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I have read several comparisons between Monero and Pirate. Can someone please explain to me the objective pros and cons about their privacy offerings? Is one more secure than the other? What are the main differences between Monero vs. Pirate?

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Let's begin by discussing their backgrounds and privacy technologies.

Monero

Monero was launched in April 2014 under the reference CryptoNote protocol. Upon launch, the privacy protections were still better than comparable solutions at the time, but the privacy was weak by today's standards.

Monero uses ring signatures, RingCT, and stealth addresses to hide the sender, receiver, and amount for all transactions. There is no way to send a public transaction using the blockchain alone. Stealth addresses disassociate outputs from addresses. Ring signatures make the sending outputs (sources of funds) in transactions unclear/ambiguous. Ring Confidential Transactions (RingCT) hides the amount. All 3 are forms of zero-knowledge proofs.

Monero's ring signatures are not perfect at protecting against every possible heuristic, but they are good enough in most cases. If you use Monero to interact in strict thread models against colluding actors (including countries and regulated exchanges), then you may need to take extra precautions to "churn" your Monero to get enough privacy to meet your threat model. However, for someone making typical transactions, Monero provides excellent privacy.

Pirate

This is a new cryptocurrency launched in 2018. It claims to be a more private implementation of Zcash. It takes the same zkSNARK technology and makes it mandatory, vastly improving privacy by decreasing the amount of leaked metadata and transparent transactions.

PirateChain hides the sender, receiver, and amount for all transactions just like Monero. However, it offers even better theoretical untraceability protection. It can better hide the sending output by making it appear to come from a wider set of possible sources (keep in mind neither cases connect these sources to identities), rather than just a dozen or so with Monero.

PirateChain relies on Komodo's dPoW security and a trusted setup.

Comparison

Monero is a much larger network with more entropy. Far more people use Monero than Pirate, so it is much easier to hide in a crowd of other people. Pirate may offer theoretical advantages, but in reality, it is likely that these benefits are outweighed by the size of the network. Pirate may offer better privacy than Zcash; even though Zcash is more widely-used, the fully-shielded portion is less-commonly used. Furthermore, at the time of writing, Pirate does not support Sapling, so it takes a powerful machine several seconds to send transactions.

Furthermore, Pirate is less secure than Monero. Monero uses its own standalone blockchain and PoW system to secure it. Pirate uses Komodo's dPoW system. This system has its own (significantly smaller) set of miners. However, they claim it is secure since they "back up" the blockchain to Bitcoin. The actual effectiveness of this security mechanism has received little to no attention, and this claim has little to no academic support. As a result, we generally assume that Monero's much larger mining network makes it more secure, since we have no good way of evaluating the effectiveness of Komodo's security. Of course, Pirate relies on a trusted setup to provide anonymity, so if this was ever compromised, then they could mint new coins without detection.

Pirate claims to be the best of Zcash (ZEC) combined with the best of Monero (XMR) and secured by Komodo's (KMD) Delayed-Proof-of-Work (dPoW)." Though it takes some of the best components of Zcash, it has yet to include the new, better Sapling code. It has nothing to do with Monero in technology or overlapping community. The security model of dPoW has not been researched extensively, so it's dangerous to take their security claims at face value.

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