diff --git a/content/optimal-privacy.md b/content/optimal-privacy.md index 70f12b99..acdc4552 100644 --- a/content/optimal-privacy.md +++ b/content/optimal-privacy.md @@ -1,5 +1,5 @@ +++ -date = "2018-12-07T21:08:39-08:00" +date = "2018-12-07T00:00:00-08:00" title = "Privacy is Consent (alt: On Optimal Privacy vs. System Efficiency)" +++ @@ -47,11 +47,11 @@ $$f(x,y) = \begin{pmatrix}0 & 1 & 0 & 1 & 0 & 1 & \dots \\\ 1 & 0 & 1 & 0 & 1 & Such a function can be partitioned based on a single bit of information e.g. whether $y$ is divisible by 2: -$$f(x,y) = \begin{pmatrix}1 & 1 & 1 & \dots\\\ 0 & 0 & 0 & \dots\\\ 1 & 1 & 1 & \dots \\\ 0 & 0 & 0 & \dots \\\ \vdots & \vdots & \vdots & \vdots \ddots \end{pmatrix}$$ +$$f(x,y) = \begin{pmatrix}1 & 1 & 1 & \dots\\\ 0 & 0 & 0 & \dots\\\ 1 & 1 & 1 & \dots \\\ 0 & 0 & 0 & \dots \\\ \vdots & \vdots & \vdots & \vdots & \ddots \end{pmatrix}$$ or not: -$$f(x,y) = \begin{pmatrix}0 & 0 & 0 & \dots \\\ 1 & 1 & 1 & \dots\\\ 0 & 0 & 0 & \dots\\\ 1 & 1 & 1 & \dots \\\ \vdots & \vdots & \vdots & \vdots \ddots \end{pmatrix}$$ +$$f(x,y) = \begin{pmatrix}0 & 0 & 0 & \dots \\\ 1 & 1 & 1 & \dots\\\ 0 & 0 & 0 & \dots\\\ 1 & 1 & 1 & \dots \\\ \vdots & \vdots & \vdots & \vdots & \ddots \end{pmatrix}$$ We can partition each matrix again, based on whether $x$ is divisible by 2 or not. Regardless of which of the above partitioned matrices we start with, the resulting matrices are the same: diff --git a/content/random-notes b/content/random-notes new file mode 100644 index 00000000..fa352930 --- /dev/null +++ b/content/random-notes @@ -0,0 +1,36 @@ +e 0 1 2 3 + ------- +0| 0 1 0 1 +1| 1 0 1 0 +2| 0 1 0 1 +3| 1 0 1 0 + +f(2,1) = 1 (y is either 1 or 3 | x is either 0 or 2) + +p1 sends 0 + + 0 1 2 3 +0| 0 1 0 1 +2| 0 1 0 1 + +p2 sends 1 + + 1 3 + --- +0| 1 1 +2| 1 1 + +Why AND Fails: + + 0 1 2 3 + -------- +0| 0 0 0 0 +1| 0 1 0 1 +2| 0 0 1 1 +3| 0 1 1 1 + +f(1,2) = 1 + +p1 sends....there is no way to send information without revealling out input...the matrix is not partitionable. + +