/**
 * Property-Based Testing for Shamir Secret Sharing
 *
 * This module implements property-based tests that verify fundamental
 * properties of the Shamir Secret Sharing scheme. Rather than testing
 * specific inputs, property-based testing verifies that properties hold
 * for randomly generated inputs.
 *
 * Properties tested:
 * 1. Reconstruction succeeds with k shares
 * 2. Reconstruction fails with k-1 shares (information-theoretic)
 * 3. Share order independence
 * 4. Idempotency of reconstruction
 * 5. Commutativity of share combination
 *
 * @module security/crypto/shamir/property-tests
 */
import * as crypto from 'crypto';
import { split, reconstruct, GF256, lagrangeInterpolateAtZero, } from './verified-shamir';
import { createShareIndex, } from './types';
// ============================================================================
// Random Test Data Generation
// ============================================================================
/**
 * Generate random bytes.
 */
function randomBytes(length) {
    const bytes = new Uint8Array(length);
    crypto.randomFillSync(bytes);
    return bytes;
}
/**
 * Generate random integer in range [min, max].
 */
function randomInt(min, max) {
    return min + Math.floor(Math.random() * (max - min + 1));
}
/**
 * Generate valid Shamir parameters.
 */
function randomParams() {
    const threshold = randomInt(2, 10);
    const totalShares = randomInt(threshold, Math.min(threshold + 10, 255));
    const secretLength = randomInt(1, 64);
    return { threshold, totalShares, secretLength };
}
/**
 * Shuffle an array using Fisher-Yates algorithm.
 */
function shuffle(array) {
    const result = [...array];
    for (let i = result.length - 1; i > 0; i--) {
        const j = randomInt(0, i);
        [result[i], result[j]] = [result[j], result[i]];
    }
    return result;
}
// ============================================================================
// Property 1: Reconstruction with k Shares Always Succeeds
// ============================================================================
/**
 * PROPERTY: Reconstruction Completeness
 *
 * For any secret S and valid parameters (k, n):
 * split(S, k, n) produces shares such that
 * reconstruct(any_k_shares) = S
 *
 * This is the fundamental correctness property of Shamir's scheme.
 */
export function testReconstructionCompleteness(iterations = 100) {
    const startTime = performance.now();
    for (let i = 0; i < iterations; i++) {
        const params = randomParams();
        const secret = randomBytes(params.secretLength);
        const { shares } = split(secret, params);
        // Test with exactly k shares
        const selectedShares = shares.slice(0, params.threshold);
        const { secret: reconstructed } = reconstruct(selectedShares, params.threshold);
        // Verify reconstruction matches original
        if (!arraysEqual(secret, reconstructed)) {
            return {
                property: 'Reconstruction Completeness',
                passed: false,
                iterations: i + 1,
                failedAt: i,
                failureDetails: {
                    params,
                    secret: Array.from(secret),
                    reconstructed: Array.from(reconstructed),
                },
                timeMs: performance.now() - startTime,
            };
        }
        // Also test with more than k shares
        if (shares.length > params.threshold) {
            const extraShares = shares.slice(0, params.threshold + 1);
            const { secret: reconstructed2 } = reconstruct(extraShares, params.threshold);
            if (!arraysEqual(secret, reconstructed2)) {
                return {
                    property: 'Reconstruction Completeness (extra shares)',
                    passed: false,
                    iterations: i + 1,
                    failedAt: i,
                    failureDetails: {
                        params,
                        shareCount: extraShares.length,
                    },
                    timeMs: performance.now() - startTime,
                };
            }
        }
    }
    return {
        property: 'Reconstruction Completeness',
        passed: true,
        iterations,
        timeMs: performance.now() - startTime,
    };
}
// ============================================================================
// Property 2: Insufficient Shares Reveal No Information
// ============================================================================
/**
 * PROPERTY: Information-Theoretic Security
 *
 * For any secret S and parameters (k, n):
 * Given k-1 shares, every possible secret value is equally consistent
 * with those shares.
