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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | Algorithms:
Niels Moeller's subquadratic GCD
- polynomial division and gcd
- polynomial documentation
7. add combinatorial, linear algebra, factorization, polynomial functions
as in SAC-2.
7. finite fields, e.g.
- gf256_log_2, gf256_antilog_2, gf256_power_of_2, gf256_add, gf256_minus,
gf256_subtract, gf256_mul, gf256_inv, gf256_div, gf256_product, gf256_exp,
gf256_term, gfmul, gfadd, gfinv, gfexp.
more polynomial operations:
x(), power, >>, <<, division, scalmult, content, primitivepart,
gcd, xgcd, no_of_real_roots, factorization.
modular polynomials: powmod etc.
7. chinese remainder algorithm, maybe Hensel-lifting as in Magnum.
8. factor and primality testing for small integers
8. primality test in Z:
+ polynomials cl_MUP_MI, cl_MUP_I
use integer FFT for multiplication in cl_UP_MI and cl_MUP_MI
+ - Pollard rho
+ - complex values of j()
- Hilbert polynomial for j() 7.6.1
+ roots of polynomials mod N 1.6.1
+ - elliptic curves, Jacobi representation
- m.P on elliptic curve
+ Atkin's algorithm
10. factoring in Z:
- small prime table,
- Pollard rho,
- multiple polynomial quadratic sieve
Document the timing class
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