Lesson plan
Bent function
1 are bent; i.e., their nonlinearity is 1 (these Hadamard matrices show the Hamming distance to each of the eight linear and affine functions) . The following formula shows that a 2-ary function is bent when its nonlinearity is 1: {{defn| 2^{2-1} - 2^{\frac{2}{2}-1} = 2 - 1 = 1 }} In the mathematical field of combinatorics, a bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables. Concretely, this means the maximum correlation between the output of the function and a linear function is minimal. In addition, the derivatives of a bent function are balanced Boolean functions, so for any change in the input variables there is a 50 percent chance that the output value will change. The maximal nonlinearity means approximating a bent function by an affine (linear) function is hard, a useful property in the defence against linear cryptanalysis. In addition, detecting a change in the output of the function yields no information about what change occurred in the inputs, making the function immune to differential cryptanalysis. Bent functions were defined and named in the 1960s by Oscar Rothaus in research not published until 1976.…
Article summary
1 are bent; i.e., their nonlinearity is 1 (these Hadamard matrices show the Hamming distance to each of the eight linear and affine functions) . The following formula shows that a 2-ary function is bent when its nonlinearity is 1: {{defn| 2^{2-1} - 2^{\frac{2}{2}-1} = 2 - 1 = 1 }} In the mathematical field of combinatorics, a bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables. Concretely, this means the maximum correlation between the output of the function and a linear function is minimal. In addition, the derivatives of a bent function are balanced Boolean functions, so for any change in the input variables there is a 50 percent chance that the output value will change. The maximal nonlinearity means approximating a bent function by an affine (linear) function is hard, a useful property in the defence against linear cryptanalysis. In addition, detecting a change in the output of the function yields no information about what change occurred in the inputs, making the function immune to differential cryptanalysis. Bent functions were defined and named in the 1960s by Oscar Rothaus in research not published until 1976.…
Key claims
- publication date: 1976 — source: Wikipedia · confidence 0.95
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- The record states that the publication date is "1976". What evidence would count against this claim?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
- Wikipedia https://en.wikipedia.org/w/index.php?oldid=1368736978
Key claims and bibliography are generated from the same tracked claims and sources as the article page.