Re: some question about RSA

"Wang" <wangxahq@yahoo.com.cn> wrote in message
news:1137197930.750468.279940@f14g2000cwb.googlegroups.com...
>I have a problem about RSA ,I need some help from this
> group.Does anyone have considered this problem in RSA
> cryptosystem?Suppose two users A and B .A ''s security parameter
> is (eA ,dA,NA),B's security parameter is (eB,dB,NB).Probably this
> equation can exist:(m)^dA mod NA=(m)^dB mod NB.Thus A 's Signature on m
> can be considered as B's Signature on m.Maybe someone consider that
> even this m exist , it has no meaning ,for m must
> be transformed from the PSS padding,but I think this m can help us to
> find A's secret key dA,at least the hardness of find dA from this FAULT
> is easier than just find dA from RSA hard problem. I write some
> programe to verify this ideal,I find this m can exist.Could someone
> give me some advice or criticize on this?Thanks

There is a very small probability that such a pair exists for any chosen
keys, I believe (but have not proven) that the probility is on the order of
1/length(hash) that this pair even exists. Further it will take on the order
of NB/2 work to find the pair, so for a 1024-bit RSA with a 160-bit hash
will be about 2^160000 work to find one such (m,NA,NB) triple. It is far,
far, far beyond the realm of possibility.
                    Joe
Received on Tue Jan 17 16:50:59 2006