Algorithmic Number Theory. Lattices, Number Fields, Curves and Cryptography
Joe Buhler, Peter Stevenhagen · Cambridge University Press eBooks · 2008
1. Solving Pell's equation Hendrik Lenstra 2. Basic algorithms in number theory Joe Buhler and Stan Wagon 3. Elliptic curves Bjorn Poonen 4. The arithmetic of number rings Peter Stevenhagen 5. Fast multiplication and applications Dan Bernstein 6. Primality testing Rene Schoof 7. Smooth numbers: computational number theory and beyond Andrew Granville 8. Smooth numbers and the quadratic sieve Carl Pomerance 9. The number field sieve Peter Stevenhagen 10. Elementary thoughts on discrete logarithms Carl Pomerance 11. The impact of the number field sieve on the discrete logarithm problem in finite fields Oliver Schirokauer 12. Lattices Hendrik Lenstra 13. Reducing lattices to find small-height values of univariate polynomials Dan Bernstein 14. Protecting communications against forgery Dan Bernstein 15. Computing Arakelov class groups Rene Schoof 16. Computational class field theory Henri Cohen and Peter Stevenhagen 17. Zeta functions over finite fields Daqing Wan 18. Counting points on varieties over finite fields Alan Lauder and Daqing Wan 19. How to get your hands on modular forms using modular symbols William Stein 20. Congruent number problems in dimension one and two Jaap Top and Noriko Yui.