Talk:Bent function

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A fact from Bent function appeared on Wikipedia's Main Page in the Did you know column on 5 October 2009 (check views). The text of the entry was as follows:

Did you know... that the cryptographic primitives CAST-128, CAST-256, Grain, and HAVAL were all designed using bent functions for cryptographic security?

A record of the entry may be seen at Wikipedia:Recent additions/2009/October.

Wikipedia

$~+~$ and $~\oplus ~$

It's a bit strange that in this article the + sign (at least sometimes) stands for the exclusive or, although it usually represents the logical disjunction.

The article states that " $x_{1}x_{2}~+~x_{3}x_{4}$ " is a bent function,
but only $x_{1}x_{2}~\oplus ~x_{3}x_{4}$ is one,
while $x_{1}x_{2}~\lor ~x_{3}x_{4}$ is not.

Maybe the $~+~$ signs should be replaced by $~\oplus ~$ ? Mate2code (talk) 18:32, 2 August 2011 (UTC)[reply]

Boolean functions written in algebraic normal form use + for XOR, since it corresponds to addition over Z/2Z. Ntsimp (talk) 18:49, 2 August 2011 (UTC)[reply]

As long as the other convention is not used in this article, thats no problem. I've added the hint, that + stands for XOR, so no one should be confused. Mate2code (talk) 19:15, 2 August 2011 (UTC)[reply]

Errr..

The article is written for mathematicians, not a general audience. Would someone please provide an explanation, in the introduction, that explains the subject in a manner comprehensible to a non-mathematician? Currently, many articles that refer to crytography (I got here from the Blowfish page) are written in a form that depends on technical terms that refer to pages which are more not less technical rendering, in this case, everything from the Blowfish article onward inaccessible to a lay readership. LookingGlass (talk) 08:48, 3 May 2014 (UTC)[reply]

I created this article myself, and I tried really hard to put a simple explanation in the lead. A bent function is a special kind of Boolean function. The name comes from the fact that it's maximally different from all the linear and affine functions. They're useful mostly in cryptography. But this is a technical subject, and the real details of how they're defined and what they're used for are going to be technical. I'd like to improve the article; what sort of explanation would be helpful? Ntsimp (talk) 17:39, 3 May 2014 (UTC)[reply]

I've added a little bit to the explanation in the lead. Does that help? Ntsimp (talk) 18:16, 3 May 2014 (UTC)[reply]

Diagrams of Bent Functions

Hi,

could you please explain the diagrams in the top-right corner of the article? Specifically, how to interpret the diagrams, and where the nonlinearity calculations come from.

Thanks! — Preceding unsigned comment added by 142.58.164.102 (talk) 20:08, 15 January 2015 (UTC)[reply]

Those were done by User:Mate2code. Frankly, I don't understand them myself. Ntsimp (talk) 23:27, 15 January 2015 (UTC)[reply]

Well, at least the 4-ary diagrams have a longer description, coming from c:Template:Nonlinearity of 4-ary Boolean functions. I will make a Wikiversity page where I explain these graphics in more detail, and link to it on the description pages. In short: The nonlinearity of a Boolean function is how much it differs from a linear function, so these diagrams show all 2*2^n linear functions (as a binary Walsh matrix and its complement), and how much the function on top differs from all of them. 01100110 is a linear function, so in the diagram you can see that the nonlinearity is 0. 00000110 is not linear - the diagram shows that the nonlinearity is 2.
The calculations (that 2-ary functions are bent when they have NL=2, and that 4-ary functions are bent when they have NL=6) are not explained in the diagrams. The article explains them, and I have no idea if they could be illustrated. The diagrams merely illustrate that the NL is 1 or 6 respectively - not that or why this makes the functions bent. mate2code 15:56, 16 January 2015 (UTC)[reply]

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+ {\displaystyle ~+~} and ⊕ {\displaystyle ~\oplus ~}

Errr..

Diagrams of Bent Functions

External links modified

$~+~$ and $~\oplus ~$