A compact navigation directory for the BTT Computational Number Theory series, covering algorithms, congruences, primes, factorisation, discrete logarithms, algebraic number theory and computational arithmetic.
44 preferred indexed guide routes are listed here as of 25 September 2026. 1 exact-title alternate copy remains live but noindex and is intentionally not promoted in this directory. The individual guides remain the topic owners.
Guides 1–10
- Computational Number Theory 1: Euclidean Algorithm, Bézout Identity and Modular Inverses
- Computational Number Theory 2: Fast Modular Exponentiation and the Chinese Remainder Theorem
- Computational Number Theory 3: Prime Sieves, Probable Primes and Primality Testing
- Computational Number Theory 4: Integer Factorisation, Pollard Methods and Computational Limits
- Computational Number Theory 5: Quadratic Residues, Legendre & Jacobi Symbols and Tonelli–Shanks
- Computational Number Theory 6: Discrete Logarithms, Baby-Step Giant-Step and Pollard Rho
- Computational Number Theory 7: Continued Fractions, Convergents and Pell Equations
- Computational Number Theory 8: Elliptic Curves over Finite Fields, Point Arithmetic and Scalar Multiplication
- Computational Number Theory 9: Finite Fields, Polynomial Arithmetic and Exact Computation
- Computational Number Theory 10: Polynomial Factorisation over Finite Fields
Guides 11–20
- Computational Number Theory 11: p-Adic Valuations, Hensel Lifting and Prime-Power Precision
- Computational Number Theory 12: Arithmetic Functions, Möbius Inversion and Fast Sieves
- Computational Number Theory 13: Montgomery & Barrett Reduction and Fast Modular Multiplication
- Computational Number Theory 14: Fast Integer Multiplication, FFT/NTT and Convolution
- Computational Number Theory 15: Integer Lattices, Gram–Schmidt and LLL Reduction
- Computational Number Theory 16: Algebraic Number Fields, Ideals, Norms and Computational Arithmetic
- Computational Number Theory 17: Binary Quadratic Forms, Reduction, Composition and Class Groups
- Computational Number Theory 18: Smith & Hermite Normal Forms, Integer Modules and Exact Lattice Arithmetic
- Computational Number Theory 19: Dirichlet Unit Theorem, Regulators and Logarithmic Unit Lattices
- Computational Number Theory 20: Class Group Algorithms, Minkowski Bounds, Relation Matrices and Principal Ideal Tests
Guides 21–30
- Computational Number Theory 21: Elliptic Curve Method (ECM) for Integer Factorisation
- Computational Number Theory 22: Quadratic Sieve, Factor Bases, Smooth Relations and Linear Algebra
- Computational Number Theory 23: Number Field Sieve, Polynomial Selection, Sieving and Square Roots
- Computational Number Theory 24: Elliptic Curve Primality Proving (ECPP) and Verifiable Prime Certificates
- Computational Number Theory 25: Pohlig–Hellman, Subgroup Decomposition and CRT Reconstruction
- Computational Number Theory 26: Pollard Rho for Discrete Logarithms, Collision Equations and Parallel Search
- Computational Number Theory 27: Index Calculus, Factor Bases, Relation Collection and Individual Logarithms
- Computational Number Theory 28: Number Field Sieve for Discrete Logarithms, Virtual Logs and Descent
- Computational Number Theory 29: Primitive Roots, Multiplicative Orders, Carmichael λ and Cyclotomic Polynomials
- Computational Number Theory 30: Gaussian Integers, Euclidean GCD and Sums of Two Squares
Guides 31–40
- Computational Number Theory 31: Cornacchia’s Algorithm, Norm Equations and Quadratic-Form Representations
- Computational Number Theory 32: Higher Power Residues, Character Sums, Jacobi Sums and Cyclotomic Arithmetic
- Computational Number Theory 33: Schoof’s Algorithm, Frobenius Traces and Elliptic-Curve Point Counting
- Computational Number Theory 34: Schoof–Elkies–Atkin, Elkies/Atkin Primes and Modular Polynomials
- Computational Number Theory 35: Elliptic-Curve Isogenies, Vélu Formulas and Isogeny Graphs
- Computational Number Theory 36: Complex Multiplication, Hilbert Class Polynomials and CM Curve Construction
- Computational Number Theory 37: Integral Bases, Discriminants, Orders and Maximal Orders
- Computational Number Theory 38: Prime-Ideal Decomposition, Ramification, Residue Degrees and Dedekind Factorisation
- Computational Number Theory 39: Local Fields, Completions, p-Adic Extensions and Ramification
- Computational Number Theory 40: S-Units, Norm Equations, Thue Equations and Lattice Reduction
Guides 41–50
- Computational Number Theory 41: Ray Class Groups, Moduli, Congruence Conditions and Generalised Ideal Classes
- Computational Number Theory 42: Computational Class Field Theory, Artin Maps and Abelian Extensions
- Computational Number Theory 43: p-Adic Logarithms, Local Unit Groups and p-Adic Regulators
- Computational Number Theory 44: PSLQ, Algebraic Number Recognition and Minimal-Polynomial Reconstruction
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