Cryptography made simple

Abstract

The chapters in Part 1 offer a brief introduction to the mathematical foundations: modular arithmetic, groups, finite fields, and probability, primality testing and factoring, discrete logarithms, elliptic curves, and lattices. Part 2 of the book shows how historical ciphers were broken, thus motivating the design of modern cryptosystems since the 1960s, this part also includes a chapter on information-theoretic security. Part 3 covers the core aspects of modern cryptography: the definition of security, modern stream ciphers, block ciphers and modes of operation, hash functions, message authentication codes, and key derivation functions, the "naive" RSA algorithm, public key encryption and signature algorithms, cryptography based on computational complexity, and certificates, key transport and key agreement. Finally, Part 4 addresses advanced prot ocols, where the parties may have different or even conflicting security goals: secret sharing schemes, commitments and oblivious transfer, zero-knowledge proofs, and secure multi-party computation.