Protection of Sensitive Messages Based on Quadratic Roots of Gaussians: Groups with Complex Modulus

• 作者: Boris S. Verkhovsky
• 来源期刊: 通讯、网络与系统学国际期刊(英文)
• 学科: 数学
• 关键词: Complex Modulus Computational Efficiency CRYPTOGRAPHIC ALGORITHM Digital Isotopes MULTIPLICATIVE Control Parameter Octadic ROOTS QUARTIC ROOTS Rabin ALGORITHM Reduction of Complexity Resolventa Secure Communication Square ROOTS
• 年，卷（期）: 2011,（5）
• 页码范围: 287-296
• 页数: 10页
• 分类号: O1

摘要

This paper considers three algorithms for the extraction of square roots of complex integers {called Gaussians} using arithmetic based on complex modulus p + iq. These algorithms are almost twice as fast as the analogous algorithms extracting square roots of either real or complex integers in arithmetic based on modulus p, where is a real prime. A cryptographic system based on these algorithms is provided in this paper. A procedure reducing the computational complexity is described as well. Main results are explained in several numeric illustrations.