I see a few small nuanced errors in all the above explanations and they are easy to make for any of us.

Let me clarify this in as straight forward but detailed manner as I can:

$I$ is a countable set and the probability ensemble indexed by $I$ is a collection of random variables denoted as: ${X_i}\in I$. I can either take the form of the natural numbers or an efficiently computable subset (Katz & Lindell, 2008). $X_n$ is the distribution and $X_i$ is the collection of elements. When we see $I = N$ the ensemble is a sequence of random variables $X_1, X_2, X_3...$

Next all we are doing is taking the differences between the $X_n$ distribution and the running of said distribution.

Then we see pseudo-randomness is just a special case of computational indistinguishability. All this means the difference epsilon is very small or negligible or trivial if you will; not exactly the same.

Further reading:

https://wiki.cc.gatech.edu/theory/images/b/b2/Lec5.pdf

Jonathan Katz & Yehuda Lindell (2008) Introduction to Modern Cryptography.

I see a few small nuanced errors in all the above explanations and they are easy to make for any of us.

Let me clarify this in as straight forward but detailed manner as I can:

$I$ is a countable set and the probability ensemble indexed by $I$ is a collection of random variables denoted as: ${X_i}\in I$. I can either take the form of the natural numbers or an efficiently computable subset (Katz & Lindell, 2008). $X_n$ is the distribution and $X_i$ is the collection of elements. When we see $I = N$ the ensemble is a sequence of random variables $X_1, X_2, X_3,\ldots$

Next all we are doing is taking the differences between the $X_n$ distribution and the running of said distribution.

Then we see pseudo-randomness is just a special case of computational indistinguishability. All this means the difference epsilon is very small or negligible or trivial if you will; not exactly the same.

Further reading:

https://wiki.cc.gatech.edu/theory/images/b/b2/Lec5.pdf

Jonathan Katz & Yehuda Lindell (2008) Introduction to Modern Cryptography.

I see a few small nuanced errors in all the above explanations and they are easy to make for any of us.

Let me clarify this in as straight forward but detailed manner as I can:

I is a countable set and the probability ensemble indexed by I is a collection of random variables denoted as: {Xi}∈I. I can either take the form of the natural numbers or an efficiently computable subset (Katz & Lindell, 2008). Xn is the distribution and Xi is the collection of elements. When we see I = N the ensemble is a sequence of random variables X1, X2, X3...

Next all we are doing is taking the differences between the Xn distribution and the running of said distribution.

Then we see pseudo-randomness is just a special case of computational indistinguishability. All this means the difference epsilon is very small or negligible or trivial if you will; not exactly the same.

Further reading:

https://wiki.cc.gatech.edu/theory/images/b/b2/Lec5.pdf

Jonathan Katz & Yehuda Lindell (2008) Introduction to Modern Cryptography.

I see a few small nuanced errors in all the above explanations and they are easy to make for any of us.

Let me clarify this in as straight forward but detailed manner as I can:

$I$ is a countable set and the probability ensemble indexed by $I$ is a collection of random variables denoted as: ${X_i}\in I$. I can either take the form of the natural numbers or an efficiently computable subset (Katz & Lindell, 2008). $X_n$ is the distribution and $X_i$ is the collection of elements. When we see $I = N$ the ensemble is a sequence of random variables $X_1, X_2, X_3...$

Next all we are doing is taking the differences between the $X_n$ distribution and the running of said distribution.

Then we see pseudo-randomness is just a special case of computational indistinguishability. All this means the difference epsilon is very small or negligible or trivial if you will; not exactly the same.

Further reading:

https://wiki.cc.gatech.edu/theory/images/b/b2/Lec5.pdf

Jonathan Katz & Yehuda Lindell (2008) Introduction to Modern Cryptography.