Mostly, I'm mystified as to the application for this. Scott can force Alice to generate a public key pair, but he can't force her never to use it for another purpose, or even ensure that she doesn't use it for some other purpose between the time she generates it at Scott's demand and uses it for Scott's application. And Scott can't discover whether Alice is using a bad random number generator, which depending on the application might be another way to cheat or be insecure.
But not worrying about that for now (despite my anecdote about how one should know what problem you're solving before trying to come up with a solution), I was going to suggest something similar to what David Wagner suggested, but with Scott telling Alice the modulus size and the *high* order 64 bits (with the top bit constrained to be 1). I can see how Alice can easily generate two primes whose product will have that *high* order part, but it seems hard to generate an RSA modulus with a specific *low* order 64 bits. As for Jack Lloyd's solution...I was also thinking of something based on Diffie-Hellman, and was going to suggest that Scott supply the prime p. I'd have had Scott generate p (as with PDM). If Alice also needs assurance that p isn't funny somehow, then she could specify the high order bits of p to Scott, or Scott could provide the seed to Alice from which he generated p. But that would force Alice to do a lot of work. I sort of like making it cheap for Alice, and making Scott, who is making Alice jump through hoops for no discernible reason, do a lot of work. Radia "David Wagner" <[EMAIL PROTECTED]> wrote: >Jeroen C. van Gelderen wrote: >>Here is a scenario: Scott wants Alice to generate a key pair after >>which he will receive Alice's public key. At the same time, Scott wants >>to make sure that this key pair is newly generated (has not been used >>before). > >You might be able to have Scott specify a 64-bit string, and then ask >Alice to come up with a RSA public key that has this string as its low >64 bits. I believe it is straightforward to modify the RSA key generation >algorithm to generate keypairs of the desired form. > >If you're worried about the security of allowing Scott to choose the >low bits of Alice's public key, you could have Scott and Alice perform >a joint coin-flipping protocol to select a random 64-bit string that >neither can control, then proceed as before. > >I haven't worked out all the details, but something like this might >be workable. > >In practice, you might also want to confirm that Alice knows her private >key (i.e., has ability to decrypt messages encrypted under her public >key). > >--------------------------------------------------------------------- >The Cryptography Mailing List >Unsubscribe by sending "unsubscribe cryptography" to >[EMAIL PROTECTED] --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to [EMAIL PROTECTED]
