Talk:Confusion and diffusion

message: Hello,
this is one of my first visits on Wikipedia, and if my editing experience is very scarce yet, I duly apologize.
OK, now to the discussion: I have recently been editing the article "confusion and diffusion" because I became aware of a statement in the article which simply is not true in my opinion.
Unfortunately my changes have been un-done so I wanted to take a chance to argue in favour of what I think is correct.
The point is that confusion and diffusion are -- at least in some lecture notes and books -- explained just in a self-respective way: confusing.
But if you happen to have read Shannon's original paper, which should be taken as the origin of any citations, the terms are made rather clear:
There are two "inputs" which lead to a ciphertext. One is the plaintext, the other one is the key. Diffusion leads to an elimination of a statistical relation between changes in single plaintext bits and changes in single ciphertext bits. If you change a plaintext bits, a cipher with good diffusion should lead to a 50 pc chance for _any_ ciphertext bit to change.
Confusion, on the other hand, does the same for the key<->ciphertext relation.
As I stated, I did the changes the day before yesterday, but they have been un-done.
Please read the original paper to get the terms correct, and then please re-do my changes. The current explanation is simply incorrect.
A link:
http://www.cs.ucla.edu/~jkong/research/security/shannon1949.pdf
: Thanks for your contributions, and Wikipedia:Welcome to Wikipedia! Your above definition isn't how I understand confusion and diffusion, but it's been a little while since I've read Shannon's paper, so it might well be different. I'll have a leaf through it now, though it would be most helpful if you could give some relevant quotes from Shannon's paper. — Matt 07:37, 11 Jun 2004 (UTC)
replies: text: To be more specific, the thing that I disagree with about your above definition is the assertion that confusion is the just the same thing as diffusion, but between key and ciphertext, not plaintext and ciphertext. I think confusion is about complexity of the relationship between the inputs and outputs, and diffusion is about the extent to which a small change in an input propagates to the output. — Matt 08:43, 11 Jun 2004 (UTC)
thread_title: Undone edits

message: Shannon writes:
Two methods (other than recourse to ideal systems) suggest themselves for frustrating a statistical analysis. These we may call the methods of diffusion and confusion. In the method of diffusion the statistical structure of M which leads to its redundancy is "dissipated" into long range statistics—i.e., into statistical structure involving long combinations of letters in the cryptogram...
The method of confusion is to make the relation between the simple statistics of E and the simple description of K a very complex and involved one.
Schneier writes in Applied Cryptography:
Confusion serves to hide any relationship between the plaintext, the ciphertext and the key. Remember how linear and differential cryptanalysis can exploit even a slight relationship between these three things? Good confusion makes the relationship statistics so complicated that even these powerful cryptanalytic tools won't work.
Diffusion spreads the influence of individual plaintext or key bits over as much of the ciphertext as possible. This also hides statistical relationships and makes cryptanalysis more difficult.
— Matt 08:04, 11 Jun 2004 (UTC)
thread_title: Quotations

message: I think that both of you, User:OT and User:Matt Crypto, are right below in some sense, even though you are disagreeing with each other. The relationship between the key and the ciphertext is complex exactly because the cryptosytem has the property that changing one bit of the key changes the ciphertext completely, and hence in order to change only one bit of the ciphertext you certainly would have to change the key completely. There are basically equivalent properties. I will try to clarify these things here now. --GaborPete (talk) 04:35, 5 April 2009 (UTC)
replies: text: I'm not really satisfied with my own work, but presently that's what I can do. --GaborPete (talk) 10:31, 5 April 2009 (UTC)

text: I have now deleted the following paragraph: --GaborPete (talk) 10:31, 5 April 2009 (UTC)
replies: text:  Substitution (a plaintext symbol is replaced by another) has been identified as a mechanism for primarily confusion (see S-box); conversely transposition (rearranging the order of symbols, see P-box) is a technique for diffusion, although other mechanisms are also used in modern practice, such as linear transformations (e.g. in Rijndael). Product ciphers use alternating substitution and transposition phases to achieve both confusion and diffusion respectively.
There are two more slightly confusing things in the present text, I will change them, too:
* I think it is dangerous to connect the word "substitution" in a substitution–permutation network with a substitution cipher. For example, in Rijndael, a main example of an SP network, an S-box substitutes 8-bit blocks by 8-bit blocks. On the other hand, when hearing "substitution cipher", one usually thinks of changing one character to another character, maybe pairs to pairs, or triplets to triplets, at most, but not octets to octets. True, an ASCII character is usually 8 bits, or something like that, but then Rijndael mixes these bits among the 8-bit blocks, not at all respecting ASCII characters or anything like that. 
* The transposition (mathematics) link is wrong. That means something else. --GaborPete (talk) 04:35, 5 April 2009 (UTC)

text:  OK, I didn't really change them, rather deleted. But I have put a sentence containing substitution cipher and transposition cipher into the substitution–permutation network article. --GaborPete (talk) 10:31, 5 April 2009 (UTC)
thread_title: Confusion

message: Shannon's 1949 paper (Communication Theory of Secrecy Systems) is a revised and declassified version of a 1945 paper (A Mathematical Theory of Cryptography - there's a copy here: https://www.iacr.org/museum/shannon45.html). They're pretty similar. I just checked and Confusion and Diffusion are actually defined in the earlier paper, so I'd like to change the article to reference that earlier piece unless someone has an objection. Shane Lin (talk) 10:08, 26 October 2015 (UTC)
thread_title: Use in "A Mathematical Theory of Cryptography" (1945)

message: The non-keyed hashes do not have confusion in its standard definition, so I have modified the lead accordingly. A good WP:RS for that assertion is remarkably hard to find, though. Dimawik (talk) 20:55, 25 April 2023 (UTC)
thread_title:  Confusion in hashes