Postkvantová kryptografie se zaměřením na hashovací algoritmy

This diploma thesis deals with the quantum threat to modern cryptography with a focus on hash functions, primary SHA-256. It begins with an explanation of the fundamental principles of quantum computing, including qubits, superposition, entanglement, interference, and quantum gates. The impact of Shor’s and Grover’s algorithms on asymmetric cryptography (e.g., RSA) and hash functions. The work provides a detailed overview of the construction, security properties, and practical applications of SHA-256 in contemporary systems such as the Bitcoin protocol (proof-of-work, Merkle trees), TLS/HTTPS certificates, eIDAS, software/firmware integrity verification, DevOps pipelines, and antivirus solutions. Special attention is paid to the resilience of hash functions and hash-based signatures against quantum attacks using Grover's algorithm. The final section discusses realistic threat time horizons, risk models, and practical migration strategies to post-quantum cryptography in various areas. The aim of the thesis is to provide a prioritized overview of which systems and domains remain relatively resilient and where early or as soon as possible solutions are needed.