A key use case of factorization in quantum computing is its application in cryptography, particularly in breaking widely used encryption schemes like RSA. Quantum computers, using algorithms such as Shor's algorithm, can factor large composite numbers exponentially faster than classical computers. This capability threatens current cryptographic systems that rely on the difficulty of factoring large numbers to secure data, such as RSA encryption, which bases its security on the computational hardness of prime factorization

. Shor's algorithm exploits quantum principles like superposition and entanglement to efficiently find the prime factors of large integers, which classical algorithms struggle to do within a practical timeframe. This quantum speedup could allow quantum computers to decrypt data protected by conventional encryption methods, potentially compromising secure communications, digital transactions, and data privacy globally

. Beyond breaking RSA, factorization via quantum computing also impacts other cryptographic protocols based on discrete logarithms and related mathematical problems. This has spurred research into post-quantum cryptography, aiming to develop encryption methods resistant to quantum attacks

. In summary, the primary use case of factorization in quantum computing is to enable rapid prime factorization that can break classical encryption schemes, thereby revolutionizing cryptography and prompting the development of new security standards for the quantum era.