Mathematical Cryptology

Based on Elementary Number Theory and Essential Numerical Algorithms

Dimitrios Poulakis

• Publisher: De Gruyter
• Year: 2026
• eBook ISBN: 9783112227534
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

This text offers a comprehensive introduction to cryptology, based on elementary number theory and essential numerical algorithms. It covers core mathematical topics —number theory, algebraic structures, matrices, determinants, and polynomials —through their use in cryptography. Symmetric-key cryptography and practical techniques are introduced, followed by algorithms and computational complexity. Public-key systems based on integer factorization and discrete logarithms, as well as hash functions and digital signatures, are discussed. Advanced topics include elliptic curve and multivariate polynomial cryptography, primality testing, and integer factorization are also explored. The book is self-contained, with all necessary proofs, theory, and tools to analyze cryptographic security and attacks.

Table of contents

• Title Page
• Copyright
• Contents
• Frontmatter
• Dedication
• Contents
• Notation
• 1 Fundamental Concepts – Historical Ciphers
• 2 Elements of Number Theory
• 3 Groups, Rings, and Matrices
• 4 Univariate Polynomials
• 5 Stream Ciphers
• 6 Block Ciphers
• 7 Numerical Algorithms
• 8 Integer Factorization and Cryptography
• 9 Discrete Logarithm and Cryptography
• 10 Hash Functions
• 11 Digital Signatures
• 12 Multivariate Polynomials and Curves
• 13 Elliptic Curve Cryptography
• 14 Primality Testing
• 15 Algorithms for Integer Factorization
• 16 Algorithms for Discrete Logarithm
• Index
• Subject Index