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Topic: Zerocoin: Anonymous Distributed E-Cash from Bitcoin - page 5. (Read 37796 times)

sr. member
Activity: 404
Merit: 362
in bitcoin we trust
Here's a concrete example of [...] a system with properties between Zerocoin, and conventional chaum banking systems. First you deposit your funds with the chaum bank, and receive a chuam token back.

The limitation I see with Chaum credentials, for off-chain transactions backed by bitcoin is that the transaction server could issue more chaum-coins than there are bitcoins, and you will never know until you find your chaum-coin is irredeemable because the bank is out of bitcoins, having redeemed them itself under a pseudonym with extra unadvertised chaum-coins it minted for the purpose.  Because they are not linkable you cant make a chaum-coin lock an on-chain bitcoin nor collectively all issued chaum-coins also cant lock a claim to the pool of on-chain backing bitcoins.  (Or more likely the bank gets away with it for a while, like an over-leveraged fiat bank with off-book liabilities until there is a run on the bank).

(And I guess its been tried, monetas OpenTransactions system implements David Wagner's blind MAC (in the form of Ben Laurie's lucre library) something similar to Chaum and I think is flexible enough to issue Chaum-alike credentials for bitcoin).

Thats because while the Chaum bank can demonstrate it is holding some bitcoins, the coins are blind and not linkable.  So you cant tell when an extra coin is used (that was not backed by bitcoin) to claim a not yet spent bitcoin, rightly belonging collectively to the set of bitcoin backed chaum-coins.

You may even be able to ditch the central bank aspect and turn it into an alt-coin consensus system where the participants come to consensus about the state of the ledger without having to trust any one participant.

That could be interesting, but the chaum-blinding doesnt directly work as the way bitcoin consensus is to put it inside a merkle hash inside a massive hashcash stamp.  Maybe you could put it inside an RSA accumulator instead, which is a more blinding friendly algebraic construct.  However that is basically what ZeroCoin is trying to optimize.

Adam
sr. member
Activity: 269
Merit: 250
What ticked me off is the quote from Wikipedia in the context of adam3us signature

Also while it is true that I invented hashcash (1997 hashcash.org), I am not claiming bitcoin is some simple extension, bitcoin has actually several key innovations that no one succeeded with before.  And not for lack of trying: there were a number of people on the cypherpunks list who were exceedingly interested in ecash, viewed it as the holy grail, and tried hard for many years (say 1995-2005 range) to figure out how to deploy ecash.



Only Satoshi can tell what kind of influence it was, do you have any quotes? If you compare technical details of those two systems then it's like computer vs abacus

You should actually read Satoshi's paper before getting involved in such arguments. Adam's work is cited directly:

Quote
To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proofof-work system similar to Adam Back's Hashcash [6], rather than newspaper or Usenet posts.

My question about a quote from Satoshi was actually a serious one, there is a lot of things I missed or don't know.

P.S. sorry for the off topic, won't post about it here any more.
member
Activity: 104
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Has this been completed?
legendary
Activity: 1120
Merit: 1152
Here's a concrete example of how a more flexible Bitcoin scripting language would allow the creation of a system with properties between Zerocoin, and conventional chaum banking systems. Credit goes to Gregory Maxwell for the basic concept:

First you deposit your funds with the chaum bank, and receive a chuam token back.

The bank maintains a txout on the blockchain with funds >= all outstanding tokens, and with a scriptPubKey of the following form:

Code:
if scriptSig contains proof of a valid token
   and spending transaction contains a txout with the same restrictions:
        return True

Now I can provide proof to the blockchain itself that I am entitled to receive the value of my token back, and I can do so without the co-operation of the bank.

Totally off-chain transactions, IE chaum-for-chaum exchanges, can be handled as well by having the bank include all outstanding tokens in a merkle tree, and signing the tip of that tree along with an ever increasing serial number:

Code:
if signature of the tip of the tree is valid:
    let n = serial number in the signature
    let m = existing serial number
    if n > m
       and spending transaction contains a txout with similar conditions, but n as the serial number:
           return True
else if block height > y:
    if spending transaction contains the redemption code (first example):
        return True

Now I can "spend" the txout with ever increasing serial numbers. This allows multiple different users, each of whom may have a different idea of what the outstanding token set is, to converge to the last valid set of tokens. If they do so randomly that will happen in about log2(n) steps.

