Get it peer-reviewed, or go away. On 4/25/07, Eugene Chukhlomin <[EMAIL PROTECTED]> wrote: > Hi list! > I discovered a new method of integer factorization for any precision > numbers, probable it should be an end of RSA era. > Details: > Let N - the ring and N = p*q > Then, (-p) in terms of ring(N) is equal (N-p) > Lemma: > p*(-q)=p*q*(-p) > and respective: > (-p)*q=p*q*(-q) > Proof: > p*(-q)=p*(N-q) - by the data, then > p*(-q)=p*(p*q-q)=p*pq-p*q=p*q*p-p*q=(p-1)*(p*q) > (-p)*q=q*(N-p) - by the data, then > (-p)*q=(p*q-p)*q=p*q*q-p*q=p*q*q-p*q=(q-1)*(p*q) > Q. E. D. > Gypothesis: > Let N = p*q = A1*B1 + A2*B2... + An*Bn > Then exists some subset(A1...An) and respective subset(B1...Bn), which > satisfies for equality: > A1*(-B1)+A2*(-B2)...+An*(-Bn) = p*(-q)=p*q*(p-1) > or > A1*(-B1)+A2*(-B2)...+An*(-Bn) = (-p)*q=p*q*(q-1) > > If found such (A1...An) and (B1...Bn), we can find p or q by dividing > p*(q-1) on p*q: > p*(q-1)=p*q*(p-1) => (p*(q-1))/(p*q)=(p-1) => (p-1)+1 = p > or > (p-1)*q=p*q*(q-1)=>((-p)*q)/(p*q)=(q-1) => (q-1)+1 = q > > Sample: 21 = 3*7 > Let's view a binary representation of this number: 10101 => 2^4 + 2^2 + > 1 => 4*4+2*2+1*1 > Then, we can try to find 7*(-3) in terms of ring(21): > 4*(-4) + 2(-2) + 1*(-1) => 4*(21-4)+2*(21-2)+1*(21-1)=>4*17+2*19+1*20 = > 68+38+20=> > 68+38+20 = 126 = 6*21 > 6+1=7 > This implementation of my gypothesis has very hard complexity (about a > log2(N)! comparations), but exists a short way with fixed complexity for > implementation of hypothesis ("plan B") - but, by ethical reason, I'll > not post it here. > Regards, > Eugene Chukhlomin > > _______________________________________________ > Full-Disclosure - We believe in it. > Charter: http://lists.grok.org.uk/full-disclosure-charter.html > Hosted and sponsored by Secunia - http://secunia.com/ >
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