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25 years ago
  1. Algorithms:
  2. Niels Moeller's subquadratic GCD
  3. - polynomial division and gcd
  4. - polynomial documentation
  5. 7. add combinatorial, linear algebra, factorization, polynomial functions
  6. as in SAC-2.
  7. 7. finite fields, e.g.
  8. - gf256_log_2, gf256_antilog_2, gf256_power_of_2, gf256_add, gf256_minus,
  9. gf256_subtract, gf256_mul, gf256_inv, gf256_div, gf256_product, gf256_exp,
  10. gf256_term, gfmul, gfadd, gfinv, gfexp.
  11. more polynomial operations:
  12. x(), power, >>, <<, division, scalmult, content, primitivepart,
  13. gcd, xgcd, no_of_real_roots, factorization.
  14. modular polynomials: powmod etc.
  15. 7. chinese remainder algorithm, maybe Hensel-lifting as in Magnum.
  16. 8. factor and primality testing for small integers
  17. 8. primality test in Z:
  18. + polynomials cl_MUP_MI, cl_MUP_I
  19. use integer FFT for multiplication in cl_UP_MI and cl_MUP_MI
  20. + - Pollard rho
  21. + - complex values of j()
  22. - Hilbert polynomial for j() 7.6.1
  23. + roots of polynomials mod N 1.6.1
  24. + - elliptic curves, Jacobi representation
  25. - m.P on elliptic curve
  26. + Atkin's algorithm
  27. 10. factoring in Z:
  28. - small prime table,
  29. - Pollard rho,
  30. - multiple polynomial quadratic sieve
  31. Document the timing class