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D.12.2.34 factorLenstraECM

Procedure from library crypto.lib (see crypto_lib).

Usage:
factorLenstraECM(N,S,B); optional: factorLenstraECM(N,S,B,d); d+1 the number of loops in the algorithm (default d=0)

Return:
a factor of N or the message no factor found

Note:
- computes a factor of N using Lenstra's ECM factorization
- the idea is that the fact that N is not prime is detected using the operations on the elliptic curve
- is similarly to Pollard's p-1-factorization

Example:
 
LIB "crypto.lib";
list L=primList(1000);
factorLenstraECM(181*32003,L,10,5);
==> 181
bigint h=10;
h=h^30+25;
factorLenstraECM(h,L,4,3);
==> 13