Cryptographic Foundations

Foundations of Modern Cryptography is a graduate-level textbook that introduces students and working engineers to the mathematics and practice of modern cryptography, from classical ciphers and security definitions through symmetric primitives (block ciphers, modes, hash functions, MACs) to public-key cryptography (RSA, elliptic curves, digital signatures, key exchange, PKI), with post-quantum cryptography (ML-KEM, ML-DSA, SLH-DSA) integrated throughout the public-key chapters rather than confined to a separate section. It pairs precise security definitions and proofs with 667 graded exercises and a runnable Python/SageMath cookbook (Appendix B), bridging the gap between theory-first texts (Katz–Lindell, Boneh–Shoup) and engineering-first texts (Schneier, Aumasson). All historical attributions, standard numbers, and quoted results have been audited against primary sources.