Number-theoretic expressions obtained through analogy between prime factorization and optical interferometry

2011/11/30 by Gabriel Seiden
Computer Science · Mathematics · Physics and Astronomy · #Chaos-based Image/Signal Encryption #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #math-ph #math.MP

paper · pdf · doi:10.1103/physreva.85.043842

arxiv created 2012/01/03 · openalex publication_date 2012/04/26 · arxiv updated 2014/02/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Prime factorization is an outstanding problem in arithmetic with important consequences in a variety of fields, most notably cryptography. Here I employ the intriguing analogy between prime factorization and optical interferometry in order to obtain analytic expressions for closely related functions, including the number of distinct prime factors.

Citations

• Factorization of Numbers with the Temporal Talbot Effect: Optical Implementation by a Sequence of Shaped Ultrashort Pulses
• A method for obtaining digital signatures and public-key cryptosystems