Methodical guidelines for performing laboratory works in the discipline "Cryptography and Post-Quantum Cryptography"

Abstract

The rapid development of information technologies, digital communication systems, cloud infrastructures, and distributed computing environments has significantly increased the importance of cryptographic protection of information. At the same time, the emergence of quantum computing technologies creates fundamentally new challenges for modern cryptography, since a considerable number of classical public-key cryptosystems rely on computational assumptions that may become insecure under large-scale quantum computation. This creates an urgent need for future specialists in software engineering, computer science, and information systems to acquire both theoretical knowledge and practical skills in the field of cryptography and post-quantum cryptographic methods. The discipline "Cryptography and Post-Quantum Cryptography" is aimed at forming fundamental competencies in the analysis of classical cryptographic algorithms, understanding their mathematical foundations, studying quantum computational threats, and mastering modern approaches to cryptographic protection under quantum adversarial models. Particular attention is devoted to the practical evaluation of cryptographic resilience under both classical and quantum attack scenarios. These methodological guidelines provide a structured laboratory course devoted to the study of cryptographic systems, quantum algorithms, cryptographic hash functions, and block ciphers under conditions of increasing relevance of quantum computing technologies. The laboratory works consistently introduce students to the transformation of cryptographic security paradigms caused by the emergence of quantum algorithms capable of significantly reducing the complexity of solving classical cryptographic problems. The first laboratory work is devoted to the analysis of quantum threats to classical public-key cryptosystems, including RSA cryptosystem, ElGamal encryption, Digital Signature Algorithm, and Elliptic Curve Digital Signature Algorithm, focusing on the mathematical vulnerabilities exposed by quantum computation. The second laboratory work examines the influence of quantum algorithms on cryptographic tasks through practical study of Shor's algorithm, which demonstrates polynomial-time factorization and discrete logarithm computation on quantum computers. The third laboratory work continues the study of quantum computational methods through the analysis of Grover's algorithm and its implications for symmetric cryptography and brute-force search complexity reduction. The fourth laboratory work focuses on cryptographic hash functions and their security under classical and quantum computational models, including the study of the Birthday Attack and the quantum Brassard–Høyer–Tapp algorithm, which demonstrates accelerated collision search under quantum computation. The fifth laboratory work is devoted to the analysis of block cipher security and the assessment of their resistance to quantum attacks, with particular emphasis on practical evaluation of symmetric cryptographic strength in post-quantum security models. A distinctive feature of these methodological guidelines is the inclusion of practical software implementations, enabling students to directly observe cryptographic processes, analyze attack complexity, and experimentally compare classical and quantum security assumptions. The appendices include program code for RSA and DSA/ECDSA-like schemes, implementations of Shor’s and Grover’s algorithms, and software models for Even–Mansour constructions together with BHT attack simulations. The completion of these laboratory works contributes to the formation of modern professional competencies in cryptographic analysis, secure system design, understanding of post-quantum migration challenges, and preparation for practical work in cybersecurity-oriented software development under rapidly evolving cryptographic standards.