MProve-Nova: A Privacy-Preserving Proof of Reserves Protocol for Monero

A proof of reserves (PoR) protocol enables a cryptocurrency exchange to prove to its users that it owns a certain amount of coins, as a first step towards proving that it is solvent. We present the design, implementation, and security analysis of MProve-Nova, a PoR protocol for Monero that leverages the Nova recursive SNARK to achieve two firsts (without requiring any trusted setup). It is the first Monero PoR protocol that reveals only the number of outputs owned by an exchange; no other information about the outputs or their key images is revealed. It is also the first Monero PoR protocol where the proof size and proof verification time are constant, i.e. they are independent of the number of outputs on the Monero blockchain and the number of outputs owned by the exchange. To achieve constant verification times, MProve-Nova requires a preprocessing step which creates two Merkle trees from all the outputs and key images on the Monero blockchain. MProve-Nova consists of two Nova-based subprotocols, a reserves commitment generator (RCG) protocol used to compute a commitment to the total reserves owned by an exchange and a non-collusion (NC) protocol used to prove non-collusion between two exchanges. For the RCG protocol, we observed proof sizes of about 28 KB and verification times of 4.3 seconds. For the NC protocol, we observed proof sizes of about 24 KB and verification times of 0.2 seconds. Proving times for both protocols increase linearly with the number of outputs owned by the exchange but remain independent of the number of outputs on the Monero blockchain. On average, the RCG protocol required about 42 minutes per 1000 outputs and the NC protocol required about 5 minutes per 1000 outputs.