The security of RSA algorithm is based on the difficulty of prime factorization, that is, the difficulty of decomposing a large prime into two smaller prime numbers. SHOR algorithm is based on the principle of quantum computing and can crack RSA algorithm in a certain time.

Quantum computer is a computer based on the principle of quantum mechanics, which can handle multiple computing states at the same time and has higher computing power than traditional computers. If quantum computer can be realized and applied to crack RSA algorithm and other cryptographic algorithms, the security of RSA algorithm will be threatened.

In 1994, the proposal of SHOR algorithm causes the security problem of RSA algorithm, because it can crack RSA algorithm in polynomial time. This has caused people's trust in RSA algorithm to decrease and questioned its long-term use.

After that, RSA strengthened the use of longer key length for digital signature and encryption to improve its security and resist the attack of SHOR algorithm, and introduced other digital signature algorithms, such as DSA and ECDSA, to meet the needs of different application scenarios. The long-term security of RSA algorithm is still a problem under study, but it can be improved by using stronger key length and other encryption algorithms.

In order to enhance the security of RSA algorithm, people have been looking for a new encryption algorithm that is more suitable for the operation of quantum computers. At present, some cryptographic algorithms based on quantum computing principles have been proposed, such as lattice-based cryptography and quantum key distribution. These algorithms are proved to be safe under certain conditions. These algorithms pose little threat to future quantum computers. With the development of quantum computing technology, these new cryptographic algorithms may replace RSA algorithm and become one of the most important cryptographic algorithms.

Application of RSA algorithm in practice

RSA algorithm also needs to pay attention to the details of security in practical use, such as the protection and management of keys, the generation of random numbers, the selection of filling methods and so on. If these details are not handled properly, it may provide attackers with exploitable loopholes, thus undermining the security of RSA algorithm.