Shannon confusion and diffusion concept I read the document(not the whole document) from Shannon where he speaks about the concepts of confusion and diffusion. I read in many places(not in the document but around the internet) that confusion is enforced using substitution. Diffusion is enforced using permutation/transposition. Ciphers must use both of them because either confusion or diffusion alone are not enough. I read that a substitution cipher can apply by itself confusion(only). Permutation/Transposition applies by itself diffusion(only). It's precisely the last case that bothers me: Can a permutation/transposition cipher by itself apply diffusion?

Shannon explains diffusion as a property that spreads statistic properties of text all over the text preventing statistic analysis. It's frequently translated to: an alteration to a plaintext symbol affects many cipher text symbols. Assuming permutation of bits or characters, how can diffusion be achieved by simple permutation? I mean, if you permute bits, there will be no other bits affected.
But if you consider a symbol a character and you permute bits, a change in a character will affect many other characters. It's a question of what is a symbol.

I also read versions of this diffusion concept where the point was just changing bits order just to avoid pattern analysis of the text. But, where is the avalanche effect in simple permutation?

So, what is the correct definition and the implications of diffusion?

I hope you understand what is troubling me.

Thank you once more
I think that you missed a pivotal point in the concept, which is the small blocks that are used to compose a secure PRF (or PRP), i.e. when you permute one bit, you actually change the value of the small block of that bit, i.e. the whole small-block is effected and thus prepared to be confused in the next round, this way you will reach a confusion of the entire big-block very fast.

I attach a good explanation of the concept as described in Lindell-Katz Book


  In addition to his work on perfect secrecy, Shannon also introduced a
  basic paradigm for constructing concise,random-looking permutations.
  The basic idea is to construct a random looking permutation $F$ with a
  large block length from many smaller random (or random-looking)
  permutations $\{f_i\}$ with small block length. Let us see how this
  works on the most basic level. Say we want $F$ to have a block length
  of $128$ bits. We can define $F$ as follows: the key $k$ for $F$ will
  specify $16$ permutations $f_1,\ldots, f_{16}$ that each have an $8$-bit
  ($1$-byte) block length. Given an input $x\in\{0, 1\}^{128}$, we parse
  it as $16$ bytes $x_1,\ldots,x_{16}$ and then set (equation 6.2)
  $F_k(x)=f_1(x)||\ldots||f_{16}(x_{16})$. These round functions
  $\{f_i\}$ are said to introduce confusion into $F$. It should be
  immediately clear, however, that F as defined above will not be
  pseudorandom. Specifically, if $x$ and $x'$ differ only in their first
  bit then $F_k(x)$ and $F_k(x')$ will differ only in their first byte
  (regardless of the key k). In contrast, if $F$ were a truly random
  permutation then changing the first bit of the input would be expected
  to affect all bytes of the output. For this reason, a diffusion step
  is introduced whereby the bits of the output are permuted, or “mixed,”
  using a mixing permutation. This has the effect of spreading a local
  change (e.g., a change in the first byte) throughout the entire block.
  The confusion/diffusion steps—together called a round —are repeated
  multiple times. This helps ensure that changing a single bit of the
  input will affect all the bits of the output.
  
  As an example, a two-round block cipher following this approach would
  operate as follows. First, confusion is introduced by computing the
  intermediate result $f_1(x_1)||\ldots||f_{16}(x_{16})$ as in Equation
  (6.2). The bits of the result are then “shuffled,” or re-ordered, to
  give $x'$. Then $f'_1(x'_1)||\ldots||f'_{16}(x'_{16})$ is computed
  (where $x'= x'_1,\ldots,x'_{16}$), using possibly different functions
  $f'_i$, and the bits of the result are permuted to give output $x''$.
  The $\{f_i\},\{f'_i\}$, and the mixing permutation(s) could be random
  and dependent on the key, as we have described above. In practice,
  however, they are specially designed and fixed, and the key is
  incorporated in a different way