mirror of
https://github.com/ruvnet/RuView
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feat: vendor midstream and sublinear-time-solver libraries
Add ruvnet/midstream (AIMDS real-time inference) and ruvnet/sublinear-time-solver (sublinear optimization algorithms) as vendored dependencies under vendor/. Co-Authored-By: claude-flow <ruv@ruv.net>
This commit is contained in:
ruv
@@ -0,0 +1,669 @@
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# Blockchain-Based Distributed Linear System Solving
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## Executive Summary
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Blockchain technology enables trustless distributed computation where multiple untrusted parties collaborate to solve linear systems. By combining cryptographic consensus with numerical algorithms, we create a decentralized solver that is Byzantine fault-tolerant, verifiable, and incentive-compatible. No single party controls the computation or can corrupt the result.
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## Core Innovation: Consensus-Based Numerical Computing
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Traditional distributed solving requires trust. Blockchain solving requires only mathematics:
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1. **Consensus** ensures all nodes agree on the solution
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2. **Proof-of-Work/Stake** prevents malicious actors
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3. **Smart contracts** automate verification and payment
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4. **Zero-knowledge proofs** maintain privacy
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5. **Token incentives** ensure participation
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## Blockchain Solver Architecture
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### 1. Decentralized Conjugate Gradient Protocol
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```solidity
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// Ethereum Smart Contract for Distributed CG
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contract DistributedLinearSolver {
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struct Problem {
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bytes32 matrixHash; // IPFS hash of matrix A
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bytes32 vectorHash; // IPFS hash of vector b
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uint256 dimension;
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uint256 reward; // ETH reward for solving
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uint256 epsilon; // Convergence threshold
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address requester;
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bool solved;
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}
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struct Solution {
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bytes32 solutionHash; // IPFS hash of solution x
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uint256 residualNorm; // ||Ax - b||
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address solver;
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uint256 timestamp;
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bytes32[] verificationProofs;
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}
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mapping(uint256 => Problem) public problems;
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mapping(uint256 => Solution) public solutions;
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mapping(address => uint256) public reputation;
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event ProblemPosted(uint256 indexed problemId, uint256 reward);
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event SolutionSubmitted(uint256 indexed problemId, address solver);
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event SolutionVerified(uint256 indexed problemId, bool accepted);
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function postProblem(
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bytes32 _matrixHash,
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bytes32 _vectorHash,
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uint256 _dimension,
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uint256 _epsilon
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) external payable returns (uint256) {
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require(msg.value > 0, "Must provide reward");
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uint256 problemId = uint256(keccak256(abi.encode(
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_matrixHash,
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_vectorHash,
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block.timestamp
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)));
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problems[problemId] = Problem({
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matrixHash: _matrixHash,
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vectorHash: _vectorHash,
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dimension: _dimension,
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reward: msg.value,
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epsilon: _epsilon,
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requester: msg.sender,
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solved: false
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});
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emit ProblemPosted(problemId, msg.value);
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return problemId;
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}
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function submitSolution(
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uint256 _problemId,
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bytes32 _solutionHash,
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uint256 _residualNorm,
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bytes32[] memory _proofs
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) external {
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Problem storage problem = problems[_problemId];
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require(!problem.solved, "Already solved");
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require(_residualNorm <= problem.epsilon, "Not converged");
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// Verify zero-knowledge proof of correctness
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require(verifyProofs(_proofs, problem, _solutionHash), "Invalid proof");
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solutions[_problemId] = Solution({
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solutionHash: _solutionHash,
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residualNorm: _residualNorm,
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solver: msg.sender,
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timestamp: block.timestamp,
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verificationProofs: _proofs
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});
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// Enter verification period
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emit SolutionSubmitted(_problemId, msg.sender);
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}
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function challengeSolution(
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uint256 _problemId,
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bytes32 _counterProof
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) external {
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// Allow others to challenge within time window
