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An Efficient Modular Exponentiation Proof Scheme. (arXiv:2209.15623v1 [cs.CR])
Oct. 3, 2022, 1:20 a.m. | Darren Li, Yves Gallot
cs.CR updates on arXiv.org arxiv.org
We present an efficient proof scheme for any instance of left-to-right
modular exponentiation, used in the Fermat probable prime test. Specifically,
we show that for any $(a,n,r,m)$ the claim $a^n\equiv r\pmod m$ can be proven
and verified with an overhead negligible compared to the computational cost of
the exponentiation. Our work generalizes the Gerbicz-Pietrzak double check
scheme, greatly improving the efficiency of general probabilistic primality
tests in distributed searches for primes such as PrimeGrid.
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