question about rsa encryption
Pete Chown
Pete.Chown at skygate.co.uk
Tue Feb 4 05:08:33 EST 2003
Scott G. Kelly wrote:
> I seem to recall reading somewhere that there is some issue with
> directly encrypting data with an RSA public key, perhaps some
> vulnerability, but I can't find any reference after a cursory look.
There are a few different ones, some simple and some complex. First of
all, imagine encrypting 0 or 1. Encryption leaves these numbers
unchanged. Now, if each possible plaintext had equal probability, this
would be extremely unlikely. However, in practice it is likely that
users may want to encrypt small numbers.
Another problem is that RSA encryptions multiply. If r(x) is the
encryption operation, then r(x) r(y) = r(xy). Informally:
r(x) r(y) = (x ** e) (y ** e)
= x * x * x * ... * y * y * y
= xy * xy * ... * xy
= (xy) ** e
= r(xy)
I think there are a few others too...
--
Pete
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