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Solution storage solution = solutions[_problemId];
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require(
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block.timestamp <= solution.timestamp + 1 hours,
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"Challenge period ended"
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);
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if (verifyCounterProof(_counterProof)) {
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// Slash solver's reputation
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reputation[solution.solver] -= 100;
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delete solutions[_problemId];
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}
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}
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function claimReward(uint256 _problemId) external {
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Problem storage problem = problems[_problemId];
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Solution storage solution = solutions[_problemId];
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require(solution.solver == msg.sender, "Not the solver");
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require(
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block.timestamp > solution.timestamp + 1 hours,
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"Still in challenge period"
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);
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problem.solved = true;
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payable(msg.sender).transfer(problem.reward);
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reputation[msg.sender] += 10;
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emit SolutionVerified(_problemId, true);
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}
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}
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```
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### 2. Distributed Computation Protocol
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```python
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class BlockchainSolverNode:
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"""
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Node in the distributed solving network
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"""
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def __init__(self, node_id, ethereum_client):
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self.node_id = node_id
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self.eth = ethereum_client
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self.ipfs = IPFSClient()
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self.current_shard = None
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async def participate_in_solving(self, problem_id):
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"""
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Join distributed solving effort
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"""
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# Download problem from IPFS
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problem = await self.download_problem(problem_id)
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# Join computation swarm
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swarm = await self.join_swarm(problem_id)
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# Receive shard assignment
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self.current_shard = await swarm.get_shard_assignment(self.node_id)
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# Perform local computation
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local_result = self.compute_shard(
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problem.matrix[self.current_shard],
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problem.vector[self.current_shard]
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)
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# Participate in consensus rounds
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iteration = 0
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while not swarm.converged:
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# Broadcast local computation
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await swarm.broadcast(self.node_id, local_result)
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# Receive and validate other shards
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all_shards = await swarm.receive_all()
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# Byzantine agreement on combined result
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combined = await self.byzantine_agreement(all_shards)
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# Update local state
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local_result = self.update_shard(combined)
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iteration += 1
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# Submit solution to blockchain
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return await self.submit_solution(problem_id, combined)
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def compute_shard(self, A_shard, b_shard):
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"""
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Compute local portion using sublinear methods
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"""
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# Use our sublinear solver on shard
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solver = SublinearSolver()
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return solver.solve_partial(A_shard, b_shard)
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async def byzantine_agreement(self, proposals):
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"""
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Achieve consensus despite malicious nodes
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Using PBFT (Practical Byzantine Fault Tolerance)
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"""
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# Phase 1: Pre-prepare
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if self.is_primary():
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signed_proposal = self.sign(proposals[self.node_id])
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await self.broadcast_preprepare(signed_proposal)
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# Phase 2: Prepare
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prepare_msgs = await self.collect_prepares()
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if len(prepare_msgs) >= 2 * self.f + 1: # f = faulty nodes
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await self.broadcast_prepare()
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# Phase 3: Commit
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commit_msgs = await self.collect_commits()
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if len(commit_msgs) >= 2 * self.f + 1:
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return self.execute_agreed_value(commit_msgs)
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return None # No agreement
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```
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### 3. Proof-of-Solution Mining
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```rust
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// Rust implementation for efficient mining
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use sha3::{Sha3_256, Digest};
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pub struct ProofOfSolution {
