I like Greg Rose's solution best: > There is a fairly standard technique for handling things like this. > > 1. encode your number N into a 133-bit string S > 2. encrypt S with your favourite 133-bit block cipher (see below) > 3. decode S to a number N' > 4. if N' >= 10^40, goto 2 (that is, re-encrypt until it is in range) > 5. N' is your answer.

This is Rich Schroeppel's trick from his Hasty Pudding cipher, a somewhat under-rated AES submission IMO. HPC originated not only this trick, but also the idea of tweakable encryption, which has turned out to be important for disk encryption. The Black-Rogaway paper referenced earlier has a proof of security of this construction. > So, you don't have a 133-bit block cipher lying around? No worries, I'll > sell you one ;-). Actually that is easy too. Take a trustworthy 128-bit > block cipher like AES. To encrypt, do: > > 1. Encrypt the first 128 bits (ECB mode) > 2. Encrypt the last 128 bits (also ECB mode). I didn't understand this at first, but I finally saw that the point is to do the encryptions in-place; step 1 replaces the first 128 bits of the data with the encryption, and similarly for step 2. This is equivalent to doing CBC mode with a fixed IV of 0, and ciphertext stealing for the final partial block of 5 bits. > To decrypt, do decryptions in the reverse order, obviously. It's easy to > see that this is a secure permutation if AES itself is, depending on > your definition of secure; if you add a third step, to re-encrypt the > first 128 bits, it is truly secure. (Without the third step, tweaking a > bit in the first 5 bits will often leave the last 5 unchanged on > decryption, which is clearly a distinguishing attack; the third > encryption makes it an all-or-nothing transform.) I am not familiar with the security proof here, do you have a reference? Or is it an exercise for the student? Hal Finney --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to [EMAIL PROTECTED]