一类伪随机二进制数列的碰撞与雪崩效应

刘华宁

数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 907-914.

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PDF(425 KB)
数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 907-914. DOI: 10.12386/A2013sxxb0086
论文

一类伪随机二进制数列的碰撞与雪崩效应

    刘华宁
作者信息 +

On the Collision and Avalanche Effect in a Family of Pseudorandom Binary Sequences

    Hua Ning LIU
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文章历史 +

摘要

p 为奇素数, f(x)∈Fp[x].设 a p 互素, a 表示 a 关于模 p 的逆, 即1≤ a≤ p-1 且 aa= 1 mod p.定义二进制数列 Ep-1=(e1,...,ep-1),其中
以及 Rp(n) 表示 n 关于模 p 的最小非负剩余.本文利用解析数论的方法, 研究了 Ep-1 的碰撞与雪崩效应.

Abstract

Assume that p is an odd prime, and f(x) ∈ Fp[x]. For (a, p) = 1, denote the multiplicative inverse of a by a with aa ≡ 1 mod p and 1 ≤ a p - 1. Let Ep-1 = {e1,...,ep-1} be defined by 

, where Rp(n) denotes the least non-negative residue of n modulo p. In this paper we study the collision and avalanche effect of Ep-1 by using the methods in analytic number theory.

关键词

二进制数列 / 碰撞 / 雪崩效应

Key words

binary sequence / collision / avalanche effect

引用本文

导出引用
刘华宁. 一类伪随机二进制数列的碰撞与雪崩效应. 数学学报, 2013, 56(6): 907-914 https://doi.org/10.12386/A2013sxxb0086
Hua Ning LIU. On the Collision and Avalanche Effect in a Family of Pseudorandom Binary Sequences. Acta Mathematica Sinica, Chinese Series, 2013, 56(6): 907-914 https://doi.org/10.12386/A2013sxxb0086

参考文献

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基金

国家自然科学基金资助项目(10901128)

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