An Efficient Modular Exponentiation Proof Scheme

09/16/2022

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by   Darren Li, et al.

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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≡ r 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.