Integer Factorization By Sieving The Delta
Vishal Mudgal

TL;DR
This paper proposes a novel factorization method based on sieving the difference between prime factors, which could potentially factorize semiprimes in constant time once certain conditions are met, and introduces a new trapdoor function.
Contribution
It introduces a new factorization approach based on sieving the difference of prime factors, avoiding reliance on congruence of squares or special properties of n.
Findings
Proposes a delta sieving factorization method.
Suggests constant-time factorization under specific conditions.
Introduces a new trapdoor encryption function.
Abstract
Let (p < q) and , where p,q are odd integers, then, it is hypothesized that factorizing this composite n will take O(1) time once the steady state value is reached for any in of some observation deck (od) with specific dial settings. We also introduce a new factorization approach by looking for in different sieve zones. Once is found and is already given, one can easily find the factors of this composite n from any one of the following quadratic equations: or . The new factorization approach does not rely on congruence of squares or any special properties of n, p or q and is only based on sieving the . In addition, some other new factorization approaches are also discussed. Finally, a new trapdoor function is presented which…
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Taxonomy
TopicsCoding theory and cryptography · Quantum Computing Algorithms and Architecture · graph theory and CDMA systems
