Cryptography


At first, we sample f(x) in the N (N is odd) equidistant points around x^*:

    \[   f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\]


where h is some step.
Then we interpolate points \{(x_k,f_k)\} by polynomial 

(1)   \begin{equation*}    P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}\end{equation*}


Its coefficients \{a_j\} are found as a solution of system of linear equations:

(2)   \begin{equation*}    \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\end{equation*}


Here are references to existing equations: (1), (2).
Here is reference to non-existing equation (??).

Representation

A Boolean function f(x):\mathbf{Z}_2^n \rightarrow \mathbf{Z}_2 such that x=(x_1,x_2,\ldots,x_n), is a mapping from n binary inputs to one binary output. We let \mathcal{B}_n represent the set of all 2^{2^n} Boolean functions of n variables. Boolean functions can be represented using a variety of different forms, each with their own usefulness in regard to cryptographic analysis.

Hi there! I’m a bike messenger by day, aspiring actor by night, and this is my website. I live in Los Angeles, have a great dog named Jack, and I like piƱa coladas. (And gettin’ caught in the rain.)

…or something like this:

The XYZ Doohickey Company was founded in 1971, and has been providing quality doohickeys to the public ever since. Located in Gotham City, XYZ employs over 2,000 people and does all kinds of awesome things for the Gotham community.

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