RSA modulus record

[Thierry Moreau]

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.
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