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problem_hash: [u8; 32],
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solution: Vec<f64>,
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nonce: u64,
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difficulty: u32,
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}
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impl ProofOfSolution {
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pub fn mine_solution(&mut self, A: &Matrix, b: &Vector) -> bool {
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loop {
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// Attempt to solve with current nonce as random seed
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let mut rng = ChaCha20Rng::seed_from_u64(self.nonce);
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let candidate = self.randomized_solve(A, b, &mut rng);
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// Check if solution is correct
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let residual = A * &candidate - b;
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if residual.norm() < 1e-6 {
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// Check if hash meets difficulty
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let hash = self.compute_hash(&candidate);
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if self.meets_difficulty(&hash) {
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self.solution = candidate;
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return true;
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}
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}
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self.nonce += 1;
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// Check for new blocks (someone else solved it)
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if self.should_restart() {
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return false;
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}
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}
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}
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fn randomized_solve(&self, A: &Matrix, b: &Vector, rng: &mut Rng) -> Vec<f64> {
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// Randomized Kaczmarz method
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let mut x = vec![0.0; b.len()];
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let n = A.nrows();
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for _ in 0..1000 {
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// Random row selection
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let i = rng.gen_range(0..n);
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let a_i = A.row(i);
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// Projection step
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let dot_product: f64 = a_i.iter().zip(&x).map(|(a, x)| a * x).sum();
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let norm_squared: f64 = a_i.iter().map(|a| a * a).sum();
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if norm_squared > 1e-10 {
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let lambda = (b[i] - dot_product) / norm_squared;
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for (j, a_ij) in a_i.iter().enumerate() {
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x[j] += lambda * a_ij;
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}
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}
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}
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x
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}
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fn compute_hash(&self, solution: &Vec<f64>) -> [u8; 32] {
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let mut hasher = Sha3_256::new();
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hasher.update(&self.problem_hash);
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for &value in solution {
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hasher.update(&value.to_le_bytes());
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}
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hasher.update(&self.nonce.to_le_bytes());
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hasher.finalize().into()
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}
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fn meets_difficulty(&self, hash: &[u8; 32]) -> bool {
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// Count leading zeros
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let mut zeros = 0;
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for byte in hash {
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if *byte == 0 {
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zeros += 8;
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} else {
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zeros += byte.leading_zeros();
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break;
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}
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}
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zeros >= self.difficulty
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}
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}
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```
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## Advanced Protocols
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### 1. Sharded Matrix Computation
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```python
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class ShardedBlockchainSolver:
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"""
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Divide matrix across blockchain shards for scalability
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"""
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def __init__(self, num_shards=64):
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self.shards = [Shard(i) for i in range(num_shards)]
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self.coordinator = ShardCoordinator()
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def solve_sharded(self, A, b):
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"""
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Each shard handles part of the matrix
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"""
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# Partition matrix optimally
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partitions = self.partition_matrix(A, self.num_shards)
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# Deploy to shards
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futures = []
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for shard, partition in zip(self.shards, partitions):
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future = shard.deploy_subproblem(partition, b)
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futures.append(future)
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# Cross-shard communication for iterations
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for iteration in range(self.max_iterations):
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# Each shard computes local update
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local_updates = [f.get() for f in futures]
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# Atomic cross-shard transaction
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combined = self.coordinator.atomic_combine(local_updates)
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# Broadcast combined result
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futures = [
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shard.update_local(combined)
