Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Zerocoin: making Bitcoin anonymous

blog.cryptographyengineering.com

Post reply on HN
Print view View original

21–30 of 86 posts

Re: Zerocoin: making Bitcoin anonymous

#21

Post by krcz »

anonymoushn wrote: post #18
jerf wrote: post #11

Earlier quoted context omitted.

No such thing: http://math.stackexchange.com/questions/14777/why-isnt-there... Get far enough into Reflection on Relativity and the author makes some interesting observations based on this tidbit: http://www.mathpages.com/rr/rrtoc.htm (But it is quite a ways in there.)

Could you point out the problem with such a distribution? It isn't immediately obvious that I cannot satisfy both axioms. Edit: The helpful explanation linked in a comment on the question you linked is defective because it applies to all continuous probability distributions.

Using uniform distribution definition from Wikipedia ("all intervals of the same length on the distribution's support are equally probable") we get P(X \in [0,1)) = P(X \in [1, 2)) = P(X \in [2, 3)) = ...

By countable additivity P(\Omega) = P(X \in [0, \infty)) = P(X \in [0, 1)) + P(\X \in [1, 2)) + ... = P(X \in [0, 1)) + P(X \in [0, 1)) + ...

And this evaluates to 0 if P(X \in [0, 1)) = 0 and to \infty if P(\X \in [0, 1)) > 0.

Re: Zerocoin: making Bitcoin anonymous

#22

Post by gizmo686 »

dragontamer wrote: post #8

Since BTC is expected to be regulated like a currency, wouldn't participating in Zerocoin be basically money laundering? If that is the case, participating in the Zerocoin network itself would be a crime. I don't think this is going to go anywhere. And if it does, then hope that the Secret Service doesn't catch you even touching this stuff...

Money laundering only applies when the money is obtained illegally in the first place. Also, Zerocoin doesn't have a network to itself, it functions within the existing bitcoin block chain. Bitcoin explicitly allows for creating alternate ways of defining who can spend a coin, this is simply one such alternate way.

Re: Zerocoin: making Bitcoin anonymous

#23

Post by ezyang »

edmundhuber wrote: post #7
ezyang wrote: post #2

Here is a puzzle for HNers. Suppose that I am a user who wants to anonymize some Bitcoins, and I am willing to wait expected time N before redeeming my Zerocoins. What is the correct probability distribution for me to pick my wait time from?

Pick someone else's and repeat it?

This would not work; suppose someone was using the point distribution "wait one hour and then withdraw", then it would be trivial to deanonymize Zerocoins.

Re: Zerocoin: making Bitcoin anonymous

#24

Post by lwat »

anonymoushn wrote: post #18
jerf wrote: post #11

Earlier quoted context omitted.

No such thing: http://math.stackexchange.com/questions/14777/why-isnt-there... Get far enough into Reflection on Relativity and the author makes some interesting observations based on this tidbit: http://www.mathpages.com/rr/rrtoc.htm (But it is quite a ways in there.)

Could you point out the problem with such a distribution? It isn't immediately obvious that I cannot satisfy both axioms. Edit: The helpful explanation linked in a comment on the question you linked is defective because it applies to all continuous probability distributions.

The probability of any finite interval P(a, b) = 0

Re: Zerocoin: making Bitcoin anonymous

#25

Post by jerf »

anonymoushn wrote: post #18
jerf wrote: post #11

Earlier quoted context omitted.

No such thing: http://math.stackexchange.com/questions/14777/why-isnt-there... Get far enough into Reflection on Relativity and the author makes some interesting observations based on this tidbit: http://www.mathpages.com/rr/rrtoc.htm (But it is quite a ways in there.)

Could you point out the problem with such a distribution? It isn't immediately obvious that I cannot satisfy both axioms. Edit: The helpful explanation linked in a comment on the question you linked is defective because it applies to all continuous probability distributions.

The key is the restriction that in the uniform distribution the probability density must be the same at all points, and if it covers infinity, it can be neither 0 nor anything greater than 0 if it's going to sum to 1. It's perfectly legal to have a probability distribution across all the reals. In fact most if not all of the well-known ones are; the Gaussian/normal distribution is defined on all reals, for instance. But it varies, and the integration from negative infinity to positive infinity sums to 1.

In fact everything that we refer to as "normal" distributions in the real world technically aren't, as the finite nature of the universe means the probability of the extremes is simply zero (give or take being totally wrong about the nature of the universe in which case all bets are off anyhow) rather than very, very small, and in many cases there's a sharp cutoff at 0, or some other arbitrary boundary, which a true normal distribution doesn't have. But it's often still the best mathematical approximation, with negligible error. (... until it isn't.... caveat emptor.)

Re: Zerocoin: making Bitcoin anonymous

#26

Post by consz »

anonymoushn wrote: post #18
jerf wrote: post #11

Earlier quoted context omitted.

No such thing: http://math.stackexchange.com/questions/14777/why-isnt-there... Get far enough into Reflection on Relativity and the author makes some interesting observations based on this tidbit: http://www.mathpages.com/rr/rrtoc.htm (But it is quite a ways in there.)

Could you point out the problem with such a distribution? It isn't immediately obvious that I cannot satisfy both axioms. Edit: The helpful explanation linked in a comment on the question you linked is defective because it applies to all continuous probability distributions.

>Edit: The helpful explanation linked in a comment on the question you linked is defective because it applies to all continuous probability distributions.

No, why do you think so?

Re: Zerocoin: making Bitcoin anonymous

#28

Post by mahyarm »

dragontamer wrote: post #8

Since BTC is expected to be regulated like a currency, wouldn't participating in Zerocoin be basically money laundering? If that is the case, participating in the Zerocoin network itself would be a crime. I don't think this is going to go anywhere. And if it does, then hope that the Secret Service doesn't catch you even touching this stuff...

Think of bitcoin as the bank account, and zerocoin as ATM withdrawals of cash. It's a leaky metaphor, but it fits.

Since withdrawing money from an ATM is not money laundering, it works.

What makes it anonymous is that anyone can now start a 'bitcoin account' with purely unconnected zerocoins without any AML paperwork to go through just like a real life equivalent of dumping stacks of cash at your no questions asked numbered bank account service.

Re: Zerocoin: making Bitcoin anonymous

#29

Post by anonymoushn »

consz wrote: post #26
anonymoushn wrote: post #18

Earlier quoted context omitted.

Could you point out the problem with such a distribution? It isn't immediately obvious that I cannot satisfy both axioms. Edit: The helpful explanation linked in a comment on the question you linked is defective because it applies to all continuous probability distributions.

>Edit: The helpful explanation linked in a comment on the question you linked is defective because it applies to all continuous probability distributions. No, why do you think so?

It contains the sentence "For any distribution, the sum of probabilities always equals 1" without the caveat that the sum is of a countable number of probabilities. It applies to every continuous distribution using the same argument, but with "the sum across all naturals" replaced with "the sum across the appropriate universe."

Re: Zerocoin: making Bitcoin anonymous

#30

Post by jasonlingx »

dragontamer wrote: post #8

Since BTC is expected to be regulated like a currency, wouldn't participating in Zerocoin be basically money laundering? If that is the case, participating in the Zerocoin network itself would be a crime. I don't think this is going to go anywhere. And if it does, then hope that the Secret Service doesn't catch you even touching this stuff...

> Since BTC is expected to be regulated like a currency Huh? I thought it's the opposite?
Post reply on HN