2021/09/20 by Vishal Mudgal, Mudgal, Vishal
Computer Science · Engineering · #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Quantum Computing Algorithms and Architecture #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2109.09599
openalex publication_date 2021/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let n = p ⋅ q (p < q) and Δ= | p-q |, 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 Δ in zone0 of some observation deck (od) with specific dial settings. We also introduce a new factorization approach by looking for Δ in different Δ sieve zones. Once Δ is found and n is already given, one can easily find the factors of this composite n from any one of the following quadratic equations: p2 + pΔ-n = 0 or q2 -qΔ-n = 0. 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 Δ. In addition, some other new factorization approaches are also discussed. Finally, a new trapdoor function is presented which is leveraged to encrypt and decrypt a message with different keys. The most fascinating part of the discovery is how addition is used in factorization of a semiprime number by making it yield the difference of its prime factors.