We have empirically demonstrated that any Turing machine can be simulated on Bitcoin and thus definitively proven it is Turing-complete¹. We have implemented a Turing machine that recognizes balanced parentheses and deployed it on the Bitcoin blockchain. Any other Turing machines can be simulated in the same way.
A Turing…
Previously, we have shown a novel and private way to purchase Bitcoin vanity addresses, using Zero-Knowledge Key-Statement Proof. …
Building upon the foundation laid out in previous parts of the series, we have demonstrated how to implement relative locktime in Bitcoin, without new opcode OP_CheckSequenceVerify.
A timelock restricts the spending of some bitcoins until a specified future time or block height. There are two types of timelocks:
The total number of transactions in a block is an important piece of information. We show how to obtain it without a trusted third party, which is considered impossible previously.
Let us denote the length of a Merkle path as n. The number of leaves, i.e., number of transactions in…
Block header contains timestamp when the block is created. But often we want to access block height, which is not included in a block header. We devise a novel technique to fetch block height trustlessly, which is included in coinbase transactions.
A coinbase transaction is the first transaction in a…
In the last post, we introduced a way to access a block and transactions within it with minimal trust. We extend it to include a chain of blocks in this article. Using the technique, we develop a simple betting contract based on block time. …
Smart contracts have no knowledge of the outside world and have to rely on oracles to import external data in general. We have shown two ways to import data from oracles before, based on Rabin signature and ECDSA. In this article, we show it is possible to access a specific…
We develop an efficient algorithm to verify arbitrary data signed by a certain party in Bitcoin smart contracts. Compared to previous signature algorithm based on Rabin signatures, it is based on ECDSA and thus reuses native Bitcoin keys to generate and verify signatures directly.
Bitcoin smart contracts require oracles to…
nChain white paper #0488 titled Zero-knowledge key-statement proofs introduces a zero-knowledge proof (ZKP) that proves a private key, corresponding to a given public key, satisfies certain requirements, while keeping the private key confidential. We have implemented it and applied it to purchasing bitcoin vanity address trustlessly. …
A forward contract is a derivative between two parties to buy or sell an asset at a specified future time at a predetermined price. Forwards are a very common instrument to hedge against volatility. …
sCrypt Inc (https://scrypt.io) is a company with a mission to provide integrated on-chain smart contracting solutions using the original BitCoin Protocol on BSV
