Abstract
In this chapter, we discuss the basics of ring signature—a kind of anonymous signature that allows a user to sign on behalf of a self-formed group such that the verifier only knows that the signer is one of the users of this group but cannot find out the identification information (such as public key) of the real signer. We give the security model and a simple construction based on discrete logarithm setting. Then, we cover a variant called linkable ring signature, which provides linkability in addition to the property of a normal ring signature. Finally, we present a commercial application of (linkable) ring signature in blockchain called Ring Confidential Transaction (RingCT), which is the privacy-preserving protocol used in Monero, one of the largest cryptocurrencies in the world.
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Notes
- 1.
As of 4th January 2018 from https://coinmarketcap.com/.
- 2.
If the setup process can be trusted, we can eliminate \(H_2\) and simply put g as the public parameter.
- 3.
We note that ck will be privately sent to the user possessing account address pk, e.g., by using public key encryption: Suppose Alice wants to send a coin to Bob. Bob will first send pk to Alice. Alice then uses pk to encrypt ck and sends the ciphertext to Bob. No one except Bob can decrypt the ciphertext to get ck.
- 4.
Note that in this case, assuming \(pk_c\) has been generated by AddGen, the challenger knows all balances of the spent accounts and output accounts involved in the adversarial spends \(\{\mathcal {S}\}_{i=1}^{\nu }\).
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Liu, J.K. (2019). Ring Signature. In: Li, KC., Chen, X., Susilo, W. (eds) Advances in Cyber Security: Principles, Techniques, and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-13-1483-4_5
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