Pairing-based cryptography is a variant of elliptic curve cryptography, which Bitcoin ECDSA signatures are based on. …

Run Monero on Bitcoin — We have implemented the first-ever Ring Signature in Bitcoin. Ring Signatures A ring signature is a type of digital signature that allows a message to be signed by a single member in a group, or a ring. …

Upgrade Bitcoin’s Elliptic Curve Without a Fork and More This is the third instalment of our collaboration with nChain. We would like to give special thanks to Dr Enrique Larraia for authoring the whitepaper this article is based on and helping guide the implementation. A standard payment transaction can be…

By Programming It in a Smart Contract — We develop a novel approach to emulate any SIGHASH flag, by simply coding the logic in a smart contract. It requires no protocol change and is thus much more practical and flexible than adding a hardcoded flag through a fork, every time a new use case is conceived. SIGHASH Flags A SIGHASH…

No Fork Needed — We have demonstrated how to implement Taproot on the original Bitcoin using contractless contract. We show that its follow-up proposal, Graftroot, can be implemented in a similar fashion. Graftroot in BTC Similar to Taproot, there are two ways to spend fund locked in an aggregated public key P, created by multiple parties: Cooperative…

Contractless Contract + MAST — We show how to implement Taproot using the original Bitcoin protocol without any changes, by combining contractless contract and Merklized Alternative Script Tree (MAST). Taproot in BTC Taproot is the biggest Bitcoin Core upgrade since 2017, supposed to improve its functionality. In Taproot, we tweak a public key P to get a new…

Hide Any Smart Contract in a Regular Payment Opportunistically — We invent a technique, called contractless contract, to faithfully execute any smart contract in a regular payment (P2PKH) transaction. It drastically improves the privacy and efficiency of arbitrary multiparty smart contract, when all parties cooperate. Contractless Contract We illustrate how contractless contract works between two parties. It can be extended to multiple…

By Reusing ECDSA Signatures — Bitcoin has many potential uses far beyond payments. Each block has a timestamp that is cryptographically secured. By recording data in a transaction and thus a block, it can be proven to any external auditor that the data has not been tampered with since a particular date. …