Abstract
We show how the Bitcoin currency system (with a small modification) can be used to obtain fairness in any two-party secure computation protocol in the following sense: if one party aborts the protocol after learning the output then the other party gets a financial compensation (in bitcoins). One possible application of such protocols is the fair contract signing: each party is forced to complete the protocol, or to pay to the other one a fine.
We also show how to link the output of this protocol to the Bitcoin currency. More precisely: we show a method to design secure two-party protocols for functionalities that result in a “forced” financial transfer from one party to the other.
Our protocols build upon the ideas of our recent paper “Secure Multiparty Computations on Bitcoin” (Cryptology ePrint Archive, Report 2013/784). Compared to that paper, our results are more general, since our protocols allow to compute any function, while in the previous paper we concentrated only on some specific tasks (commitment schemes and lotteries). On the other hand, as opposed to “Secure Multiparty Computations on Bitcoin”, to obtain security we need to modify the Bitcoin specification so that the transactions are “non-malleable” (we discuss this concept in more detail in the paper).
This work was supported by the WELCOME/2010-4/2 grant founded within the framework of the EU Innovative Economy (National Cohesion Strategy) Operational Programme.
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Notes
- 1.
A real-life example of such situation is the recent case when the German tax authorities paid 4 million euro to an anonymous informant for a CD containing information about the German tax evaders with bank accounts in Switzerland [13].
- 2.
In the original Bitcoin documentation this is called “simplified \(T_{x}\)”.
- 3.
Technically in Bitcoin \([T_{x}]\) is not directly passed as an argument to \(\pi '_{i}\). We adopt this convention to make the exposition clearer.
- 4.
The reason is that it is impossible to construct a signature, in such a way, that it is a part of the message being signed.
- 5.
In this paper we usually treat input scripts as arguments for the corresponding output scripts. In reality, however, they are scripts in Bitcoin scripting language, which are supposed to push arguments for an output script on the stack.
- 6.
To read more about such deposits see [26].
- 7.
The server signs a transactions \( Fuse \) without seeing the transaction \( Put \) and a malicious client could try to send a hash of an existing transaction instead of \( Put \). Therefore, the server should use a fresh key every time to prevent itself from being tricked into signing a transaction spending some other transaction of its to the client.
- 8.
The only exception are the so-called generation transactions, which create new bitcoins and can have arbitrary input scripts (the script is called “coinbase” in this case). However, it is not difficult to ensure that each such transaction has a different hash, by using a new pair of keys for each generation.
- 9.
Except of that, what she can learn from her inputs and from the function being computed.
- 10.
The number of outputs created this way is limited and not greater than \(30\) as a bitcoin is not infinitely divisible. The smallest amount of bitcoins is called “satoshi” and is equal to \(10^{-8}\)
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We would like to thank the anonymous reviewers for their valuable comments.
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Andrychowicz, M., Dziembowski, S., Malinowski, D., Mazurek, Ł. (2014). Fair Two-Party Computations via Bitcoin Deposits. In: Böhme, R., Brenner, M., Moore, T., Smith, M. (eds) Financial Cryptography and Data Security. FC 2014. Lecture Notes in Computer Science(), vol 8438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44774-1_8
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