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As a method to construct provably secure hash functions, the use of families of expander graphs is known. Two approaches are employed in their instantiation: one using theCayley graph Cayley graph of a finite group and the other utilizing the isogeny graphs between supersingular elliptic curves (more generally, superspecial abelian varieties). This paper provides explanations for these constructions and summarizes recent developments.

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Hashing by Walking Over Expanders: A Recipe for Constructing Provably Secure Hash Functions

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  • 出版模式：

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  • 发表日期：

    2026年

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  • Yusuke Aikawa

摘要

As a method to construct provably secure hash functions, the use of families of expander graphs is known. Two approaches are employed in their instantiation: one using theCayley graph Cayley graph of a finite group and the other utilizing the isogeny graphs between supersingular elliptic curves (more generally, superspecial abelian varieties). This paper provides explanations for these constructions and summarizes recent developments.