question about rsa encryption

Pete Chown Pete.Chown at
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...


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