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Eurocrypt '95


DDDU/Vol 2 No 8 August 95

Eurocrypt '95 was held a few weeks ago in St. Malo, in Brittany on the northern coast of France. This was the most international Eurocrypt ever, with over 350 participants from countries such as Russia, Rumania, Brazil, South Africa, Bulgaria, Singapore, and the Czech Republic. It was a great conference in a beautiful location (with more wine than you normally see at cryptography conferences).

The 33 papers presented were generally of high quality, although there were no major revelations. From my perspective, the two most clever ideas came from the rump session. (Rump sessions are reserved for unique ideas and works in progress. This year, there were 24 talks of 5 minutes each.)

The first clever idea is from Adi Shamir, one of the inventors of RSA. In RSA, the modulus is n=pq, with public exponent e and private exponent d. Shamir observed that if the receiver knows that the message to be encrypted is smaller than p, then the recipient only needs to decrypt mod p. In mathematical language, if the plaintext is x<p, then the ciphertext is c=xe mod n. Decryption is simply x = cd mod p.

Shamir's idea applies to especially paranoid users who want to use enormous moduli - 5000 bits, for example. Factoring such a large modulus is impossible with today's technology, but encryption and decryption are slow if p and q are of equal size. However, if p is 500 bits long and q is 4500 bits long, then the best current factoring algorithms - the quadratic sieve and the number field sieve - don't work any faster. But if x is limited to 500 bits, decryption goes very quickly. Since we can always choose a small value for e, encryption is still efficient.

Another obvious application of Shamir's idea is in current implementations with, for instance, p and q of about 256 bits. If RSA is just used for key exchange, then x can almost always be less than 256 bits. The idea of decrypting mod p and mod q separately has been around for some years, but as far as I know, Shamir is the first to make this particular observation.

The second clever idea was from Louis Guillou and Jean-Jacques Quisquater, who questioned whether RSA signatures are really longer than DSA signatures. Since an RSA modulus is usually at least 512 bits and DSA signatures are 320 bits, it seems obvious that DSA is shorter.

However, if you use a hash function (SHA, for example), then the actual message signed will only be 160 bits long. This hash would normally be signed using the RSA algorithm, and then appended to the message. The clever idea is to fill up the remainder of the 512 bits with part of the message, rather than wasting it by filling it up with padding. This part of the message is recovered during signature verification. Thus, RSA uses 160 bits plus the message length, while DSA uses 320 bits plus the message length!

Actually, things are not quite this straightforward. For instance, an RSA signature cannot be less than 512 bits, so DSA is faster for very short messages. For large messages, RSA will always win, no matter how long a modulus you use. This is an amazingly clever idea - simple and useful - but one I have never seen before.

If you're interested, the full Eurocrypt '95 conference proceedings are available from Springer-Verlag in their Lecture Notes for Computer Science series: Advances in Cryptology - Eurocrypt '95, edited by Louis C. Guillou and Jean-Jacques Quisquater (ISBN 3-540-594-094).


Bruce, who is author of Applied Cryptography (John Wiley & Sons, 1993), is a Dr. Dobb's Journal contributing editor. He can be contacted at [email protected].


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