Abstract： In recent years, with the development of quantum computing, quantum algorithms led by Shor′s algorithm have shown a serious threat to the public key cryptography. On the one hand, researchers study the implementation of quantum algorithms on public key cryptography attacks, and on the other hand, they begin to establish post-quantum cryptographic algorithm standards. On this issue, this article firstly introduces several commonly used public-key cryptographic algorithms and some quantum algorithms. Secondly, it focuses on the current research status of public-key cryptographic algorithms attacked by Shor′s algorithm and quantum optimization algorithms, especially the attack implementation of RSA and ECC and the current difficulties in implementation. Finally, combined with the current research progress of public key cryptography attacks under quantum computing and the development of post-quantum cryptography, some suggestions and prospects are made for the future development planning of research institutes.
Key words : public-key cryptography,；RSA,；ECC；Shor algorithm,；quantum optimization algorithm
