Abstract

Abstract. In the digital age, cryptography is widely used in various important systems such as financial, military and government ones, medical records etc.
 The life of modern people is closely connected with the cryptography. We send messages via instant messengers without even considering in which way the security of communications and data is ensured. We buy things both online and transfer money with confidence in transaction security. The level of digitization of our society is constantly increasing, and the digital data needs a reliable protection, which makes cryptography a current topic.
 Cryptographic systems ensure our security and the basic properties of information, such as privacy, integrity, availability.
 However, with the beginning of the development of quantum computers, the field of cryptography has developed in a new direction. Quantum cryptography is a science that studies the methods of communication systems protection. It is based on the idea that patterns of quantum physics (physical properties described by the laws of quantum optics, quantum electrodynamics, or quantum field theory) are inviolable. The current state of development and usage of powerful quantum computers, as well as their mathematical and software, is strictly confidential and securely protected. Only clear-cut information about quantum computers and their usage in cryptography is provided.
 NIST has announced an open competition to select quantum-resistant public-key cryptographic algorithms. After the third round, CRYSTALS-KYBER, CRYSTALS Dilithium, FALCON, and SPHINCS+ were proposed to be standardized. NIST has already recommended moving from the sizes of keys and algorithms that provide 80 security bits to the sizes of keys and algorithms that provide 112 or 128 security bits in order to protect against classic attacks.
 Post-quantum cryptography, which with its complexities still requires a more detailed study, challenge science once more. However, it is unknown when the changes will occur and when the quantum era will begin, as well as what consequences they will have. It is only possible to predict how many advantages will have quantum calculations compared to usual, and how different the new quantum models will be from classic ones.

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