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31 lines
1.1 KiB
31 lines
1.1 KiB
- polynomial division and gcd
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- polynomial documentation
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7. add combinatorial, linear algebra, factorization, polynomial functions
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as in SAC-2.
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7. finite fields, e.g.
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- gf256_log_2, gf256_antilog_2, gf256_power_of_2, gf256_add, gf256_minus,
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gf256_subtract, gf256_mul, gf256_inv, gf256_div, gf256_product, gf256_exp,
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gf256_term, gfmul, gfadd, gfinv, gfexp.
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more polynomial operations:
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x(), power, >>, <<, division, scalmult, content, primitivepart,
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gcd, xgcd, no_of_real_roots, factorization.
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modular polynomials: powmod etc.
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7. chinese remainder algorithm, maybe Hensel-lifting as in Magnum.
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8. factor and primality testing for small integers
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8. primality test in Z:
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+ polynomials cl_MUP_MI, cl_MUP_I
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use integer FFT for multiplication in cl_UP_MI and cl_MUP_MI
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+ - Pollard rho
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+ - complex values of j()
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- Hilbert polynomial for j() 7.6.1
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+ roots of polynomials mod N 1.6.1
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+ - elliptic curves, Jacobi representation
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- m.P on elliptic curve
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+ Atkin's algorithm
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10. factoring in Z:
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- small prime table,
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- Pollard rho,
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- multiple polynomial quadratic sieve
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Document the timing class
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