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Old 2018-07-05, 21:05   #1
bhelmes's Avatar
Mar 2016

32·41 Posts
Default 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
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Old 2018-08-08, 20:19   #2
bhelmes's Avatar
Mar 2016

32×41 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

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