Modern and quantum encryption algorithms

This thesis integrates modern and quantum cryptographic approaches within a common mathematical framework and comparatively examines the security paradigms of both fields. In the classical part, historical schemes such as Caesar and substitution ciphers are analyzed not merely as introductory examples but within the context of modular arithmetic and group actions. Building upon these foundations, the Feistel architecture, the notions of pseudorandom permutations and functions, and reduction-based proof techniques are discussed. Furthermore, the measurability of design principles such as nonlinearity, diffusion, and confusion is addressed. Specifically, in the case of the Data Encryption Standard, S-boxes are evaluated through quantitative measures such as algebraic normal form and differential probability. Thus, the fundamental assumptions underlying the relationship between security and computational hardness are clarified within a systematic logical framework. In the quantum part, the security framework based on physical laws is presented. The BB84 and E91 protocols are examined side by side: BB84 relying on basis choice and measurement statistics, and E91 on Bell-type correlations. The necessity of simultaneously minimizing correctness and secrecy errors is emphasized, while potential eavesdropping scenarios are bounded using observed error rates and suitable Bell tests for E91. Under finite-size sampling conditions, smooth inequalities are employed to determine the extent to which the length of the secret key must be reduced. In the applied section, a Python-based simulation of BB84 communication is developed. The model accounts for channel loss, depolarization, detector efficiency, dark counts, basis mismatch, and intercept–resend eavesdropping strategies. Following an end-to-end workflow of parameter estimation, error correction leakage, and privacy amplification, both the sifted key rate and effective leakage sizes are obtained. Sensitivity analyses reveal that even small increases in error rate disproportionately reduce key generation, while the secure operating region rapidly contracts into a narrow "operational window" defined by distance, noise, and detector parameters. The results demonstrate that positive key generation remains sustainable under low-noise and medium-distance conditions, whereas increasing either noise or distance quickly undermines security.