Integer Factorization By Sieving The Delta

arXiv2109.09599MaRDI QIDQ6378092

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Publication date: 20 September 2021

Abstract: Let $n=mathrmp!cdot!mathrmq$ (p < q) and $Delta=lvertp-qvert$, 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 $Delta$ in $zon{e}_0$ of some observation deck (od) with specific dial settings. We also introduce a new factorization approach by looking for $Delta$ in different $Delta$ sieve zones. Once $Delta$ 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: $p^2+pDelta-n=0$ or $q^2-qDelta-n=0$. 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 $Delta$. 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.

Has companion code repository: https://github.com/vdeltasieve/arjun

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