北京邮电大学学报
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吴宇航1,张凤荣2,唐国尧1,韦永壮3,王保仓2
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摘要: Bernstein-Vazirani(BV)算法最初用于求解线性函数的系数,后来研究人员提出了使用BV算法求解向量值函数的线性结构的算法。首先,扩展了原始的求解向量值函数的线性结构的问题,提出了“弱线性结构”的定义。在此基础上,分析了线性结构问题的几种扩展,延申了BV算法的应用。其次,基于扩展线性结构问题,提出了可应用在量子环境下寻找分组密码的高概率差分的新量子算法。与已有的算法相比,所给算法在一次得到多个高概率的差分,时间复杂度可以降低至 。
关键词: BV算法, 向量值函数, 线性结构, 高概率差分
Abstract: The Bernstein-Vazirani (BV) algorithm was originally used to solve the coefficients of linear functions, and later researchers proposed an algorithm using the BV algorithm to solve the linear structure of a vector valued function. Firstly, we extend the original problem of solving the linear structure of vector-valued functions, and propose a definition of "weak linear structure". On this basis, we analyze several extensions of linear structure problem and extend the application of BV algorithm. Secondly, based on the extended linear structure problem, we propose a new quantum algorithm which can be applied to find the high-probability difference of block cipher in quantum environment. Compared with the existing algorithm, the proposed algorithm can obtain multiple differences with high probability at one time, and the time complexity can be reduced to .
Key words: BV algorithm, vector-valued function, linear structure, high-probability difference
中图分类号:
TN918.4
吴宇航 张凤荣 唐国尧 韦永壮 王保仓. 基于Bernstein-Vazirani算法的量子差分查找新算法[J]. 北京邮电大学学报.
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