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This is continuation-question based on: If PRESENT had different permutations s would that protect it against Statistical Saturation Attack? Can we protect PRESENT from Statistical Saturation Attacks by using:

  1. unique perms for each round or just some rounds? (In this case, how many might some have to be?)
  2. random, key-dependent (say), perms for some or all rounds?

Moreover, if these ideas can indeed protect PRESENT against SS attacks:

  1. Could we use fewer than 31 rounds without causing vulnerabilities to other attacks?

See also What affect does the permutation layer have on the avalanche effect?

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