After the timeout the txout goes into the state of allowing people to get their funds back, and again, without the co-operation of the service any token can be turned back into Bitcoins. Of course, some of the tokens may be of too small a value to economically redeem, but in that case we're just back to the "pure-punishment" case.

I'm leaving out a lot of details of course, but in general what's nice is we get the anonymity of Zerocoin and off-chain microtransactions in one system. The trust in the central bank maintaining the ledgers is fairly minimal, and there can be as many of these banks as you want. The system can easily scale to extremely large transaction volumes without a corresponding increase of the blocksize. There may also be some clever way to remove the requirement for the bank and maintain the ledger via an alt-coin consensus system.

We could implement this with a soft-fork to Bitcoin that extends the scripting language with new opcodes and merklized abstract syntax tree support. My very rough guess is that it's a year long project to get the new scripting code written and tested, and maybe another year to deploy on mainnet.
legendary
Activity: 1120
Merit: 1152
So maybe the privacy policy types of things get decided by competing sub-chains and off-chain transactions in such a bitcoin world.  And seemingly its not obvious how to do sub-chains and off-chain transactions without trust for double-spend protection.  (Which is why things like fidelity bonds come up in this scenario).

A good way to think about the issue is that a digital currency can be either based on consensus, authority, or detection and punishment.

Authority is the easiest to understand, that's just how PayPal works. Authority-based currencies have the best scaling properties because with 1 authority, n transactions results in n work. Trust in an authority-based system is absolute at the protocol level.

Consensus is how Bitcoin works, but because everyone needs to have the full transaction history, n transactions results in n^2 work. Of course, you can cheat and reduce the number of full nodes out there, but it starts looking increasingly like an authority based currency. Trust here is again absolute, but you are only trusting a majority of participants in the consensus voting scheme.

Detection and punishment systems are a mixture of the two. You trust some local authority, but you maintain automated ways to detect that fraud has occurred, and automated ways to punish that fraud. Unfortunately in Bitcoin as it stands the best way we can punish fraud seems to be to just stop doing business; fidelity bonds make that action expensive for the fraudulent party, but they aren't perfect. With some changes to how Bitcoin scripts work we can turn a proof of fraud into a direct punishment, or even an action that triggers a refund of the funds held by the third party, but that will require a soft-fork at least and a new scripting system. How these systems scale really depends on how efficient detection is, but n*log(n) work appears to be a good rough estimate.

We do need more work on the mechanics of detection, especially with looking into the possibly of changing the scripting language so that punishment/refunds can be done directly.

At the same time, at worst the scaling approach many are advocating turns Bitcoin into an authority based system in the long run, and at best turns it into a detection and punishment system, albeit one with fairly limited punishments that themselves can cause serious problems for the system in terms of technical complexity and stability.
sr. member
Activity: 404
Merit: 362
in bitcoin we trust
So apart from the political blather this bit seems to be like a potentially interesting idea, perhaps other people had the same idea before

But I do think bitcoin ideally needs to find an efficient way to fix the fungibility problems with taint.  [...] If there were identities separate from coin addresses, you could imagine payee/recipient losing privacy on payer complaint, without the payee losing ability to make further payments with payment privacy.  ie the payee is expected to repay the value, not that the coins themselves become traceable.

ie why not as a design objective try to separate identity from coins.  So you make the coins payee and payer anonymous, and then each user has a wallet identity/pseudonym that maybe optionally disclosed to the other party, or revealed to other party or to the auditor in event of dispute.  In that way we avoid taint, and yet the privacy and anonymity of the payment system becomes more arbitrarily tunable and even negotiable between parties, or set by system default.  Taint and tracability of taint is bad because it affects fungibility (in a p2p respendable ecash system like bitcoin, random users end up holding retroactively tainted and reduced value or unspendable coins through no fault of their own, and this erodes confidence).  But a system may like to offer or aim for a specific privacy level or traceability of amounts and identities.  Those things thereby become separable.  Nice Smiley

Now all we have to do is find a way to make zerocoin efficient.  (And that seems to be the question of the hour - its not at all obvious how to do that).

