On Wed, Sep 08, 2004 at 12:44:39PM -0700, Major Variola (ret) wrote: [...]
In an RSA cryptosystem the public exponent is typically low, often 3 or 65537 (for efficiency reasons only a few bits are set; the other constraint is that your message, raised to that power, wraps in your modulus, which makes 65537 a little better). The private exponent is big.
Therefore, traditional encryption is "fast", and decryption is slow; the reverse is that signing is slow, verifying a signature is fast. This can be used to achieve Seth's required "fast to make, slow to verify". To achieve the required "user-controllable", the user gets to set the number of bits in the modulus. One might have to use extraordinarily long moduli (making 4Kbits look puny), depending on the time-scale of "slow" and "fast", but so what, primes are free :-)
and might even be re-used.
If this passes group-muster pass it on..
Can't be too short, less than about a third the size of the modulus you start running into problems [*], which, with the sizes you're suggesting (you would need, what, a 100K+ bit key to do this?) would make signature generation pretty slow too. Easier to do standard RSA and then encrypt the whole thing with a 64 or 80 bit symmetric key. [*] http://crypto.stanford.edu/~dabo/papers/RSA-survey.pdf -Jack