On the power of cascade ciphers

  • Authors:
  • S. Even;O. Goldreich

  • Affiliations:
  • Department of Computer Science, Duke University, Durham, NC and Technion--Israel Institute of Technology, Haifa, Israel;Laboratory for Computer Science, Massachusetts Institute of Technology, 545, Technology Square, Cambridge, MA and Technion--Israel Institute of Technology, Haifa, Israel

  • Venue:
  • ACM Transactions on Computer Systems (TOCS)
  • Year:
  • 1985

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Abstract

The unicity distance of a cascade of random ciphers, with respect to known plaintext attack, is shown to be the sum of the key lengths. A time-space trade-off for the exhaustive cracking of a cascade of ciphers is shown. The structure of the set of permutations realized by a cascade is studied; it is shown that only l.2k exhaustive experiments are necessary to determine the behavior of a cascade of l stages, each having k key bits. It is concluded that the cascade of random ciphers is not a random cipher. Yet, it is shown that, with high probability, the number of permutations realizable by a cascade of l random ciphers, each having k key bits, is 2lk. Next, it is shown that two stages are not worse than one, by a simple reduction of the cracking problem of any of the stages to the cracking problem of the cascade. Finally, it is shown that proving a nonpolynomial lower bound on the cracking problem of long cascades is a hard task, since such a bound implies that P ≉ NP.