Self-Dual Hadamard Bent Sequence

SHI Minjia, LI Yaya, CHENG Wei, CRNKOVIĆ Dean, KROTOV Denis, SOLÉ Patrick

Journal of Systems Science & Complexity ›› 2023, Vol. 36 ›› Issue (2) : 894-908.

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Journal of Systems Science & Complexity ›› 2023, Vol. 36 ›› Issue (2) : 894-908. DOI: 10.1007/s11424-023-2276-8

Self-Dual Hadamard Bent Sequence

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Abstract

A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application (Solé, et al., 2021). The authors study the self-dual class in length at most 196. The authors use three competing methods of generation: Exhaustion, Linear Algebra and Gröbner bases. Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples. The authors conjecture that if v is an even perfect square, a self-dual bent sequence of length v always exists. The authors introduce the strong automorphism group of Hadamard matrices, which acts on their associated self-dual bent sequences. The authors give an efficient algorithm to compute that group.

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Bent sequences / bush-type Hadamard matrices / Hadamard matrices / PUF functions / regular Hadamard matrices

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SHI Minjia , LI Yaya , CHENG Wei , CRNKOVIĆ Dean , KROTOV Denis , SOLÉ Patrick. Self-Dual Hadamard Bent Sequence. Journal of Systems Science and Complexity, 2023, 36(2): 894-908 https://doi.org/10.1007/s11424-023-2276-8

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Funding

This work is supported in part by the National Natural Science Foundation of China under Grant No. 12071001.
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