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New families of quadratic almost perfect nonlinear trinomials and multinomials. (English) Zbl 1153.11058
The authors present two families of APN functions on certain finite binary fields, one on fields of order \(2^{2k}\) for \(k\) not divisible by 2, and the other on fields of order \(2^{3k}\) for \(k\) not divisible by 3. The polynomials they present are specific in terms of their roots and number of terms. The polynomials in the first family have between three and \(k+2\) terms, the second family’s polynomials have three terms.

MSC:
11T06 Polynomials over finite fields
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94A60 Cryptography
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