Cryptographic applications of Brahmagupta-Bhaskara equation

被引：20

作者：

Murthy, N. Rama ^{[1
]}

Swamy, M. N. S. ^{[1
]}

机构：

[1] Concordia Univ, Dept Elect & Comp Engn, Montreal, PQ H3G 1M8, Canada

来源：

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS | 2006年 / 53卷 / 07期

基金：

加拿大自然科学与工程研究理事会;

关键词：

authentication; Brahmagupta-Bhaskara (BB) equation; communication and network security; cryptography; digital encryption; Diophantine equations; Pell equation;

D O I：

10.1109/TCSI.2006.875177

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The Brahmagupta-Bhiskara (BB) equation is a quadratic Diophantine equation of the form N X-2 + k = Y-2, where k is an integer (positive or negative) and N is a positive integer such that root N is irrational. A particular case of the BB equation with k = 1 is also known as Pell equation in literature. This equation in the Galois Field GF(p), where p is an odd prime has some practically useful properties. Application of these properties in two different fields of cryptography, namely, digital encryption and user authentication are discussed in this paper. For those applications, where software computation of the roots of the BB equation is unacceptable for being too slow, a hardware architecture for using the BB equation in GF(p) is given that is useful for implementation in VLSI form.

引用

页码：1565 / 1571

页数：7

共 14 条

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