full-disclosure - Re: Rapid integer factorization = end of RSA?

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Date: Thu, 26 Apr 2007 14:07:31 +0400
From: Eugene Chukhlomin <chukh29ru@...oline.su>
To: full-disclosure@...ts.grok.org.uk
Subject: Re: Rapid integer factorization = end of RSA?

>Funny way to pull the -1 out from the parenthesis.
>p * (-q) = p * (-1) * q = p * q * (-1)       (mod pq)
>That is, p * (-q) = 0      (mod pq).

Well, let's proof:
some days ago RSA-640 was factored, therefore I'll use this number for proofing.
N = p*q = 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609 
p = 1634733645809253848443133883865090859841783670033092312181110852389333100104508151212118167511579
q = 1900871281664822113126851573935413975471896789968515493666638539088027103802104498957191261465571

Hence p*(-q) = p*(N-q), we have: 
1634733645809253848443133883865090859841783670033092312181110852389333100104508151212118167511579*(3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609-1900871281664822113126851573935413975471896789968515493666638539088027103802104498957191261465571) = 5079801149330465928652035530544913704964519649664113022948507643221268839586387905945718488562426349551024378408981587404238854112680081565808050803367178098655476230508056302202082021498932996241380749611265431048278537997959344921052965979997472486960464297533557254211807262177876539002;

and, by my gypothesis:
p*(-q) = p*q *(p-1) = p*(N-q)
163473364580925384844313388386509085984178363092312181110852389333100104508151212118167511579*1900871281664822113126851573935413975471896789968515493666638539088027103802104498957191261465571*1634733645809253848443133883865090859841783670033092312181110852389333100104508151212118167511578 = 5079801149330465928652035530544913704964519649664113022948507643221268839586387905945718488562426349551024378408981587404238854112680081565808050803367178098655476230508056302202082021498932996241380749611265431048278537997959344921052965979997472486960464297533557254211807262177876539002;
Q.E.D

Any new idea?

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