University of New Mexico ClassicalBalanced, AntiBalanced and NeutroBalanced functions Vadiraja Bhatta G. R. 1 , Shashi Kant Pandey 2 , P. R. Mishra 3 , Prasanna Poojary 4,* 1 Department of Mathematics, Center for Cryptography, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India; vadiraja.bhatta@manipal.edu 2 orcid:0000-0002-0818-6984, Department of Mathematics, Maharaja Surajmal Institute, GGSIP University, Delhi 110 058, India; shashikantshvet@gmail.com 3 Scientific Analysis Group, Metcalfe House Complex, DRDO Delhi 110054, India; prasanna.r.mishra@gmail.com 4 Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, India; poojaryprasanna34@gmail.com, poojary.prasanna@manipal.edu * Correspondence: poojary.prasanna@manipal.edu Abstract. In this paper, we extend the concepts of Neutrosophy to Boolean function and define ClassicalBal- anced, AntiBalanced and NeutroBalanced functions. We consider functions of the form f (x)= Tr(x d ), where the exponent d may be Gold exponent, Kasami exponent, Welch exponent or any arbitrary positive integer. We, for different values of d, examine nature of these functions with respect to the above stated three categories. Keywords: Balanced function; Neutrosophy; AntiBalanced function; NeutroBalanced function; Cryptography. —————————————————————————————————————————- 1. Introduction In an algebraic structure, the axioms are valid and the operations are defined everywhere. We cannot do much mathematics just on sets. We need some sort of algebraic structures for analysis. In real life situations when we require to combine the elements of a particular domain in a certain manner, it may happen the combination is not meaningful for certain pairs. It may be undefined, indeterminate or multivalued. In such situation, we cannot have an algebraic structure and we are left with no option but to modify the combining operations. What if we have the theoretical platform to deal with such operation the way they are. This line of thinking lead to evolution of Neutrosophy. The history of Neutrosophy is dated back to 1998 when Florentin Smarandache propounde the notion of Neutrosophy in [3]. However, Vadiraja Bhatta G. R., Shashi Kant Pandey, P.R. Mishra, Prasanna Poojary, ClassicalBalanced, AntiBal- anced and NeutroBalanced functions Neutrosophic Sets and Systems, Vol. 48, 2022