Charge Dollar bills with Bitcoins to create inflation-resitant cash. This idea originated in an old post on Bitcoin Talk. Here's a detailed writeup.
Now the note is worth 1 USD + 5000 sats.
A trust-minimised stablecoin for Bitcoin-backed fiat money. It mimics traditional banking. Dollar tokens (USDx) are created and destroyed based on collaterized loans.
This protocol requires that within a period of 4 years the BTC price always increases.
A simple 2-of-3 seed splitting scheme for BIP39 seed phrases by Ruben Somsen.
backup_1 = word_1 xor word_13
backup_2 = word_2 xor word_14
This is a scheme for stealth addresses which requires little computational overhead for the recipient to scan the chain. It builds upon many previous ideas. It reduces the overhead for scans from O( #TXs ) to O( #users ).
A = aGB = bGs = abG
For a threshold point over n points we can assign "weights" or "number of votes per key":
(T₁,w₁), (T₂,w₂), ...,(Tₙ,wₙ).
Instead of using each Tᵢ only once, we also use the keys Tᵢ+H(Tᵢ|1)G, Tᵢ+H(Tᵢ|2)G, ..., Tᵢ+H(Tᵢ|wᵢ)G during the creation of the threshold point. So, if Alice learns Tᵢ she learns the key for all of its votes.
Let's define the total number of votes as N = sum{wᵢ}. Now, we can choose any threshold t < N by enumerating all sums of subsets of size t. We can apply the OR operator to these sums to condense the threshold condition into a single point.
| // SPDX-License-Identifier: GPL-3.0 | |
| pragma solidity ^0.5.10; | |
| import "https://github.com/summa-tx/bitcoin-spv/blob/master/solidity/contracts/ViewBTC.sol"; | |
| import "https://github.com/summa-tx/bitcoin-spv/blob/master/solidity/contracts/ViewSPV.sol"; | |
| contract Peg { | |
| // | |
| // Security Parameters |
We construct an OR operator for adaptor points:
If Alice learns the dlog of T₁, or T₂, ..., or Tₙ, then she also learns the dlog of X.
This is possible using verifiable encryption (see "Juggling" by Shlomovits et al.). An OR operator allows to condense complex spending conditions into a single point. This prevents the combinatorial explosions which usually occur when using multi-oracles. An OR operator makes spending conditions easily composable. In theory, it even enables arbitrary computations on values provided by oracles.
Applications for the OR operator include Discreet Log Contracts (DLCs), adaptor signatures, and Point Time Locked Contracts (PTLCs):
We expect an oracle will publish some number 𝑁 by signing each of its n bits.
Given a constant c, we want to express the spending condition 𝑁 ≥ c in a single adaptor point.
The key idea is to construct an OR operator for adaptor points. This is possible with verifiable encryption. An OR operator allows to condense complex spending conditions into a single point. This prevents the combinatorical explosions that usually occure when using multi-oracles. An OR operator makes spending conditions easily composable. In theory, it even enables arbitrary computations.
We define B₁ to Bₙ to represent the adaptor points for oracle signatures of those bits of 𝑁 that are equal to 1:
A decaying MultiSig that requires no bitcoin script other than regular MultiSigs.
A 3-of-3 that decays into a 2-of-3 at block height x.
Alice, Bob, and Carol create a 3-of-3 regular MultiSig output.
Alice signs the output with nLocktime = x and SIGHASH_NONE.
She sends this partially signed TX to Bob and Carol.