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Mathematics Behind the Zcash
(2020)

Among all the new developed cryptocurrencies from Bitcoin, Zcash comes out to be the strongest cryptocurrency providing both transparency and anonymity to the transactions and its users by deploying the strong mathematics of zk-SNARKs.
We discussed the zero knowledge proofs which is a basic building block for providing the functionality to zk-SNARKs. It offers schnorr and sigma protocols with interactive and noninteractive versions. Non-interactive proofs are further used in Zcash transactions where the validation of sent transaction is proved by cryptographic proof.
Further, we deploy zk-SNARKs proofs following common reference string as public parameter when transaction is made. The proof allows sender to prove that she knows a secret for an instance such that the proof is succinct, can be verified very efficiently and does not leak the
secret. Non-malleability, small proofs and very effective verification make zk-SNARKs a classic tool in Zcash. Since we deal with NP problems therefore we have considered the elliptic curve cryptography to provide the same security like RSA but with smaller parameter size.
Lastly, we explain Zcash transaction process after minting the coin, the corresponding transaction completely hides the sender, receiver and amount of transaction using zero knowledge proof.
As future considerations, we talk about the improvements that can be done in term of decentralization, efficiency by comparing with top ranked cryptocurrencies namely Ethereum and Monero, privacy preserving against the thread of quantum computers and enhancements in shielded transactions.