A Lattice-Based Method for Recovering the Unknown Parameters of Truncated Multiple Recursive Generators with Constant

IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
Hanbing Yu;Qunxiong Zheng
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引用次数: 0

Abstract

Multiple recursive generators with constant, as the high-order extension of linear congruence generators, form an important class of pseudorandom number generators that are widely used in cryptography. The predictability of truncated sequences output by multiple recursive generators with constant that predicts the whole sequences by the truncated high-order bits of the sequences, is a crucial problem in cryptography. This paper studies the predictability of truncated multiple recursive generators with constant. Given a few truncated digits of high-order bits output by a multiple recursive generator with constant, we first convert the multiple recursive generator with constant to multiple recursive generator and then adopt the method we proposed recently to recover the modulus, the coefficients, and the differences of initial state. In particular, we give an estimation of the number of truncated digits required for recovering the differences of initial state by using the expected norm of target vector. We prove by exponential sums that the number of truncated digits required for uniquely determining both the initial state and the constant is finite and give an upper bound. Extensive experiments confirm the correctness of our method.
一种基于网格的方法,用于恢复具有常数的截断多重递归发生器的未知参数
带常数的多重递归发生器作为线性全等发生器的高阶扩展,构成了一类重要的伪随机数发生器,被广泛应用于密码学领域。有常数的多重递归发生器通过序列的截断高阶位来预测整个序列,其输出的截断序列的可预测性是密码学中的一个关键问题。本文研究了带常数的截断多重递归发生器的可预测性。给定由带常数的多重递归发生器输出的高阶比特的几位截断数,我们首先将带常数的多重递归发生器转换为多重递归发生器,然后采用我们最近提出的方法来恢复模、系数和初始状态的差值。特别是,我们利用目标向量的期望规范估算了恢复初始状态差值所需的截断位数。我们通过指数和证明了唯一确定初始状态和常数所需的截断位数是有限的,并给出了一个上限。大量实验证实了我们方法的正确性。
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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来源期刊
Chinese Journal of Electronics
Chinese Journal of Electronics 工程技术-工程:电子与电气
CiteScore
3.70
自引率
16.70%
发文量
342
审稿时长
12.0 months
期刊介绍: CJE focuses on the emerging fields of electronics, publishing innovative and transformative research papers. Most of the papers published in CJE are from universities and research institutes, presenting their innovative research results. Both theoretical and practical contributions are encouraged, and original research papers reporting novel solutions to the hot topics in electronics are strongly recommended.
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