One-out-of-Many Proofs: Or How to Leak a Secret and Spend a Coin

I’m going to EUROCRYPT 2015 to present a new zero-knowledge proof that I’ve developed together with Markulf Kohlweiss from Microsoft Research. Zero-knowledge proofs enable you to demonstrate that a particular statement is true without revealing anything else than the fact it is true. In our case the statements are one-out-of-many statements, intuitively that out of a number of items one of them has a special property, and we greatly reduce the size of the proofs compared to previous works in the area. Two applications where one-out-of-many proofs come in handy are ring signatures and Zerocoin.

Ring signatures can be used to sign a message anonymously as a member of a group of people, i.e., all a ring signature says is that somebody from the group signed the message but not who it was. Consider for instance a whistleblower who wants to leak her company is dumping dangerous chemicals in the ocean, yet wants to remain anonymous due to the risk of being fired. By using a ring signature she can demonstrate that she works for the company, which makes the claim more convincing, without revealing which employee she is. Our one-out-of-many proofs can be used to construct very efficient ring signatures by giving a one-out-of-many proof that the signer holds a secret key corresponding to a public key for one of the people in the ring.

Zerocoin is a new virtual currency proposal where coins gain value once they’ve been accepted on a public bulletin board. Each coin contains a commitment to a secret random serial number that only the owner knows. To anonymously spend a coin the owner publishes the serial number and gives a one-out-of-many proof that the serial number corresponds to one of the public coins. The serial number prevents double spending of a coin; nobody will accept a transaction with a previously used serial number. The zero-knowledge property of the one-out-of-many proof provides anonymity; it is not disclosed which coin the serial number corresponds to. Zerocoin has been suggested as a privacy enhancing add-on to Bitcoin.

The full research paper is available on the Cryptology ePrint Archive.

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