GF(p)上计算对数的改进算法及其密码学意义

Democratizing Cryptography Pub Date : 2022-08-24 DOI:10.1145/3549993.3550009

S. Pohlig, M. E. Hellman

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引用次数: 17

摘要

当且仅当在GF (p)上计算对数算法不可行时，描述了一个安全的密码系统。以前发表的计算该函数的算法在时间和空间上都需要O (p 1 / 2)的复杂度。提出了一种改进算法，当p−1只有小素数因子时，其复杂度为O (log 2p)。在密码系统中必须避免这样的p值。本文还描述了新算法的建设性应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An Improved Algorithm for Computing Logarithms over GF(p) and Its Cryptographic Significance

A cryptographic system is described which is secure if and only if computing log arithms over GF ( p ) is infeasible. Previously published algorithms for computing this function require O ( p 1 / 2 ) complexity in both time and space. An improved algo rithm is derived which requires O ( log 2 p ) complexity if p − 1 has only small prime factors. Such values of p must be avoided in the cryptosystem. Constructive uses for the new algorithm are also described.

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Democratizing Cryptography

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