Actually its an open question how far bitcoin direct chain transactions scale, so maybe there is some hierarchy of off-chain (or sub-chain) that evolves eg around miners, exchanges, or p2p sub-chains that offer lower value coins, that backed by the main chain but not detail validated by it.  The supposition being that if bitcoin does hit a scalability limit (fails to scale as fast as its adoption), the minimum effective transaction value amount that is economical to send due to fees will go up, a lot.  Maybe the main chain is used for inter-chain clearing and investment level bitcoin holdings.

So maybe the privacy policy types of things get decided by competing sub-chains and off-chain transactions in such a bitcoin world.  And seemingly its not obvious how to do sub-chains and off-chain transactions without trust for double-spend protection.  (Which is why things like fidelity bonds come up in this scenario).

Adam
sr. member
Activity: 404
Merit: 362
in bitcoin we trust
I thought Gavin said ordinary people don't care much about anonymity. I'm not sure I concur, but it is a valid and important distinction between privacy and anonymity. With the right tools bitcoin does well with the former. Zerocoin addresses the latter.

You can get privacy without anonymity, eg as with the committed coins idea https://bitcointalksearch.org/topic/blind-symmetric-commitment-for-stronger-byzantine-voting-resilience-206303, only the sender and the recipient get to see the coins and who is spending to who.  (Unfortunately the committed coin privacy is not ideal because later people in the transaction chain of committed-form respends necessarily have to learn all previous details for validation reasons).

Some of the privacy focused ecash systems distinguished between payer anonymity and payee anonymity.  As a buyer you dont necessarily want all your payments to allow the public, the (ecash) bank nor the merchant to track which say ebooks you are reading.  It none of their business.

However the usual argument to blackmail crime scenario is that the criminal cant do that if there is only conditional payee anonymity (ie the spender colluding with the ecash bank can identify who the receiver is).  In bitcoin there is no bank to collude with, but you could imagine arbitrators in that role, or that the payee is identified to the payer (but no one else).  And of course the identify the recipient ignores identity theft, and assumes criminals are mindless non-adaptive automatons so its a fairly weak argument IMO.  In any system that strips privacy, the people who suffer loss of dignity and privacy invasion are the normal users, the criminals can still get privacy via identity theft, fake identities, buying fake identities from corrupt employees of government id issuers etc.  And criminals still launder money en-masse even with regular banks.   HSBC which reportedly laundered $880m of significantly dirty mexican drug cartel and even terrorist money and faces a $1.9b fine.  http://www.guardian.co.uk/business/2013/may/23/hsbc-court-threat-money-laundering-charges  Probably HSBC are going to walk away with the fine only (too big to jail despite the posturing).

Another possibility is it would be technically possible for the spender to be convinced who the recipient is without being able to prove it to other people eg with a ring signature, non-transferable signature, or designated verifier signature (the spender being the designated verifier).

Being able to sell things anonymously is a different and actually separable feature.  But people have also made pretty convincing arguments about why individuals should have the right to retain privacy while selling physical or virtual goods in a free society.

But I do think bitcoin ideally needs to find an efficient way to fix the fungibility problems with taint.  Payer privacy without payee privacy might not fully fix that as a payer who claims he didnt make the payment (claims the thief made the payment using the victims wallet to the thief) the victim would then identify the recipient.  If there were identities separate from coin addresses, you could imagine payee/recipient losing privacy on payer complaint, without the payee losing ability to make further payments with payment privacy.  ie the payee is expected to repay the value, not that the coins themselves become traceable.  However even then when identity is some random public key with no certification, its really not much of a threat to burn an identity.  Fidelity bonds perhaps are closer to network identities with some cost to losing.

Even in the physical world with conventional banks, once non-petty criminals are involved "identifying the perpetrator" becomes a fuzzy and useless fig-leaf fast as they identify a victim, or a fake identity bought from a corrupt government employee, or dupe the issuer - the RA stage is usually inherently pretty weak.  Criminals rent identities (money mule), buy or create fake identities, shell companies etc.

Finally to note a payment system could obviously have emergency tracability added to it as noted in the zerocoin paper.  Its typically easy technically to selectively weaken a protocol.  The problem is if you want it at all, you want emergency tracabiliy to be restricted to genuine emergencies, not drag-net fishing, not tracing of petty crimes.  Law enforcement are not always so clever about drawing lines there so you get mission creep until jay walking is an emergency.  eg in the UK I read a local council abused crime surveillance cameras to trace people who were bending the rules about which area they lived in to get their kids into a better school!  Next up people not pooper scooping their dog.  You know those things were weakly approved by society for terrorism clean up and maybe, arguably, serious organized crime.

