Cryptography: How Mathematics Protects Our Digital World

Cryptography: How Mathematics Protects Our Digital World takes you from secret writing and Enigma to the systems behind secure connections, private messages and digital signatures. It begins with familiar questions and builds the knowledge needed to understand modern methods.

You do not need previous knowledge of cryptography. Mathematical ideas are introduced gradually, with clear definitions, small worked examples and explanations of each formula and its symbols. Programming examples are optional.

Across 20 chapters, you will explore:

• Bits, prime numbers, remainders, probability and randomness.
• AES, ChaCha20 and authenticated encryption.
• Hashes, passwords and key derivation.
• Public keys, RSA, ElGamal and elliptic curves.
• Digital signatures, certificates and key management.
• TLS 1.3, secure messaging and common implementation failures.
• Software testing, quantum computing and post-quantum cryptography.
• Methods for proving and computing with private data.

Diagrams, comparison tables and explained review answers support the main text. Reference sections help you return to mathematical methods and technical terms, while notes and sources let you explore the original research.

The book explains both the strengths and the limits of cryptographic methods. You will learn to follow a calculation, identify its assumptions and understand why a sound design still needs careful implementation.

Written for curious beginners, students and readers who want to understand the reasoning behind digital security.