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What's the difference between substitution and permutation in DES? From my understanding substitution is replacing the data with new data and permutation is just rearranging the data?

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You pretty much answered your own question:

  • Substitution replaces a section of data with another chunk of data
  • Transposition moves data from one place to another

Substitution is usually responsible for non-linearity or "confusion", while transposition is useful for "diffusion" and ensuring that changes in one bit propagate to the rest of the state.

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