IJPAM: Volume 57, No. 1 (2009)

SECRET SHARING SCHEMES
BASED ON ALMOST-BENT FUNCTIONS

J.C. Ku-Cauich$^1$, H. Tapia-Recillas$^2$
$^{1,2}$Departamento de Matemáticas
Universidad Autónoma Metropolitana-Iztapalapa
Col. Vicentina, Del. Iztapalapa, México, D.F., 09340, MEXICO
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.A class of linear codes over the finite field ${\bf F}_{2^{h}}$ ($h \geq 1$, an integer) based on almost-bent functions is introduced and the length, dimension and bounds (upper/lower) of the weight of the nonzero codewords of these codes are determined. A secret sharing scheme based on these codes whose secret space is the field ${\bf F}_{2^{h}}$ is given as well as two such schemes whose secret space is of the form ${\bf F}_{2}^{m}$ which are extensions of a scheme with secret space is ${\bf F}_{2}$.

Received: October 2, 2009

AMS Subject Classification: 94B05, 94A62

Key Words and Phrases: almost-bent functions, linear codes, secret sharing schemes

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 1