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 2018-07-05, 21:05 #1 bhelmes     Mar 2016 39710 Posts biquadratic complex function and possible factorisation A peaceful night for all persons, if i have a biquadratic function for a complex vector such as f(v)=vMv mod f where v=a+bi with a,b element N and M a 2*2 Matrix with l,m,m,o element N and the resulting vector is calculated by modulo f for a and b, where f is element N and not prime, are there special points for a and b which are suitable for a factorisation ? I suppose M refer to an irrducible polynomial over N. For the special case M=E where E is the neutral Element f(a,b)=a²-b² if = 0 then a factorisation is certainly possible Are there other possibilities ? Greetings from the complex lattice Bernhard
 2018-08-08, 20:19 #2 bhelmes     Mar 2016 6158 Posts A peaceful evening for all persons, i implemented some algorithms with a combination of bilinear forms and a pollard rho algorithm. 40 digit numbers are possible to factorize for me, but not more. I checked parallel 8 curves and looked up for some results. If i use a small cluster with 30 cores, is there a real chance to increase the probability for factoring higher numbers ? Greetings from the factoring algorithms, which can be really nice Bernhard

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