File size: 3,164 Bytes
1cdfc83 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 | // Application 3: Threshold Cryptography — Cardinality-Revealing Aggregation
// In k-of-n threshold schemes: DSS-weighted shares produce an aggregate
// where the sum reveals k (signer count) without revealing WHICH k signed.
import { computeGreedySequence, buildCardinalityTable } from './greedy.mjs';
export function runThresholdCryptoDemo() {
console.log('='.repeat(70));
console.log(' THRESHOLD SIGNATURE — DSS CARDINALITY ORACLE');
console.log(' "How many signed?" without "Who signed?"');
console.log('='.repeat(70));
console.log();
const NUM_SIGNERS = 10;
const THRESHOLD = 6;
const weights = computeGreedySequence(NUM_SIGNERS);
const table = buildCardinalityTable(weights);
const signerNames = [
'Alice', 'Bob', 'Carol', 'Dave', 'Eve',
'Frank', 'Grace', 'Heidi', 'Ivan', 'Judy'
];
console.log(`Threshold scheme: ${THRESHOLD}-of-${NUM_SIGNERS}`);
console.log(`Signers: [${signerNames.join(', ')}]`);
console.log(`DSS commitment weights: [${weights.join(', ')}]`);
console.log();
// Simulate signing rounds
const rounds = [
{ name: 'Exactly threshold (6/10)', signers: [0, 2, 4, 5, 7, 9] },
{ name: 'Over threshold (8/10)', signers: [0, 1, 2, 3, 5, 6, 8, 9] },
{ name: 'Under threshold (4/10)', signers: [1, 3, 6, 8] },
{ name: 'All signed (10/10)', signers: [0,1,2,3,4,5,6,7,8,9] },
{ name: 'Minimal quorum (6/10) different set', signers: [1, 3, 5, 7, 8, 9] },
];
console.log('VERIFICATION ROUNDS:');
console.log('-'.repeat(70));
for (const round of rounds) {
const activeWeights = round.signers.map(i => weights[i]);
const aggregate = activeWeights.reduce((a, b) => a + b, 0);
const detectedK = table.get(aggregate) ?? -1;
const valid = detectedK >= THRESHOLD;
const activeNames = round.signers.map(i => signerNames[i]);
console.log(`\n Round: ${round.name}`);
console.log(` Signers: [${activeNames.join(', ')}]`);
console.log(` Aggregate commitment: ${aggregate}`);
console.log(` DSS Oracle: "${detectedK} signers participated"`);
console.log(` Threshold met: ${valid ? 'VALID' : 'REJECTED'}`);
if (valid) {
// Show that multiple signer sets could produce this cardinality
// but the DSS property guarantees the COUNT is unambiguous
const possibleSets = comb(NUM_SIGNERS, detectedK);
console.log(` Privacy: ${possibleSets} possible ${detectedK}-signer sets (identity hidden)`);
}
}
console.log('\n' + '-'.repeat(70));
console.log('\nSECURITY PROPERTIES:');
console.log(' 1. SOUNDNESS: Cannot fake k signatures with fewer (DSS prevents sum collision across cardinalities)');
console.log(' 2. PRIVACY: Aggregate reveals count, not identity');
console.log(' 3. EFFICIENCY: O(1) threshold check vs O(C(n,k)) verification');
console.log();
return { weights, rounds, table };
}
function comb(n, k) {
if (k > n) return 0;
if (k === 0 || k === n) return 1;
let result = 1;
for (let i = 0; i < k; i++) {
result = result * (n - i) / (i + 1);
}
return Math.round(result);
}
|