RobinLinus

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RobinLinus

The following script allows everyone to spend; the shorter your signature the earlier you can spend.

OP_SIZE
OP_CHECKSEQUENCEVERIFY OP_DROP

OP_CHECKSIGVERIFY

The point R = 1/2 G has the smallest known x coordinate -- x = 0x3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63. If the public key is chosen P = 1 G then the ECDSA signature becomes s=2(H(m)+x). So, the smaller H(m) the smaller s (as long as it is bigger than x ~ 2^165). Thus, the above output is spendable by the miner mining the lowest TX hash.

RobinLinus

Decaying MultiSig using nLockTime

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.

1. Alice, Bob, and Carol create a 3-of-3 regular MultiSig output.

2. Alice signs the output with nLocktime = x and SIGHASH_NONE.

3. She sends this partially signed TX to Bob and Carol.

RobinLinus

Order Relations for DLCs

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.

Number Format

We define B₁ to Bₙ to represent the adaptor points for oracle signatures of those bits of 𝑁 that are equal to 1:

RobinLinus

OR Operator for DLCs and PTLCs

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.

Motivation

Applications for the OR operator include Discreet Log Contracts (DLCs), adaptor signatures, and Point Time Locked Contracts (PTLCs):

RobinLinus

// 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

RobinLinus

Weighted Threshold Points

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.

RobinLinus

Improved Stealth Addresses

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 ).

Protocol

• All senders register on their first send a public key in a public directory.
• Recipients perform a DH key exchange with each sender key in the directory to derive all their potential receive addresses.
  • Sender key: A = aG
  • Recipient key: B = bG
• Shared secret: s = abG

RobinLinus

XOR Seed Splitting

A simple 2-of-3 seed splitting scheme for BIP39 seed phrases by Ruben Somsen.

Encrypt

1. Split your 24 seed words into share_A and share_B of 12 words each.
2. Pairwise XOR the words of the first share with the second share to derive the 12 words of share_C, the backup.

backup_1 = word_1 xor word_13
backup_2 = word_2 xor word_14

RobinLinus

Bitcoin-backed Fiat Money

A trust-minimised stablecoin for Bitcoin-backed fiat money. It mimics traditional banking. Dollar tokens (USDx) are created and destroyed based on collaterized loans.

Basic Protocol

1. Alice sends a collateral of 1 BTC to a bank to receive a loan of e.g. $40000 in USDx tokens created by the bank.
2. To redeem her collateral Alice has to pay back her loan within 4 years. To "pay back" means Alice destroys 40000 USDx.
3. If Alice does not pay her loan back on time then the bank sells her collateral to the market. To "sell" means the buyer destroys 40000 USDx.

This protocol requires that within a period of 4 years the BTC price always increases.