A bent function is a Boolean function 
whose Walsh transform
 |
has 
for every 
, where 
is the dot product over
the finite field 
(Rothaus 1976). Bent functions exist only when 
is even. For example, 
, with arithmetic in 
, is bent.
Every Boolean function has a unique representation as a multilinear polynomial over 
. For even 
, the polynomial degree
of a bent function is at most 
(Rothaus 1976). The converse question of representing every
Boolean function of degree at most 
as a sum of two bent functions is Tokareva's
conjecture.
