Name
Abstract | ||
|---|---|---|
We present a new characterization of semi-bent and bent quadratic functions on finite fields. First, we determine when a GF(2)-linear combination of Gold functions Tr(x2i+1) is semi-bent over GF(2n), n odd, by a polynomial GCD computation. By analyzing this GCD condition, we provide simpler characterizations of semi-bent functions. For example, we deduce that all linear combinations of Gold functions give rise to semi-bent functions over GF(2p) when p belongs to a certain class of primes. Second, we generalize our results to fields GF(pn) where p is an odd prime and n is odd. In that case, we can determine whether a GF(p)-linear combination of Gold functions Tr(xpi+1) is (generalized) semi-bent or bent by a polynomial GCD computation. Similar to the binary case, simple characterizations of these p-ary semi-bent and bent functions are provided. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s10623-005-6345-x | Des. Codes Cryptography |
Keywords | Field | DocType |
linear combination,bent function,polynomial gcd computation,bent quadratic function,fields gf,finite fields,gcd condition,p-ary semi-bent,new characterization,binary case,semi-bent function,gold function,bent functions,finite field | Prime (order theory),Discrete mathematics,Linear combination,Combinatorics,Finite field,Polynomial,Bent function,Bent molecular geometry,Quadratic function,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
38 | 2 | 1573-7586 |
Citations | PageRank | References |
36 | 1.70 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Khoongming Khoo | 1 | 250 | 23.29 |
| Guang Gong | 2 | 1717 | 160.71 |
| Douglas R. Stinson | 3 | 2387 | 274.83 |