Singular Manual: PollardRho

| #### D.12.2.21 PollardRho Procedure from library `crypto.lib` (see crypto_lib). Usage: PollardRho(n,k,allFactors); optional: PollardRho(n,k,allFactors,L); L a list of the first k primes Return: a list of factors of n (which could be just n),if allFactors=0 a list of all factors of n ,if allFactors=1 Note: probabilistic rho-algorithm of Pollard to find a factor of n in k loops. Creates a sequence x_i such that (x_i)^2=(x_2i)^2 mod n for some i, computes gcd(x_i-x_2i,n) to find a divisor. To define the sequence choose x,a and define x_n+1=x_n^2+a mod n, x_1=x. If allFactors is 1, it tries to find recursively all prime factors using the Soloway-Strassen test. Example:
    LIB "crypto.lib";
    bigint h=10;
    bigint p=h^30+4;
    PollardRho(p,5000,0);
    ==> [1]:
    ==>    2
    ==> [2]:
    ==>    157
    ==> [3]:
    ==>    18737561
    ==> [4]:
    ==>    84982068258408294013
See also: primefactors.

User manual for Singular version 4.4.1, 2025, generated by texi2html.