Some ecash crypto papers have talked about system limits like payments are fully untraceable if they are under some amount (eg $10k like paper cash reporting limits) or under some amount per day per user.  Another limit can be the "emergency" access is limited to 1% of traffic period, more is not cryptographically possible.  Or I think alternatively and more simply access requires cooperation from involved users would be a nice balance.  Everyone has to transact with someone, and most transacting parties have no particular interest to protect some organized crime activity that rented a server or car from them.

Anyway the whole thing is a big mess.  And it's hard to maintain binary fungibility in the face of grey fuzzy privacy/traceability, and court ordered mission creep.  Computers do binary well so to me that is the natural physics of crypto and p2p virtual payments: irreverasable is cheaper than charge-backs (cash over credit cards), and there is no partially irrevocable.

Probably in an actual free society, people would understand that more people being killed by furniture falling on them than by terrorists should be sort of factored in in terms of spending and focus, and societal balance.  Obviously the people charged with cleaning up and infiltrating these things are too involved for perspective, but they work for society not the other way around.

The UK had its share of history with IRA blowing various stuff up, the US news typically in that era referred to the IRA as freedom fighters, some US factions even funded them, and yet the sky did not fall, eventually the UK lost their face of "we do not talk with terrorists", the IRA became involved  in the political process, some political prisoners were freed, and now things are not blowing up.  The UK government got up to some pretty shady things in the history of the troubles also.  Its just possible that the current problems have an element of blow-back and two sides to any argument also.  Its kind of interesting from inability to learn from history that the UK government finally admitted and will compensate victims of its past torture of kenyan resistance fighters and civilians including Obama's grandfather in kenya troubles, and here is Obama presiding over the next generation of the same picture (the powerful torturing the weak for attempting asymmetric and reactive warfare).  That still seems to me like a retrograde step, trials were heard at nuremberg about such activities in the past for good reason.

Adam
legendary
Activity: 905
Merit: 1012
I thought Gavin said ordinary people don't care much about anonymity. I'm not sure I concur, but it is a valid and important distinction between privacy and anonymity. With the right tools bitcoin does well with the former. Zerocoin addresses the latter.
legendary
Activity: 1526
Merit: 1134
Only Satoshi can tell what kind of influence it was, do you have any quotes? If you compare technical details of those two systems then it's like computer vs abacus

You should actually read Satoshi's paper before getting involved in such arguments. Adam's work is cited directly:

Quote
To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proofof-work system similar to Adam Back's Hashcash [6], rather than newspaper or Usenet posts.

See section 4.

And yes, discussions about p2p mixing are quite old, that thread I'm quoted in is from July 2012.

I'm not sure Gavin is correct when he says ordinary people don't care about privacy. They care very much, hence the proliferation of scare stories in the media, the success of Facebook over MySpace, etc. That doesn't mean people will go to any lengths to get it from any and all parties though. Not all privacy adversaries are created equal.

legendary
Activity: 3920
Merit: 2349
Eadem mutata resurgo
Adam : any chance you can get that stuff into Latex or some equation displayer ... my eye's are allergic to math with ascii text Sad

One way is to write them at this site
http://www.codecogs.com/latex/eqneditor.php

... and link them into the text here either as gif or html if the forum supports it.(bit hacky but it works)
sr. member
Activity: 404
Merit: 362
in bitcoin we trust
thank you for that concise explanation. i think i am 70% "there" to understand the basic properties of zerocoin.

can you elaborate or give links on the operators "^" and "*" is this the actual power and multiplication? then how can c be prime if it is defined as a multiplication of two powers?

[edit used sup and sub for exponent and subscripts]
^ is power modulo some prime or RSA modulus depending on the situation and * is modular multiplication.

So the A=uc1c2...cn is modulo N an RSA modulus N=P*Q two primes P & Q.  A is the accumulator.   Note c1c2..ck gets pretty big as users cant reduce it as they dont know phi(N) = (P-1)(Q-1) - no one does as its deleted after parameter generation.  u is some fairly chosen quadratic residue (square numbers mod N) ie there exists u' st u=u'2 mod N.

