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Elements of Cryptanalysis: From Al-Kindi to Post-Quantum Standards

Part I: Foundations of Cryptanalysis

Chapter 1: Introduction to Cryptanalysis
Chapter 1: Introduction to Cryptanalysis (SageMath)
Chapter 2: Permutations and Substitution Ciphers
Chapter 2: Permutations and Substitution Ciphers (SageMath)
Chapter 3: Frequency Analysis
Chapter 3: Frequency Analysis (SageMath)

Part II: Classical Polyalphabetic Ciphers

Chapter 4: Monoalphabetic Cryptanalysis
Chapter 4: Monoalphabetic Cryptanalysis (SageMath)
Chapter 5: The Vigenère Cipher and Kasiski Examination
Chapter 5: The Vigenère Cipher and Kasiski Examination (SageMath)
Chapter 6: Index of Coincidence
Chapter 6: Index of Coincidence (SageMath)
Cracking Challenges (SageMath)

Part III: Polygraphic Ciphers

Chapter 7: The Hill Cipher
Chapter 7: The Hill Cipher (SageMath)
Chapter 8: The Playfair Cipher
Chapter 8: The Playfair Cipher (SageMath)
Chapter 9: Automated Cryptanalysis – Hill Climbing with N-grams
Chapter 9: Automated Cryptanalysis (SageMath)

Part IV: The Enigma Machine

Chapter 10: Enigma – Design and Electromechanical Operation
Chapter 11: The Polish Codebreakers: Rejewski’s Mathematical Attack
Chapter 11b: The Zygalski Sheet Method
Chapter 12: Bletchley Park and the Bombe

Part V: Information Theory and Block Cipher Design

Chapter 13 — Shannon’s Theory of Secrecy Systems
Chapter 14: Block Cipher Design Principles
Chapter 14: Block Cipher
Chapter 15 — The Data Encryption Standard
Chapter 15: The Data Encryption Standard (SageMath)

Part VI: Linear Cryptanalysis

Chapter 16: Foundations of Linear Cryptanalysis
Chapter 16: Linear Cryptanalysis Foundations (SageMath)
Chapter 17: Linear Approximation Tables and Trail Construction
Chapter 18: Breaking an SPN with Linear Cryptanalysis

Part VII: Differential Cryptanalysis

Chapter 19 — Foundations of Differential Cryptanalysis
Chapter 19: Differential Cryptanalysis Foundations (SageMath)
Chapter 20 – Difference Distribution and Differential Trails
Chapter 21: Breaking an SPN with Differential Cryptanalysis

Part VIII: The Advanced Encryption Standard

Chapter 22: Finite Field Arithmetic in GF(2\(^8\))
Chapter 22: Finite Fields and GF(2^8) (SageMath)
Chapter 23: The AES (Rijndael) Design
Chapter 23: AES Design and Implementation (SageMath)
Chapter 24 — AES Security and the Wide Trail Strategy

Part IX: RSA and Integer Factorization

Chapter 25 — The RSA Cryptosystem
Chapter 25: The RSA Cryptosystem (SageMath)
Chapter 26: Attacks on RSA
Chapter 27: Integer Factoring Algorithms

Part X: Diffie-Hellman and Discrete Logarithms

Chapter 28: Diffie-Hellman Key Exchange and the Discrete Logarithm Problem
Chapter 29: The ElGamal Cryptosystem
Chapter 29: The ElGamal Cryptosystem (SageMath)
Chapter 30: Index Calculus
Chapter 30: The Index Calculus Method (SageMath)

Part XI: Elliptic Curve Cryptography

Chapter 31: Elliptic Curves and the Group Law
Chapter 31: Elliptic Curves and the Group Law (SageMath)
Chapter 32: Structure of Point Groups on Elliptic Curves
Chapter 32: Point Groups on Elliptic Curves (SageMath)
Chapter 33: ECC in Practice — ECDH, ECDSA, and Attacks
Chapter 33: Elliptic Curve Cryptography in Practice (SageMath)

Part XII: Algebraic Cryptanalysis

Chapter 34 — Gröbner Bases and Algebraic Foundations
Chapter 34: Gröbner Bases for Cryptanalysis (SageMath)
Chapter 35: Algebraic Modeling of S-Boxes
Chapter 35: Algebraic Analysis of S-Boxes (SageMath)
Chapter 36: Algebraic Attacks on Stream and Block Ciphers

Part XIII: The Quantum Threat

Chapter 37: Quantum Computing Foundations for Cryptanalysis
Chapter 38 — Shor’s Algorithm for Factoring and Discrete Logarithms
Chapter 39 — Grover’s Search Algorithm

Part XIV: Lattice-Based Cryptography

Chapter 40: Lattice Problems — SVP, CVP, and LWE
Chapter 41: ML-KEM (Kyber) – Design and Implementation
Chapter 42: Attacks on Lattice-Based Schemes

Part XV: Code-Based Cryptography and Frontiers

Chapter 43 — Code-Based Cryptography: McEliece and Goppa Codes
Chapter 44: NIST Post-Quantum Cryptography Standards
Chapter 45: Synthesis — From Al-Kindi to Post-Quantum
Appendix: Annotated Bibliography

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By Bartosz Naskręcki

© Copyright 2026 Bartosz Naskręcki (co-generated with Claude).