A construction of a cipher from a single pseudorandom permutation

  • Shimon Even
  • Yishay Mansour
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 739)


Shannon defined a random cipher as a collection of randomly chosen permutations, one for each value of the key.

We suggest a scheme for a block cipher which uses only one randomly chosen permutation, F. The key, consisting of two blocks, K1 and K2 is used in the following way: The message block is XORed with K1 before applying F, and the outcome is XORed with K2, to produce the cryptogram block. This removes the need to store, or generate a multitude of permutations.

Although the resulting cipher is not random, we claim that it is secure. First, it is shown that if F is chosen randomly then, with high probability the scheme is secure against any polynomial-time algorithmic attack. Next, it is shown that if F is chosen pseudorandomly, the system remains secure against oracle-type attacks.

The scheme may lead to a system more efficient than systems such as the DES and its siblings, since the designer has to worry about one thing only: How to implement one pseudorandomly chosen permutation. This may be easier than getting one for each key.


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  1. [1]
    C.E. Shannon, “Communication Theory of Secrecy Systems”, Bell System Tech. J., Vol. 28, 1949, pp. 656–715.Google Scholar
  2. [2]
    National Bureau of Standards, “Data Encryption Standard”, Federal Information Processing Standard, U.S. Department of CommerceFIPS PUB 46, Washington, DC, 1977.Google Scholar
  3. [3]
    M. Luby and C. Rackoff, “How to Construct Pseudorandom Permutations from Pseudorandom Functions”, SIAM J. on Computing, Vol. 17, No. 2, 1988, pp. 373–386.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Shimon Even
    • 1
  • Yishay Mansour
    • 2
  1. 1.Comp. Sci. Dept.Technion, Israel Institute of TechnologyHaifaIsrael
  2. 2.IBM T.J. Watson Research CenterYorktown Heights

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