Counterexamples for Frobenius primality test
Sergey Khashin
TL;DR
This paper investigates the Frobenius primality test, providing new theoretical insights into its properties and establishing lower bounds, challenging previous overestimations of its error probability.
Contribution
It offers the first rigorous analysis of simple divisors of FPP-numbers and establishes lower bounds for the Frobenius primality test, advancing understanding of its reliability.
Findings
Properties of simple divisors of FPP-numbers proved
Lower bounds for FPP established
Previous error probability assessments are overestimated
Abstract
At present one can not find a single counterexample to even a simplest version of Frobenius primality test. The assessment of probability of the mistake, presented in [I.B. Damgard and G.S.Frandsen, Journal of Cryptology, 2006] is strongly overestimated. In the present paper, the properties of simple divisors of FPP-numbers are proved. The lower bound for FPP are given.
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Taxonomy
TopicsAnalytic Number Theory Research · Coding theory and cryptography · Cryptography and Residue Arithmetic