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Batching Cipolla-Lehmer-Müller's square root algorithm with hashing to elliptic curves
March 24, 2023, 8:54 a.m. |
IACR News www.iacr.org
ePrint Report: Batching Cipolla-Lehmer-Müller's square root algorithm with hashing to elliptic curves
Dmitrii Koshelev
The present article provides a novel hash function $\mathcal{H}$ to any elliptic curve of $j$-invariant $\neq 0, 1728$ over a finite field $\mathbb{F}_{\!q}$ of large characteristic. The unique bottleneck of $\mathcal{H}$ consists in extracting a square root in $\mathbb{F}_{\!q}$ as well as for most hash functions. However, $\mathcal{H}$ is designed in such a way that the root can be found by (Cipolla-Lehmer-)Müller's algorithm in constant time. …
algorithm article elliptic eprint report function functions hash hash function hash functions hashing large novel report root square
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