This is the P & Q where you unfortunately get to trust someone to delete them.

Next for each coin c=gshr mod p, where p is a fixed prime (not the same prime as P) actually a strong prime (where p = 2q+1, or even p=2wq+1 for some integer w, to get a smaller q).  Because c=gshr mod p c can be prime ie gshr is clearly not prime by definition (it divides by g, h, g2 etc) but gshr mod p can be prime.  It quite a bit of work of trying random commitments to find a prime c though.  I tried coding it in openSSL and it wasnt that fast eg c=gshr check if its prime, if not c'=c h mod p (so that c'=gshr+1 mod p) and repeat.  Prime density is not so great at those sizes.

g and h are two generators in the shnorr group of size q.

So its curiously using two completely different groups - an RSA group for the accumulator and a Schnorr group for the pedersen commitment sounds odd but it doesnt really matter they are independent.

Now you can easily choose a c with two commitments in it (trying to get two zerocoins for the price of one bitcoin): prime c=gs1hr1 gs2hr2 mod p=gs1+s2hr1+r2 mod p.  

However to cheat and prove/spend two separate witnesses and zerocoins paid for with one bitcoin you need to prove you know A=w1c1 mod N and also A=w2c2 mod N with w1=uc2c3...cn mod N and w2=uc1c3...cn mod N.  However A=uc c2c3...cn) mod N because we paid for zerocoin c with our bitcoin.

So the only way to cheat is find c1,c2 such that c=c1 c2 or c=c1c2 mod phi(N).  You cant find c=c1 c2 because c is prime.  And you cant find c=c1 c2 mod phi(N) because you dont know phi(N) = (P-1)(Q-1) because P & Q are deleted during zercoin genesis.

If you could find such a c1 and c2 you would have found phi(N) by definition, and using that you can factor N trivially - ie thats impossible unless you can break RSA.  (You need phi(N) because you have to reduce the exponent by phi(N) with RSA ie A = uc1c2 mod N = uc1c2 mod N = uc1c2 mod phi(N)) mod N.

Now if you did know phi(N) = (P-1)(Q-1) you could clearly create multiple zerocoins for the price of one bitcoin.  So thats the trust in the person who sets up the value of N during zerocoin genesis.

Adam
legendary
Activity: 1106
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Sorry if this is somewhat off-topic, but could OpenTransaction's off-chain transactions and blind signatures help with this at all? (even though it would depend on some third party running an OT server)

OT already have its cash-only mode which is as anonymous as it gets.

The point of ZeroCoin, AFAICT, is precisely not to depend on a server and just use the blockchain to achieve the same result. (I confess I haven't read ZeroCoin's paper and I have no idea how it works)
legendary
Activity: 1680
Merit: 1035
Sorry if this is somewhat off-topic, but could OpenTransaction's off-chain transactions and blind signatures help with this at all? (even though it would depend on some third party running an OT server)
hero member
Activity: 668
Merit: 501
thank you for that concise explanation. i think i am 70% "there" to understand the basic properties of zerocoin.

can you elaborate or give links on the operators "^" and "*" is this the actual power and multiplication? then how can c be prime if it is defined as a multiplication of two powers?
sr. member
Activity: 404
Merit: 362
in bitcoin we trust
Call me crazy, but if the algorithm is able to determine that you own the blinded coins, couldn't you in effect determine which blinded coins? By just doing the proof of work for each mint? And just use that to connect the dots?

The ZKP in zerocoin is able to prove you know a w and c such that A=w^c (where w=witness, c=commitment/coin and A is the global accumulator value at a given point in time) without revealing w and c.  c has the form c=g^s*h^r where s is the coin serial number (revealed) and r is a random number never revealed.  c=g^s*h^r is a pedersen commitment, you can think of it like a hash function c=H(s,r) in that its hard to find either s or r (because it one way).  Also its collision resistant so its hard to find another s,r value eg to find g^s*h^r==g^s'*h^r' even if you know what s and r are.  That like symmetric hash function also hard to find H(s,r)==H(s',r').  The difference is pedersen commitments involve algebraic operations on big numbers and the hardness of discrete logs and so are easier to prove things about (ie because you can usefully multiply them etc - hash functions like SHA256 just make a big mess of their inputs to achieve collision resistance.)

