References about a boolean function involving hamming weight Some weeks ago, I read an article about an interesting boolean function with some applications to cryptography. Then, I forgot about the article and now I cannot find it. Hence here I am asking if someone is familiar with this function and can give me some references. Thank you in advance.
Fix a positive integer $n$. The function boolean function $f$, taking a $n$bits words $\mathbf{x}$ as input and returning a single bit as output is defined by
$$f(\mathbf{x}) = x_{w(\mathbf{x}) \!\!\!\mod\!\! n} ,$$
where $w(\mathbf{x})$ is the Hamming weight of $\mathbf{x}$ (number of bits equal to 1) and $\mathbf{x} = x_0 x_1 \dots x_{n-1}$ (with $x_i \in \{0,1\}$).
It is the hidden weighted bit function. There is more than one paper related to cryptographic applications of this function, but the full definition may be found, for example, in Chapter 3 of this paper:
Cryptographic properties of the hidden weighted bit function