciences
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：221
• 期：3
• 页码：461-478
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer US
• ISSN：1573-8795
• 卷排序：221

文摘

In this paper, we propose a universal algorithm designed for solving large sparse linear systems over finite fields with a large prime number of elements. Such systems arise in the solution of the discrete logarithm problem modulo a prime number. The algorithm has been developed for parallel computing systems with various parallel architectures and properties. The new method inherits the structural properties of the Lanczos method. However, it provides flexible control over the complexity of parallel computations and the intensity of exchanges.