Affiliation:
1. School of Sciences and Humanities, Nazarbayev University , 53 Kabanbay Batyr , Nur-Sultan , Kazakhstan
Abstract
Abstract
We introduce a new approach to (deterministic) integer factorisation, which could be described in the cryptographically fashionable term of “factoring with hints”: we prove that, for any ϵ > 0, given the knowledge of the factorisations of O(N
1/3+ϵ
) terms surrounding N = pq product of two large primes, we can recover deterministically p and q in O(N
1/3+ϵ
) bit operations. This shows that the factorisations of close integers are non trivially related and that consequently one can expect more results along this line of thought.
Subject
Applied Mathematics,Computational Mathematics,Computer Science Applications
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