Incomplete information games on Bitcoin: Solving blockchain privacy dilemma using zero knowledge
Games with incomplete information can be developed on Bitcoin today since sCrypt has implemented zk-SNARKs.
Articles By Xiaohui Liu:
Programmable zero knowledge proofs using zk-SNARKs: part 3
sCrypt reimplement ZKKSP by leveraging the programmability of zkSNARKs. They simply combine elliptic curve point multiplication used in Part 2 and hashing library that resulted to Circom code.
Programmable zero knowledge proofs using zk-SNARKs: Part 2
sCrypt shows how to implement another sophisticated cryptographic primitive by simply “programming” it in zero knowledge language Circom: ring signatures.
Programmable zero knowledge proofs using zk-SNARKs: part 1
Developing a ZKP for a problem often requires the invention of a whole new cryptographic algorithm. It has no standard recipe and requires extensive and in-depth knowledge of cryptography.
ZK-friendly hash function MiMC in Bitcoin
The MiMC hash function is specifically designed to minimize circuit size and thus ZKP cost by using only additions and multiplications.
ZK-Rollups on Bitcoin: Way more scalable than on Ethereum
In this post, sCrypt implemented the first-ever ZK-Rollup (ZKR) directly on Bitcoin. They also showed why ZKR works better on Bitcoin than on Ethereum.
zk-SNARKs on Bitcoin: Run Zcash on Bitcoin
zk-SNARK is a powerful primitive for blockchain privacy and scalability, and in this article, sCrypt showed what zk-SNARK is and how to implement it on Bitcoin.
BLS signatures on Bitcoin—Pairing-based cryptography: Part 2
sCrypt have demonstrated how to verify a single BLS signature on Bitcoin and how BLS’s main power lies in aggregated signatures and keys.
Introducing Solidity to sCrypt transpiler: Run Ethereum smart contracts on Bitcoin
The transpiler facilitates developers to migrate their applications onto the Bitcoin network from Ethereum and other Solidity/EVM-compatible blockchains without writing code from scratch.
Bilinear pairings on Bitcoin—Pairing-based cryptography: Part 1
In this article, sCrypt demonstrates how pairings can be implemented directly on Bitcoin and thus enable all kinds of pairing-based cryptography applications previously thought impossible.
Ring signatures in Bitcoin: Run Monero on Bitcoin
A ring signature is a digital signature that allows a message to be signed by a member of a group, or a ring. It proves that someone in the ring signs, but there is no way to tell who the signer is.
Zero-knowledge puzzles
sCrypt generalizes the proof of knowledge of a private key using zero-knowledge proof techniques, constructing arbitrary complex puzzles, called zero-knowledge puzzles, as spending conditions.