Research Progress on Low-Resource Quantum Algorithms for Integer Factorization

Key Points

• The study aims to advance low-resource quantum algorithms for efficient integer factorization to assess threats to RSA encryption.
• Developed HAIFA, a hybrid decomposition algorithm combining classical reduction and quantum optimization.
• Achieved the first 48-bit integer factorization on quantum hardware, setting a world record.
• Introduced a universal computational framework (STAIF) that reduces theoretical spatial complexity from O(n^3/2) to O(n log n).
• HAIFA demonstrated successful 48-bit integer factorization on quantum hardware, achieving a significant milestone.
• STAIF's theoretical framework allows enhanced computational efficiency, verified experimentally with relevant parameters.