Re: [boost] Infinite precision integer draft

From: Geoffrey Irving (irving_at_[hidden])
Date: 2006-05-30 12:20:59

On Tue, May 30, 2006 at 05:24:04PM +0200, Carlo Wood wrote:
> On Mon, May 29, 2006 at 05:04:46PM -0700, Geoffrey Irving wrote:
> > For an extremely common example of switching between different moduli,
> > look at this:
> > 
> >     http://mathworld.wolfram.com/ChineseRemainderTheorem.html
> > 
> > For example, RSA uses m_1 = p, m_2 = q prime, where M = pq is the public key.
> 
> I'm not convinced, to me it seems that all variables in those
> cases are just integers. The above page says:
> 
> Let r and s be positive integers which are relatively prime
> 
> <snip>
> 
>   Z<r> x = N;
>   Z<s> y = N;

As pointed out by someone else already, what if r = 2^30402457-1?

More fundamentally, encryption usually fails if the secret prime numbers are
hard coded into the encryption code as template arguments.  Unless you want
the encryption code to recompile itself whenever it generates a new random
key, that is.

Geoffrey