## ALGEBRAIC CONSTRUCTION OF SEMI BENT FUNCTION VIA KNOWN POWER FUNCTION

## ALGEBRAIC CONSTRUCTION OF SEMI BENT FUNCTION VIA KNOWN POWER FUNCTION

*P. Poojary, Harikrishnan P. K., V. Bhatta G. R*

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## Abstract

The study of semi bent functions (2- plateaued Boolean function) has at- tracted the attention of many researchers due to their cryptographic and combinatorial properties. In this paper, we have given the algebraic construction of semi bent func- tions dened over the nite eld F2n (n even) using the notion of trace function and Gold power exponent. Algebraically constructed semi bent functions have some special cryp- tographical properties such as high nonlinearity, algebraic immunity, and low correlation immunity as expected to use them eectively in cryptosystems. We have illustrated the existence of these properties with suitable examples.

## Keywords

Boolean function, trace, cryptography, nonlinearity, algebraic immunity.