Singular Manual: rho

| #### D.12.2.17 rho Procedure from library `crypto.lib` (see crypto_lib). Usage: rho(b,y,p); Return: the discrete logarithm x=log_b(y): b^x=y mod p Note: Pollard's rho: choose random f_0 in 0,...,p-2 ,e_0=0, define x_0=b^f_0, define x_i=y^e_i*b^f_i as below. For i large enough there is i with x_(i/2)=x_i. Let s:=e_(i/2)-e_i mod p-1 and t:=f_i-f_(i/2) mod p-1, d=gcd(s,p-1)=u*s+v*(p-1) then x=tu/d +j*(p-1)/d for some j (to be found by trying) Example:
    LIB "crypto.lib";
    bigint b=2;
    bigint y=10;
    bigint p=101;
    rho(b,y,p);
    ==> 25

User manual for Singular version 4.3.2, 2023, generated by texi2html.