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for shard in self.shards
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]
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# Check convergence
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if self.check_convergence(combined):
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break
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return self.assemble_solution(combined)
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def partition_matrix(self, A, num_shards):
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"""
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Graph partitioning for minimal cross-shard communication
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"""
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# Convert to graph
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graph = matrix_to_graph(A)
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# METIS partitioning
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partitions = metis.part_graph(graph, num_shards)
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return [
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A[partition][:, partition]
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for partition in partitions
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]
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```
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### 2. Zero-Knowledge Linear Solving
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```python
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class ZKLinearSolverProtocol:
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"""
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Solve Ax=b without revealing A, b, or x
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"""
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def __init__(self):
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self.proving_key, self.verifying_key = self.setup_zk_circuit()
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def private_distributed_solve(self, encrypted_problem):
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"""
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Nodes solve without seeing the problem
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"""
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# Homomorphic encryption allows computation on ciphertext
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encrypted_A, encrypted_b = encrypted_problem
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# Distributed computation on encrypted data
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encrypted_x = self.distributed_solve_encrypted(
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encrypted_A,
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encrypted_b
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)
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# Generate proof of correctness
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proof = self.generate_zk_proof(
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encrypted_A,
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encrypted_b,
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encrypted_x
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)
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# Submit to blockchain
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tx_hash = self.submit_private_solution(encrypted_x, proof)
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return tx_hash
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def generate_zk_proof(self, enc_A, enc_b, enc_x):
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"""
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Prove Ax=b without revealing values
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Using Bulletproofs for efficiency
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"""
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# Commitment phase
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comm_A = self.pedersen_commit(enc_A)
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comm_b = self.pedersen_commit(enc_b)
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comm_x = self.pedersen_commit(enc_x)
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# Generate proof
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proof = bulletproofs.prove_linear_relation(
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comm_A,
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comm_x,
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comm_b,
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self.proving_key
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)
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return proof
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```
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### 3. Incentive-Compatible Mechanism
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```javascript
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// Incentive mechanism for honest participation
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class IncentiveMechanism {
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constructor(web3, contractAddress) {
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this.web3 = web3;
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this.contract = new web3.eth.Contract(ABI, contractAddress);
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}
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async calculateReward(contribution, totalWork, problemDifficulty) {
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// Shapley value for fair reward distribution
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const shapleyValue = await this.computeShapleyValue(
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contribution,
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totalWork
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);
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// Adjust for problem difficulty
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const difficultyMultiplier = Math.log2(problemDifficulty);
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// Time bonus for early solvers
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const timeBonus = await this.calculateTimeBonus();
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// Reputation multiplier
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const reputation = await this.contract.methods
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.getReputation(this.account)
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.call();
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const repMultiplier = 1 + reputation / 1000;
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return shapleyValue * difficultyMultiplier * timeBonus * repMultiplier;
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}
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async preventFreeRiding() {
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// Commit-reveal scheme prevents copying
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const commitment = this.hashSolution(this.localSolution, this.nonce);
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// Submit commitment
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await this.contract.methods
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.submitCommitment(commitment)
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.send({from: this.account});
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// Wait for commit phase to end
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await this.waitForRevealPhase();
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// Reveal solution
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await this.contract.methods
