# Hyperbent Boolean Function

Discussion in 'General Electronics Chat' started by mrwizardhts, Sep 3, 2013.

1. ### mrwizardhts Thread Starter New Member

Sep 3, 2013
5
0
A paper by Gong and Youssef " Hyperbent Functions" (Google) describe the construction of boolean functions with cryptographic qualities stronger than the bent functions. ( for example the AND, NAND, OR and NOR functions with two variables are bent functions). Could someone take a quick look at this paper and see if you can convert the hyperbent function into an actual circuit diagram for me? I am not a mathematician, obviously!

2. ### Wendy Moderator

Mar 24, 2008
20,772
2,540
This sounds a lot like homework, but we'll assume it isn't. You still need to show the schematic before someone can help you. That or provide a link to the problem.

This is really not a pure math problem, more of a basic problem in digital electronics. Therefor I am moving this thread to a different location.

3. ### #12 Expert

Nov 30, 2010
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I was under the impression that Boolean functions are inherently cryptographic.

4. ### mrwizardhts Thread Starter New Member

Sep 3, 2013
5
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Hello #12
In a manner of speaking you are correct because boolean gates "erase information " and therefore obscure the relationship between the input and output of a function.

Last edited: Sep 4, 2013
5. ### mrwizardhts Thread Starter New Member

Sep 3, 2013
5
0
Hello #12
In a manner of speaking you are correct because boolean gates "erase information " and therefore obscure the relationship between the input and output of a function.

6. ### #12 Expert

Nov 30, 2010
16,703
7,338
I was just joking about how difficult I find Boolean equations.

7. ### Austin Clark Active Member

Dec 28, 2011
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I'd say it's more akin to lossy compression, not cryptography.

However, I suppose a combinatorial boolean function could be built to provide a unique output for each unique input, so that if you knew the function and its output you could figure out the one possible input.

I'd be neat to make an FPGA do this. Though I feel like the circuit required to create a one-to-one relationship between input/output would be massive for inputs with more than a few bytes. Assuming the function wasn't too simple or mundane, and assigned inputs to outputs "randomly".
Maybe you could make things easier with synchronous elements?

Hmm....

Last edited: Sep 4, 2013
8. ### mrwizardhts Thread Starter New Member

Sep 3, 2013
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Hi Mr Clark,
My comments to # 12 really have nothing to do with my original question , which remains un-answered. It was just a shot in the dark, the math in the Gong and Youssef paper is going to be way over the heads of most of the users of this site

9. ### Austin Clark Active Member

Dec 28, 2011
409
44
Yes, I understand, I just thought it was interesting, and went on my own tangent

I assume this is the paper you're referring to?
http://www.iacr.org/archive/eurocrypt2001/20450404.pdf

Papers like these make me think they intentionally write unintelligibly.

10. ### mrwizardhts Thread Starter New Member

Sep 3, 2013
5
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Yes Mr. Clark, that is the paper. My first intuition about generating a "hyperbent" function was to take the simplest bent function, a two input AND gate and make it a three input AND gate, the reasoning would be that for an AND gate three out of the possible four boolean arguments resolve to zero so an adversary has to guess which values produced the zero( on random inputs of course). So with a three input AND gate there are seven arguments that resolve to zero so you can see it would be even harder to guess . I would like to find out how close my intuition was ;-)