On affine sub-families of Grain-like structures

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• 作者：Yupeng Jiang ; Dongdai Lin
• 关键词：Grain ; Cascade connection ; Sub ; family ; Primitive divisor
• 刊名：Designs, Codes and Cryptography
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：82
• 期：3
• 页码：531-542
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Coding and Information Theory; Data Structures, Cryptology and Information Theory; Data Encryption; Discrete Mathematics in Computer Science; Information and Communication, Circuits;
• 出版者：Springer US
• ISSN：1573-7586
• 卷排序：82

文摘

Grain is one of eSTREAM hardware-oriented finalists. It contains a cascade connection of an 80-bit primitive linear feedback shift registers (\({{\mathrm{LFSR}}}\)) into an 80-bit nonlinear feedback shift register (\({{\mathrm{NFSR}}}\)). The variant Grain-128 has a cascade connection with both \({{\mathrm{LFSR}}}\) and \({{\mathrm{NFSR}}}\) of order 128. We consider Grain-like structures, i.e., the cascade connection of a primitive \({{\mathrm{LFSR}}}\) into an \({{\mathrm{NFSR}}}\) of the same order. It is easy to know that in such a structure, all the affine sub-families of the \({{\mathrm{NFSR}}}\) are also the affine sub-families of the cascade connection. We prove that if the degree of the characteristic function of the \({{\mathrm{NFSR}}}\) is bigger than 2, then affine sub-families of the cascade connection must also be affine sub-families of the \({{\mathrm{NFSR}}}\). The same result holds if the order of the primitive \({{\mathrm{LFSR}}}\) is bigger than the order of the \({{\mathrm{NFSR}}}\).