NDLI: On affine sub-families of Grain-like structures

Content Provider	Springer Nature Link
Author	Jiang, Yupeng Lin, Dongdai
Copyright Year	2016
Abstract	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 $${{\mathrm{NFSR}}}$$ .
Ending Page	542
Page Count	12
Starting Page	531
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	3
Volume Number	82
Language	English
Publisher	Springer US
Publisher Date	2016-01-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Information and Communication, Circuits Grain Data Encryption Primitive divisor Sub-family Sequences (mod $m$ ) Data Structures, Cryptology and Information Theory Discrete Mathematics in Computer Science Shift register sequences and sequences over finite alphabets Coding and Information Theory Cryptography Combinatorics Cascade connection
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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