Cryptology ePrint Archive: Report 2020/312

Arcturus: efficient proofs for confidential transactions

Sarang Noether

Abstract: Confidential transactions are used in distributed digital assets to demonstrate the balance of values hidden in commitments, while retaining signer ambiguity. Previous work describes a signer-ambiguous proof of knowledge of the opening of commitments to zero at the same index across multiple public commitment sets and the evaluation of a verifiable random function used as a linking tag, and uses this to build a linkable ring signature called Triptych that can be used as a building block for a confidential transaction model. In this work, we extend Triptych to build Arcturus, a proving system that proves knowledge of openings of multiple commitments to zero within a single set, correct construction of a verifiable random function evaluated at each opening, and value balance across a separate list of commitments within a single proof. While soundness depends on a novel dual discrete-logarithm hardness assumption, we use data from the Monero blockchain to show that Arcturus can be used in a confidential transaction model to provide faster total batch verification time than other state-of-the-art constructions without a trusted setup.

Category / Keywords: applications / digital signatures

Date: received 12 Mar 2020, last revised 7 Apr 2020

Contact author: sarang noether at protonmail com

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Note: Fixed notation and renamed for clarity.

Version: 20200407:140741 (All versions of this report)

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