Problem of stability of modern cryptosystems against the background of the emergence of quantum computers

Abstract

Every year, the production of quantum computers is becoming more productive and cheaper - for example, “The Tsuchongzi” computer uses 56 qubits and is able to solve problems that highlight the possibility of quantum acceleration within a few hours, while classical supercomputers require tens of thousands of years. Currently, IBM allows any Internet user to remotely connect and work on a real quantum computer, albeit with a power of several qubits. Modern cryptography is based on the fact that it is difficult to carry out factorization of integers or discrete logarithm by classical algorithms. But with the use of Shor's algorithm on a quantum computer, these difficulties are easily bypassed. Some of the most popular cryptographic systems - RSA (integer factorization), DH (discrete logarithm), and ECDSA (elliptic curves over finite fields) - will no longer be a reliable tool for data encryption with the advent of productive quantum computers. In this article, post-quantum cryptographic systems are studied and compared with the classical RSA system.