Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields
Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields
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DOI：
10.3390/math9050556
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发表时间：
2021-03-01
期刊：
影响因子：
2.4
通讯作者：
Ortiz, Andres
中科院分区：
文献类型：
--
作者：
Cotrina, Guillermo;Peinado, Alberto;Ortiz, Andres
提出了一种产生高斯分布伪随机数的新方法。该生成器是GF（2（n））中线性反馈移位寄存器循环旋转生成器的推广。由于在GF（2（n））中的LFSR的二进制等价模型中发现的隐式旋转，在扩展域中不再需要在二进制情况下应用于LFSR的旋转。新的提议与当前密码学的趋势一致，即使用扩展字段作为加速伪随机生成器比特率的一种方式。这一建议使得LFSR在密码学中的应用从经典的均匀分布序列的产生进一步扩展到其他领域，如量子密钥分配方案，其中需要具有高斯分布的序列。该论文包含对产生的数字的统计分析以及与其他高斯生成器的比较。
A new proposal to generate pseudorandom numbers with Gaussian distribution is presented. The generator is a generalization to the extended field GF(2(n)) of the one using cyclic rotations of linear feedback shift registers (LFSRs) originally defined in GF(2). The rotations applied to LFSRs in the binary case are no longer needed in the extended field due to the implicit rotations found in the binary equivalent model of LFSRs in GF(2(n)). The new proposal is aligned with the current trend in cryptography of using extended fields as a way to speed up the bitrate of the pseudorandom generators. This proposal allows the use of LFSRs in cryptography to be taken further, from the generation of the classical uniformly distributed sequences to other areas, such as quantum key distribution schemes, in which sequences with Gaussian distribution are needed. The paper contains the statistical analysis of the numbers produced and a comparison with other Gaussian generators.