[Resource Topic] 2021/984: On the Use of the Legendre Symbol in Symmetric Cipher Design

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On the Use of the Legendre Symbol in Symmetric Cipher Design

Authors: Alan Szepieniec


This paper proposes the use of Legendre symbols as component gates in the design of ciphers tailored for use in cryptographic proof systems. Legendre symbols correspond to high-degree maps, but can be evaluated much faster. As a result, a cipher that uses Legendre symbols can offer the same security as one that uses high-degree maps but without incurring the penalty of a comparatively slow evaluation time. After discussing the design considerations induced by the use of Legendre symbol gates, we present a concrete design that follows this strategy, along with an elaborate security analysis thereof. This cipher is called Grendel.

ePrint: https://eprint.iacr.org/2021/984

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