So putting that together zerocoin have a ZK signature of knowledge ZKSoK[tx]{(c,w,r):A==w^c and c==g^s*h^r} ie c,w,r are not revealed, tx is the transaction that is revealed and signed by the zerocoin spend/signature (eg tx = spend this zerocoin to this bitcoin address), s is revealed and stored and is the serial number that is recorded to avoid double-spending.  ie combining it shows that A==w^(g^s*h^r) and they were able to find a somewhat large way to prove that without revealing c,w,r.  Its large because it involves multiple cut-and-choose rounds as each round is only 50:50 convincing that what the prover claims is true.  After 80 rounds its security is 1/2^80 which is quite good.  (Though bitcoin aims for 2^128 which is more, they only used 80 to save space - 40kB was already unfortunately large for the zerocoin spend ZK "signature".

s is revealed and is the coin serial number, so its important that r is not revealed otherwise anyone could calculate c=g^s*h^r and just scan for that in the list of zerocoins de-anonymize the coin spends .  Fortunately because of the collision resistance of the pedersen commitment (hash function) not even the owner of the coin can create different s, r equal to the same c so he cant get two coins from one that way.  But to prevent the owner of the coin creating c=g^s'*h^r' * g^s * h^r and then proving two separate coins (and that would work because A = u^(c1*c2 *... cn) for all zerocoins ci) they further require that c be a prime number.  So you're not proving its prime via the ZKP when spending, but you are proving it when you create the zerocoin - all the miners check if c is prime (as c is revealed at that point).  So thats why c is prime.  (I had to ask Matthew Green that it was puzzling me as making c prime is moderately expensive, and why it takes 0.5 - 2 seconds to just create a zerocoin, and the Camenisch and Lysyanskaya paper the zerocoin accumulator comes from uses c prime only for  different reason that zero coin doesnt need - membership deletion).

It seems counter-intuitive that you can prove things without revealing them but thats what ECDSA does too - it proves that the signer knows the EC discrete log.  Its basically because you can see that only someone who knew the discrete log could have computed the signature, and yet anyone can see that the signature is valid.  The ZKP is the same just more complicated.

Adam
sr. member
Activity: 287
Merit: 250
Call me crazy, but if the algorithm is able to determine that you own the blinded coins, couldn't you in effect determine which blinded coins? By just doing the proof of work for each mint? And just use that to connect the dots?
sr. member
Activity: 404
Merit: 362
in bitcoin we trust
Adam very well was in a position to be Satoshi - bitcoin is just a different application of the same technical ideas. I will take his word that he is not. If you want to debate it, you should probably do it somewhere else.

Taking a leaf from Meni Rosenfeld  https://bitcointalksearch.org/topic/meni-rosenfelds-vanity-thread-121314 I figured I'd create a thread for people such as Serith (and he seems not alone) to dis me in. 

https://bitcointalksearch.org/topic/m.2371674

Go for it Smiley


And now back to the ring signature sub-thread.  Ring signatures and accumulators are closely related with the convenient exception that ring signatures are directly anonymous (not requiring a ZKP of set membership like zerocoin and Sander & Ta-Shma's auditable electronic cash that predates zerocoin in its auditability.)

Most of the ring signatures are however also not compact (with signature size linear in the number of members of the ring).  With bitcoin thats the anonymity set size, analogous to the total number of zerocoins so in any real use thats probably worse than zerocoin.

This Shoup ring signature however has a small constant size:

http://www.shoup.net/papers/subring.pdf

(trying to decipher now) however it is based on an accumulator and sigma-proof (ZKP) not figured out how efficient that proof is yet to understand if its better or worse than zerocoins set membership proof, nor even if it could be directly used (membership proofs dont have to prevent multiple-uses, zerocoin does).

Adam
legendary
Activity: 905
Merit: 1012
Adam very well was in a position to be Satoshi - bitcoin is just a different application of the same technical ideas. I will take his word that he is not. If you want to debate it, you should probably do it somewhere else.
sr. member
Activity: 269
Merit: 250
Adam is justifiably proud of Hashcash, and it was an important influence on Bitcoin.

Only Satoshi can tell what kind of influence it was, do you have any quotes? If you compare technical details of those two systems then it's like computer vs abacus
hero member
Activity: 714
Merit: 500
Martijn Meijering
Adam is justifiably proud of Hashcash, and it was an important influence on Bitcoin.
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