Analyze Shor Algorithm Optimization Trends and Suggest Optimization Directions

Quantum computers leverage the principles of quantum mechanics to solve complex problems beyond the capabilities of classical computers, such as prime factorization, which poses a significant threat to cryptographic algorithms like RSA and ECC. Although current quantum resources are insufficient for effective decryption, ongoing research focuses on optimizing Shor's algorithm to overcome these limitations. Shor's algorithm, a quantum algorithm designed for efficient integer factorization, exploits quantum parallelism and entanglement to perform prime factorization exponentially faster than classical algorithms. This paper reviews recent trends in Shor algorithm optimization, particularly in enhancing the efficiency of ripple-carry operators and the Karatsuba algorithm in multiplication and proposes a multiplication method that applies the Strassen algorithm to constant adders