I'm curious to understand what the main differences between Monero, DASH and to-be released Zcash are. I would also like to know what is the main improvement in Zcash, when compared to Dash and Monero.
Monero - A cryptocurrency that uses ring signatures, a type of cryptography that enables untraceable transactions. It is extremely unlikely that a transaction can be traced to a particular user. Monero is based on the CryptoNote protocol and possesses significant algorithmic differences relating to blockchain obfuscation
DASH - rebranded from "Darkcoin" to "Dash" on March 25, 2015. Dashcoin is an anonymous cryptocurrency and the first automatically mutating cryptocurrency created with CryptoNote technology. It offers instant transactions (InstantSend), private transactions (PrivateSend) and token fungibility.
ZCash - is said to offer total payment confidentiality while still maintaining a decentralized network that runs on public blockchain. Zcash transactions hide the sender, receiver, and transaction value. One must have the correct view key in order to see a transaction. This cryptocurrency uses zk-SNARK, which allows a network to have a secure ledger of transactions without making the parties and amounts transferred public.
From the Zcash protocol specification:
The basis of the privacy properties of Zcash is that when a note is spent, the spender only proves that some commitment for it had been revealed, without revealing which one. This implies that a spent note cannot be linked to the transaction in which it was created. That is, from an adversary’s point of view the set of possibilities for a given note input to a transaction —its note traceability set— includes all previous notes that the adversary does not control or know to have been spent. [footnote 3] This contrasts with other proposals for private payment systems, such as CoinJoin [Bitcoin-CoinJoin] or CryptoNote [vanSaberh2014], that are based on mixing of a limited number of transactions and that therefore have smaller note traceability sets.
Footnote 3 is:
We make this claim only for fully shielded transactions. It does not exclude the possibility that an adversary may use data present in the cleartext of a transaction such as the number of inputs and outputs, or metadata-based heuristics such as timing, to make probabilistic inferences about transaction linkage. For consequences of this in the case of partially shielded transactions, see [Peterson2017], [Quesnelle2017], and [KYMM2018].
Monero is a CryptoNote-based currency. It improves on the original CryptoNote by adopting some ideas from Confidential Transactions in order to hide transaction amounts (RingCT), but this does not change the fundamental limitation in traceability set size of the mixing approach. That is, Zcash fully shielded transactions have a fundamental advantage in the achieved privacy/anonymity relative to Monero. As the caveat explains, this advantage does not apply to Zcash partially shielded or transparent transactions (the aim is to deprecate these as soon as the fully shielded protocol provides comparable functionality).
Disclosure of interest: I'm a Zcash developer and I wrote the above section of the protocol spec.