Development of Quantum Cryptanalysis Algorithms
Alexei Petrenko, Sergei Petrenko · River Publishers eBooks · 2023
This chapter evaluates the stability of the modern cryptographic algorithms to clarify the tasks of cryptanalysis of asymmetric encryption schemes and digital signature based on factorization and discrete logarithm problems in various algebraic structures in a quantum computing model. It considers the features of modeling quantum cryptanalysis algorithms on a quantum scheme, and shows the differences between these algorithms and classical algorithms. The quantum algorithm is performed by implementing a series of sequential unitary operations. Grover&s;s algorithm provides a quadratic increase in speed, while some other quantum algorithms, for example, the Shor factorization algorithm, give an exponential gain compared to the corresponding classical algorithms. Grover&s;s algorithm is modified into an algorithm for recovering the symmetric encryption key from the message text and ciphertext. The stability of the RSA asymmetric encryption system is based on the super-polynomial computational complexity of factorization of natural numbers. However, there is a quantum algorithm whose complexity is polynomial.