Number-theoretic algorithms in cryptography

Includes index

Includes bibliography (p. 223-239) and references

Ch. 1. Primality testing and construction of large primes Ch. 2. Factorization of integers with exponential complexity Ch. 3. Factorization of integers with subexponential complexity Ch. 4. Application of elliptic curves to primality testing and factorization of integers Ch. 5. Algorithms for computing discrete logarithm Ch. 6. Factorization of polynomials over finite fields Ch. 7. Reduced lattice bases and their applications Ch. 8. Factorization of polynomials over the field of rational numbers with polynomial complexity Ch. 9. Discrete Fourier transform and its applications Ch. 10. High-precision integer arithmetic Ch. 11. Solving systems of linear equations over finite fields

Algorithmic number theory is a branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. This book describes the various algorithms used in cryptography.