International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Security amplification by composition: The case of doubly-iterated, ideal ciphers

William Aiello
Mihir Bellare
Giovanni Di Crescenzo
Ramarathnam Venkatesan
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Abstract: We investigate, in the Shannon model, the security of constructions corresponding to double and (two-key) triple DES. That is, we consider F<sub>k1</sub>(F<sub>k2</sub>(.)) and F<sub>k1</sub>(F<sub>k2</sub><sup>-1</sup>(F<sub>k1</sub>(.))) with the component functions being ideal ciphers. This models the resistance of these constructions to ``generic'' attacks like meet in the middle attacks. We obtain the first proof that composition actually increases the security in some meaningful sense. We compute a bound on the probability of breaking the double cipher as a function of the number of computations of the base cipher made, and the number of examples of the composed cipher seen, and show that the success probability is the square of that for a single key cipher. The same bound holds for the two-key triple cipher. The first bound is tight and shows that meet in the middle is the best possible generic attack against the double cipher.
  title={Security amplification by composition: The case of doubly-iterated, ideal ciphers},
  booktitle={IACR Eprint archive},
  keywords={DES, Double DES, cipher, block cipher, cascade, composition, Shannon.},
  note={Appeared in the THEORY OF CRYPTOGRAPHY LIBRARY and has been included in the ePrint Archive. 10500 received August 31st, 1998.},
  author={William Aiello and Mihir Bellare and Giovanni Di Crescenzo and Ramarathnam Venkatesan},