[133399] in cryptography@c2.net mail archive
Re: RSA modulus record
daemon@ATHENA.MIT.EDU (Thierry Moreau)
Wed Sep 17 09:55:47 2008
Date: Wed, 17 Sep 2008 07:16:21 -0500
From: Thierry Moreau <thierry.moreau@connotech.com>
To: "Weger, B.M.M. de" <b.m.m.d.weger@TUE.nl>
CC: cryptography@metzdowd.com
In-Reply-To: <DFA3206A564B80499B87B89B49BCD313038CC99E@EXCHANGE3.campus.tue.nl>
Weger, B.M.M. de wrote:
> Hi,
>
> There's a new biggest known RSA modulus.
> It is (in hexadecimal notation):
>
> FF...(total of 9289166 F's)...FFDFF...(total of 1488985
> F's)...FF800...(total of 9289165 0's)...001
>
> It is guaranteed to be the product of two different large primes,
> and it has more than 80 million bits. Impressive security...
>
But it is trivially factored as (2^43112609-1) * (2^37156667-1)
Factorization based modulus need to be drawn from a pool of numbers
"without special properties", so that their factorization is not
facilitated by special-purpose algorithms. There is ample academic work
aiming to refine "without special properties", and there is also ample
(debated) academic work which assumes that "without special property" is
a reasonable assumption in practice.
The fun part is to reconcile theory and practice, e.g. a decade of RSA
industrial application before retrofitting the probabilistic property in
RSA, while probabilistic cryptosystems has been around in academic work
amost since the early days of published work on PK crypto.
Regards,
- Thierry Moreau
CONNOTECH Experts-conseils inc.
9130 Place de Montgolfier
Montreal, Qc
Canada H2M 2A1
Tel.: (514)385-5691
Fax: (514)385-5900
web site: http://www.connotech.com
e-mail: thierry.moreau@connotech.com
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