In modern times, cryptography has been considered as a branch of both mathematics and computer science, and is tightly related to information security. With the accelerated progress of the Internet and the increase of digital communication, the need for stronger and more effective methods of cryptographic protection has become more pronounced. With the rapid increase in computing power, the potential for breaking cryptographic algorithms also increases. This fact in modern cryptography creates a need for stronger and more advanced cryptographic algorithms. One development direction of modern cryptography is post-quantum cryptography, which can withstand the attacks of quantum computers. In addition to the potential threats to traditional cryptographic techniques, there is also the potential to integrate artificial intelligence tools with the process of developing and implementing cryptographic algorithms. For instance, advanced machine learning algorithms can be used to identify potential vulnerabilities in cryptographic systems and algorithms and improve their security. As technology continues to evolve, new techniques are being developed in the field of cryptography in order to stay one step ahead of new threats. In this paper, the current achievements of modern cryptography are explored and the research perspectives in this field are explained.