International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 21 January 2014

Longjiang Qu, Shaojing Fu, Qingping Dai, Chao Li
ePrint Report ePrint Report
In this paper we study the problem that when a Boolean function can

be represented as the sum of two bent functions. This problem was

recently presented by N. Tokareva in studying the number of bent

functions. Firstly, many functions, such as

quadratic Boolean functions, Maiorana-MacFarland bent functions,

partial spread functions etc, are proved to be able to be

represented as the sum of two bent functions. Methods to construct

such functions from low dimension ones are also introduced. N.

Tokareva\'s main hypothesis is proved for $n\\leq 6$. Moreover,

two hypotheses which are equivalent to N. Tokareva\'s main hypothesis

are presented. These hypotheses may lead to new ideas or methods to

solve this problem. At last, necessary and sufficient conditions on

the problem when the sum of several bent functions is again a bent

function are given.

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