Public-Key Cryptography: Code-Based and Knapsack Systems

Modern cryptography relies heavily on complex mathematical problems to secure data against emerging computational threats. This course introduces you to public-key cryptosystems constructed around NP-hard computational problems, providing the groundwork for understanding code-based and lattice-adjacent security concepts. You will gain a thorough conceptual grounding in error-correcting codes, Goppa codes, and the structural mechanics behind classic and post-quantum cryptographic primitives. What you will learn: Understand the core principles of NP-hardness and how hard computational problems enable public-key encryption; Analyze error-correcting linear codes, parity-check matrices, and the hardness of general decoding; Examine the McEliece cryptosystem and how Goppa codes facilitate secure public-key encryption resistant to quantum attacks; Explore the subset sum problem, superincreasing sequences, and the Merkle-Hellman knapsack cryptosystem; Evaluate attack models, vulnerabilities, and modern post-quantum security considerations. The course starts with essential mathematical terminology and foundational definitions before walking step-by-step through algebraic coding theory and cryptosystem implementations. This course is designed for curious learners, computer science students, and software developers interested in cryptography without prior advanced cryptanalysis experience. Start reading today to deepen your understanding of modern and post-quantum cryptographic systems.