IACR News item: 23 July 2021
Alan Szepieniec
ePrint Report
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.
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.
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