Thread by @ErgoBTC

What is entropy & how can it be used to evaluate your Bitcoin transaction “privacy”?

Entropy is defined as:
A measure of disorder or randomness in a closed system.

It has many applications in dynamic systems and is most often used in physics but also applies to information.

Claude Shannon solidified the field of scientific research known as Information Theory in his 1948 paper entitled: A Mathematical Theory of Communication

His original paper can be found here:
math.harvard.edu/~ctm/home/text…

Shannon quantified the amount of information content in a message as ‘entropy’. Showing that the more a message resembles random noise, the more information it can hold.

Entropy is a way to quantify the uncertainty in a system which can be used to directly evaluate the expense of determining the information in a message.

Source:

Ok, but what does this actually mean in plain English?

Entropy is the average number of YES/NO questions required to obtain all the information (in the correct order) in a given message.

Mathematically, entropy is the log2(probability) of guessing the information in a message.

In the case of bitcoin transactions, LaurentMT combined the work of Claude Shannon and Kristov Atlas to quantify the computational expense of evaluating a bitcoin transaction in Botlzmann.

medium.com/@laurentmt/int…

The number of interpretations of a transaction is quantified using CoinJoin Sudoku and the linkability matrix of a transactions inputs and outputs.

github.com/kristovatlas/c…

The interpretations are used to determine the entropy of the transaction.

E = log2(N)

Where:
E = entropy of the transaction
N = number of combinations (mapping of inputs to outputs)

github.com/Samourai-Walle…
gist.github.com/LaurentMT/d361…

“Privacy” on the blockchain is a misleading term.

It’s open, we can see everything.

I think the term privacy or anonymity should be substituted for uncertainty or computational expense.

But good luck with that.

Entropy does not include other factors affecting privacy which are more subjective including:

Clustering
Transaction graph analysis
Merging of inputs
Timing attacks

But entropy is a decent evaluation of the computational expense of evaluating just the transaction itself.

So for a bitcoin transaction:

with a constant number of inputs and outputs,

the more uniform the inputs and outputs are,

the more computationally expensive it is to analyze,

the more “private” it is.

/end