1.Ring signatures as currently implemented in CryptoNote currencies also have limitations concerning practical ring size (the number of other outputs you are taking) as the size of a transaction grows linearly as the ring size increases. This is why by Monero has a relatively small ring size of 11. This means on a per transaction basis, the anonymity is limited by the number of participants in the ring. Blockchain analysts although they might not be able to prove transactions are linked, they can calculate the odds that they are. This is primary drawback of Cryptonote is that it doesn’t break the links between transactions but merely obscures it with decoy inputs and outputs.
Another criticism of CryptoNote is that if there’s a weakness in its ring signature implementation or a reasonably powerful quantum computer becomes feasible, the entire blockchain history is deanonymized and retroactively exposed.
2.A minted zerocoin is represented by a public bitstring, which is a commitment to the serial number but hides the serial number at the time of minting. Users are supposed to choose a random serial number to ensure that it is unique (with very high probability). However, an attacker can, instead of taking a new random serial number, freely choose the serial number when he mints a zerocoin.
This leads to the following attack: An honest user tries to spend her (honestly generated) zerocoin and sends the spend transaction (including the serial number) to the network. An attacker, which is assumed to have control over the victim’s network, now blocks that message such that it never reaches the nodes of the cryptocurrency. Then the attacker mints a new malicious zerocoin with the exact same serial number. The attacker can now spend this maliciously zerocoin, revealing the serial number.
Some care is required when doing Sigma mints and spends. Users have to keep coins minted before they intend to spend to prevent timing attacks
- Lelantus is a creation of Zcoin’s cryptographer Aram Jivanyan. Lelantus extends the original Zerocoin functionality to support confidential transactions while also significantly improving on the protocol performance. Lelantus further expands on Sigma by removing the requirement for fixed denominations and also allowing for direct anonymous payments that do not reveal amounts.
4.Pro. Very high anonymity in the many thousands (if not more) with a single mint and spend transaction and completely breaks transaction links between addresses.
Con. Incorrect implementation or leakage of trusted setup parameters can lead to forgery of coins.
5.It is the number of how many decoys that can be included in a transaction using ring signatures on Monero.It can be possible to analyze since but 11 is a low anonymity set but the anonymity level increase with the number of transactions.