bugtraq - Re: Breaking RSA: Totient indirect factorization

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Message-ID: <TheMailAgent.2f6b4f64426e8a@11e8ec11c4779f1fbea10>
Date: Thu, 15 Nov 2007 10:29:19 +0200 (IST)
From: Alexander Klimov <alserkli@...ox.ru>
To: bugtraq@...urityfocus.com
Subject: Re: Breaking RSA: Totient indirect factorization

On Wed, 14 Nov 2007, gandlf wrote:
> 1) m = p*q            -> RSA modulus
>
> [...]
>
> Algorithm
> ---------
>
> - Repeat "a = a^n mod m" with n from 2 to m, saving all the results
>   in a table until a == 1 (Statement 4).

:-)

So what is the expected running time of your algorithm? For example,
how long it will take on average to factor a 1024-bit modulus?

> Impact
> ------
>
> PKI vendors must change modulus generator algorithms to discard
> totients with lower factors.

You may be interested in ``Are 'Strong' Primes Needed for RSA?'' by
Ron Rivest and Robert Silverman.

-- 
Regards,
ASK