Xorshift1024*, Xorshift1024+, Xorshift128+ and Xoroshiro128+ Fail Statistical Tests for Linearity
Xorshift1024*, Xorshift1024+, Xorshift128+ and Xoroshiro128+ Fail Statistical Tests for Linearity
复制标题
Xorshift1024*、Xorshift1024、Xorshift128 和 Xoroshiro128 未通过线性统计测试
DOI：
10.1016/j.cam.2018.10.019
复制
发表时间：
2018
影响因子：
2.4
通讯作者：
Melissa E. O'Neill
中科院分区：
文献类型：
--
作者：
D. Lemire;Melissa E. O'Neill
L’ecuyer & Simard的big crush统计测试套件揭示了许多流行随机数生成器（包括Marsaglia的Xorshift生成器）的统计缺陷。Vigna最近提出了Xorshift方案的一些64位变体，这些变体被进一步打乱(例如：， xorshift1024*, xorshift1024+, xorshift128+, xorshift128+)。与未加加密的对应对象不同，它们在每个64位单词（最高有效、最低有效、最高有效、最低有效等）交错32位块时传递Big Crush。我们报告说，当从每个64位字中以相反的顺序取32个最低顺序的比特时，这些打乱的生成器系统地失败了Big Crush -特别是线性复杂度和检测线性的矩阵秩测试。
L’Ecuyer & Simard’sBig Crushstatistical test suite has revealed statistical flaws in many popular random number generators including Marsaglia’s Xorshift generators. Vigna recently proposed some 64-bit variations on the Xorshift scheme that are furtherscrambled(i.e., xorshift1024*, xorshift1024+, xorshift128+, xoroshiro128+). Unlike their unscrambled counterparts, they pass Big Crush when interleaving blocks of 32 bits for each 64-bit word (most significant, least significant, most significant, least significant, etc.). We report that these scrambled generators systematically fail Big Crush – specifically the linear-complexity and matrix-rank tests that detect linearity – when taking the 32 lowest-order bits in reverse order from each 64-bit word.