An Evidence-Driven Classification Framework forShor’s Algorithm: Implementations,Optimizations, and Cryptographic Impact

Shor’s algorithm remains the most important example of quantum advantage,with significant implications for integer factorization and public-key cryptog-raphy. Despite its well-established theoretical foundations, practical realizationis constrained by circuit depth, quantum arithmetic overhead, noise sensitivity,verification complexity, and fault-tolerance requirements. This paper introducesQ Class, an evolutionary-applicable, function-oriented, evidence-based classifi-cation system for assessing the practical evolution, maturity, and cryptographicrelevance of Shor’s algorithm. The framework is validated through a systematicmapping of literature published since Shor’s original 1994 paper. It offers thepractical evolution of Shor’s algorithm a new direction rather than algorithmicnovelty, highlighting persistent bottlenecks and research priorities.