Introduction to finite fields and their applications
Introduction to finite fields and their applications
Number Theory for Computing
Relationships between Bent Functions and Complementary Plateaued Functions
ICISC '99 Proceedings of the Second International Conference on Information Security and Cryptology
New constructions for resilient and highly nonlinear boolean functions
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
On cryptographic properties of the cosets of R(1, m)
IEEE Transactions on Information Theory
New families of binary sequences with low correlation
IEEE Transactions on Information Theory
New Families of Binary Low Correlation Zone Sequences Based on Interleaved Quadratic Form Sequences
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A Generalization of the Bent-Function Sequence Construction
ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part III
Efficient computation of the best quadratic approximations of cubic boolean functions
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
On the link of some semi-bent functions with Kloosterman sums
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
A construction of weakly and non-weakly regular bent functions
Journal of Combinatorial Theory Series A
When does G(x )+γTr(H(x)) permute Fpn?
Finite Fields and Their Applications
Quadratic functions with prescribed spectra
Designs, Codes and Cryptography
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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.