Cross correlation of two Boolean functions I have been studying Cryptographic Boolean Functions and got stuck with the calculation of cross correlation of two boolean functions. I know the formula is $$c_{f,g}(y) = \sum_{x \in V_{n}} f(x)\cdot g(x\oplus y).$$ What I don't understand is if $f = g$ and $y$ is $0$ shouldn't the correlation be $2^n$? When I calculate, if $f$ and $h$ has the value $0$, $f(x)\cdot g(x)$ will yield $0$, but shouldn't I have $1$ in order to reach $2^n$ in the end? I am sorry if this question sounds silly but I have really spent so much time trying to figure out. Any help would be greatly appreciated.
In theoretical computer science literature, boolean functions are defined as 
$$
f\colon \operatorname{GF}(2)^n \to \{\pm 1\},
$$
and the usual link with functions defined as
$$
\tilde{f}\colon \operatorname{GF}(2)^n \to \{0,1\}
$$
is via $$f(x)=(-1)^{\tilde{f}(x)}.$$

Edit Here's a standard reference from the Boolean function literature.