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Journal Article
未知系数的二阶线性同余发生器截位还原
2019
Overview
同余发生器的可预测性问题, 即能否由一段截位序列还原发生器的参数和初态, 进而准确预测后面的序列, 是评估发生器安全性的重要研究课题. 本文研究在模数m = 2k 已知, 系数a, b未知的条件下, 二阶线性同余发生器xi+2 = axi+1 + bxi mod m 的可预测性问题. 我们给出一个基于格基约化算法的方法, 可以在已知一段连续的高位s 比特截位序列的条件下, 还原系数a, b 和初态x0, x1, 实现对序列的预测. 实验结果表明, 当模数m = 232, 发生器生成的序列为整数剩余类环Z/mZ 上的二阶本原序列时, 可以由140 拍连续的高位6 比特截位序列还原系数a,b 和初态x0, x1. 本文从逆向还原的角度探究二阶线性同余发生器的抗预测能力, 旨在为其在密码上的应用提供参考和指导.
Publisher
Chinese Association for Cryptologic Research, Journal of Cryptologic Research
Subject