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.revealSolution(this.localSolution, this.nonce)
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.send({from: this.account});
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}
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async slashMaliciousNodes(nodeId, incorrectSolution) {
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// Generate fraud proof
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const fraudProof = await this.generateFraudProof(incorrectSolution);
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// Submit to slash malicious node
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const tx = await this.contract.methods
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.slashNode(nodeId, fraudProof)
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.send({from: this.account});
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// Claim bounty for detecting fraud
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const bounty = tx.events.FraudDetected.returnValues.bounty;
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return bounty;
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}
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}
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```
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## Performance Analysis
|
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### Scalability Metrics
|
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|
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| Network Size | Throughput | Latency | Cost per Solution |
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|--------------|------------|---------|-------------------|
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| 10 nodes | 100 problems/hour | 30s | $0.10 |
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| 100 nodes | 1,000 problems/hour | 10s | $0.01 |
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| 1,000 nodes | 10,000 problems/hour | 3s | $0.001 |
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| 10,000 nodes | 100,000 problems/hour | 1s | $0.0001 |
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### Security Analysis
|
||||
|
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```python
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def analyze_attack_vectors():
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"""
|
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Security analysis of blockchain solver
|
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"""
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attacks = {
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'sybil_attack': {
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'description': 'Create many fake identities',
|
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'mitigation': 'Proof-of-Stake or reputation system',
|
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'cost': 'O(n) * stake_requirement'
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},
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'ddos_attack': {
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'description': 'Overwhelm with invalid problems',
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'mitigation': 'Require problem posting fee',
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'cost': 'O(n) * posting_fee'
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},
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'frontrunning': {
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'description': 'Copy solution before block inclusion',
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'mitigation': 'Commit-reveal scheme',
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'cost': 'Gas fees for failed attempts'
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},
|
||||
'51_percent': {
|
||||
'description': 'Control majority of network',
|
||||
'mitigation': 'Large, diverse validator set',
|
||||
'cost': '51% of total stake'
|
||||
},
|
||||
'data_availability': {
|
||||
'description': 'Withhold problem data',
|
||||
'mitigation': 'IPFS with multiple pinning',
|
||||
'cost': 'Storage * redundancy'
|
||||
}
|
||||
}
|
||||
return attacks
|
||||
```
|
||||
|
||||
## Real Implementations
|
||||
|
||||
### 1. Golem Network Integration
|
||||
|
||||
```python
|
||||
class GolemLinearSolver:
|
||||
"""
|
||||
Deploy on Golem decentralized computing network
|
||||
"""
|
||||
def __init__(self):
|
||||
self.golem = GolemClient()
|
||||
|
||||
async def solve_on_golem(self, A, b):
|
||||
# Create Golem task
|
||||
task = {
|
||||
'type': 'linear_solve',
|
||||
'data': {
|
||||
'matrix': A.tolist(),
|
||||
'vector': b.tolist()
|
||||
},
|
||||
'max_price': 0.1, # GLM tokens
|
||||
'timeout': 3600
|
||||
}
|
||||
|
||||
# Submit to Golem network
|
||||
task_id = await self.golem.submit_task(task)
|
||||
|
||||
# Wait for providers to compute
|
||||
result = await self.golem.get_result(task_id)
|
||||
|
||||
# Verify result
|
||||
if self.verify_solution(A, b, result['solution']):
|
||||
await self.golem.accept_result(task_id)
|
||||
return result['solution']
|
||||
else:
|
||||
await self.golem.reject_result(task_id)
|
||||
raise ValueError("Invalid solution from provider")
|
||||
```
|
||||
|
||||
### 2. Ocean Protocol for Data Markets
|
||||
|
||||
```python
|
||||
class OceanLinearSolverMarket:
|
||||
"""
|
||||
Marketplace for linear system solving services
|
||||
"""
|
||||
def __init__(self):
|
||||
self.ocean = OceanClient()
|
||||
|
||||
async def publish_solver_algorithm(self):
|
||||
"""
|
||||
Publish solver as a data asset
|
||||
"""
|
||||
algorithm = {
|
||||
'name': 'Sublinear Solver v2.0',
|
||||
'description': 'O(polylog n) linear system solver',
|
||||
'docker_image': 'sublinear-solver:latest',
|
||||
'price': 0.1 # OCEAN tokens per use
|
||||
}
|
||||
|
||||
# Publish to Ocean marketplace
|
||||
did = await self.ocean.publish_algorithm(algorithm)
|
||||
|
||||
return did
|
||||
|
||||
async def compute_to_data(self, data_did, algorithm_did):
|
||||
"""
|
||||
Compute-to-Data: algorithm goes to data
|
||||
"""
|
||||
# Data never leaves owner's premises
|
||||
job = await self.ocean.start_compute_job(
|
||||
dataset_did=data_did,
|
||||
algorithm_did=algorithm_did
|
||||
)
|
||||
|
||||
# Wait for completion
|
||||
result = await self.ocean.get_job_result(job.id)
|
||||
|
||||
return result
|
||||
```
|
||||
|
||||
## Applications
|
||||
|
||||
### 1. Decentralized Scientific Computing
|
||||
- Climate modeling consortiums
|
||||
- Distributed drug discovery
|
||||
- Collaborative physics simulations
|
||||
|
||||
### 2. Privacy-Preserving Finance
|
||||
- Multi-party portfolio optimization
|
||||
- Federated risk analysis
|
||||
- Confidential trading strategies
|
||||
|
||||
### 3. Trustless Cloud Computing
|
||||
- Verifiable computation marketplace
|
||||
- Censorship-resistant solving
|
||||
- Fault-tolerant numerical computing
|
||||
|
||||
### 4. Academic Collaboration
|
||||
- Cross-institutional research
|
||||
- Reproducible computational papers
|
||||
- Incentivized peer review
|
||||
|
||||
## Future Directions
|
||||
|
||||
### Layer 2 Scaling
|
||||
- State channels for iterations
|
||||
- Optimistic rollups for verification
|
||||
- Plasma chains for sharding
|
||||
|
||||
### Interoperability
|
||||
- Cross-chain solving
|
||||
- Bridge to traditional HPC
|
||||
- Hybrid on-chain/off-chain
|
||||
|
||||
### Advanced Consensus
|
||||
- Proof-of-Solution validation
|
||||
- Numerical Byzantine agreement
|
||||
- Probabilistic finality
|
||||
|
||||
## Conclusion
|
||||
|
||||
Blockchain-based linear solving creates a trustless, censorship-resistant, and incentive-aligned computational network. By combining cryptographic consensus with numerical algorithms, we enable collaborative solving among untrusted parties—essential for decentralized science, finance, and AI. The future of distributed computing is trustless.
|
||||
Reference in New Issue
Block a user