## Reference from ESORICS proceedings

First European Symposium On Research In Computer Security (ESORICS 90)

**Pseudorandom Permutations Based on the D.E.S. Scheme**

*Jacques Patarin*

**Keywords :** Cryptology, D.E.S., Psudorandom generators

**Abstract :** We will mainly present the results exposed by Michel Luby and Charles Rackoff
in "How to construct pseudorandom permutations from pseudorandom functions", SIAM
J. Comput., 1988, and the new results on that subject.
No demonstrations will be given here but in an article for Eurocode 90, I will
give a complete proof of the main results. (This proof will be sensibly simpler
and more complete than the one given by Luby and Rackoff).
The two main results are:
1. A three iteration DES scheme where the S-boxes are replaced by random
functions (or by a pseudo-random function generator) will give us an invertible
pseudorandom function generator. That is to say a cryptosystem which is secure
against chose plaintext attacks.
2. A four (or more) iterations DES Scheme where the S-boxes are replaced by
random functions (or by a pseudorandom function generator) will give us an
invertible super pseudorandom permutation generator. That is to say a
cryptosystem which is secure againts chose plaintext and chosen ciphertext
attacks.

(Pages 185-187)

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