Lecture 3: Mastering Stream Ciphers, Random Numbers & the One-Time Pad 🔐

Professor Paar commences by delineating the three major branches of cryptography, specifically emphasizing symmetric cryptography. He then elaborates on the nature and applications of stream ciphers, highlighting their utilization in modern technologies like cellular communication. Stream ciphers, Paar explains, operate by encrypting individual bits, contrasting them with block ciphers that process data in fixed-size blocks. He emphasizes the inherent simplicity of both encryption and decryption in stream ciphers, utilizing a visual representation to illustrate this concept. Paar proceeds to explore the relationship between stream ciphers and the shift cipher, emphasizing the modular operation that underpins both. The lecture then delves into the critical role of random numbers in robust cryptographic systems, introducing three fundamental types of random number generators: True Random Number Generators (TRNGs), Pseudo-Random Number Generators (PRNGs), and Cryptographically Secure Pseudo-Random Number Generators (CPRNGs). Paar clarifies that TRNGs derive their randomness from physical processes and are considered truly unpredictable. He emphasizes their limitations, namely, their slow generation speeds and the inherent impossibility of recreating their outputs. This leads to a discussion on PRNGs, which generate random numbers deterministically and possess good statistical properties but are deemed unsuitable for cryptographic applications due to their predictability. Paar then transitions to CPRNGs, which are designed to be computationally secure. He defines this concept as the infeasibility of predicting future outputs based on prior outputs using even extensive computational resources. This segment culminates in a detailed examination of the Linear Congruential Generator (LCG), a prevalent PRNG susceptible to cryptanalytic attacks due to its reliance on linear equations with two unknowns. Finally, Professor Paar concludes the lecture with a comprehensive summary of the One Time Pad (OTP), which is considered the gold standard in cryptographic security. He elaborates on its remarkable characteristic of being unconditionally secure, meaning its security is impervious to any computational attack, regardless of computational power. He concludes by highlighting the significant challenge of key distribution that necessitates secure transmission of the OTP key.