Re: factoring integers on a classical computer in polynomial-time

From: Pubkeybreaker (Robert_silverman_at_raytheon.com)
Date: 03/24/05 

Date: 24 Mar 2005 09:29:08 -0800

May I suggest that you go learn some number theory?

Your algorithm does not work.

(1) You fail to show that a solution for alpha, beta even exists in
step 2.
(I will give a hint: a solution might not exist, see below)

(2) You fail to show that your method even halts. i.e. that criterion
(3) is ever satisfied.
I can not see where condition (4) will ever be satisfied.

Take N = 91. Set a = b = n = 1.

We have 91 = (2 alpha + 1)(2 beta + 1) mod 4, whence alpha = 1 and
beta = 0.
(3) and (4) are not satisfied, so we now take a = 3 and b = 1 and n =
2 giving

91 = (4 alpha + 3)(4 beta + 1) mod 8, whence alpha = 0 and beta = 0 by
inspection.
(3) and (4) are still not satisfied so we get a = 3 and b = 1 and n = 3
 giving

91 = (8 alpha +3)(8 beta + 1) mod 16 and OOOPS! no solution
exists.

What is it with people??? Why don't they even try trivial testing of
their 'fantasy method'
before posting? Is it ego?

Mr. Feinstein: I do not know you, but I have read many of your posts.
You lack
understanding of elementary number theory and elementary analysis of
algorithms.
GO ACQUIRE IT. Try reading some books. I can recommend some, if you
like.

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