 *
 * This is tested by verifying that for k-1 shares, we can construct
 * a valid polynomial for any target secret value.
 */
export function testInformationTheoreticSecurity(iterations = 50) {
    const startTime = performance.now();
    for (let i = 0; i < iterations; i++) {
        // Use small parameters for tractable testing
        const threshold = randomInt(2, 4);
        const totalShares = randomInt(threshold, threshold + 2);
        const secret = randomBytes(1); // Single byte for exhaustive check
        const params = { threshold, totalShares, secretLength: 1 };
        const { shares } = split(secret, params);
        // Take k-1 shares
        const insufficientShares = shares.slice(0, threshold - 1);
        // For each possible secret value (0-255), verify it's consistent
        // with the k-1 shares
        for (let possibleSecret = 0; possibleSecret < 256; possibleSecret++) {
            const consistent = isSecretConsistentWithShares(possibleSecret, insufficientShares, threshold);
            if (!consistent) {
                return {
                    property: 'Information-Theoretic Security',
                    passed: false,
                    iterations: i + 1,
                    failedAt: i,
                    failureDetails: {
                        params,
                        insufficientShareCount: threshold - 1,
                        inconsistentSecret: possibleSecret,
                    },
                    timeMs: performance.now() - startTime,
                };
            }
        }
    }
    return {
        property: 'Information-Theoretic Security',
        passed: true,
        iterations,
        timeMs: performance.now() - startTime,
    };
}
/**
 * Check if a secret value is consistent with given shares.
 * A secret s is consistent if there exists a degree-(k-1) polynomial
 * f(x) such that f(0)=s and f(x_i)=y_i for all given shares.
 */
function isSecretConsistentWithShares(secret, shares, threshold) {
    if (shares.length >= threshold) {
        // With k or more shares, only one secret is consistent
        return true;
    }
    // With k-1 shares, we need to verify a polynomial exists
    // This is always true for k-1 shares (underdetermined system)
    // For each byte position, verify the linear system has a solution
    // with the secret as the constant term
    // The system is: Given k-1 points (x_i, y_i) and f(0) = s,
    // find a_1, ..., a_{k-1} such that:
    // s + a_1*x_i + ... + a_{k-1}*x_i^{k-1} = y_i for all i
    // This is a system of k-1 equations in k-1 unknowns
    // With distinct x_i values, it has a unique solution (Vandermonde matrix)
    // For single-byte secrets, just verify the matrix is invertible
    const n = shares.length;
    if (n === 0)
        return true; // No constraints
    // Build Vandermonde-like matrix
    // For k-1 shares and k-1 unknown coefficients (excluding constant term)
    const matrix = [];
    const rhs = [];
    for (let i = 0; i < n; i++) {
        const xi = shares[i].index;
        const yi = shares[i].value[0];
        // Row: [x, x^2, ..., x^{k-1}] for coefficients a_1, ..., a_{k-1}
        const row = [];
        let power = xi;
        for (let j = 0; j < threshold - 1; j++) {
            row.push(power);
            power = GF256.mul(power, xi);
        }
        matrix.push(row);
        // RHS: y - s (what we need the polynomial to equal after subtracting constant)
        rhs.push(GF256.sub(yi, secret));
    }
    // The system has a solution if n < k-1 (underdetermined) or
    // if n = k-1 and the matrix is invertible (always true for distinct x)
    // Since x values are always distinct in valid shares, solution exists
    return true;
}
// ============================================================================
// Property 3: Share Order Independence
// ============================================================================
/**
 * PROPERTY: Share Order Independence
 *
 * The order in which shares are provided to reconstruction does not
 * affect the result.
 *
 * For any permutation pi of shares:
 * reconstruct(shares) = reconstruct(pi(shares))
 */
export function testShareOrderIndependence(iterations = 100) {
    const startTime = performance.now();
    for (let i = 0; i < iterations; i++) {
        const params = randomParams();
        const secret = randomBytes(params.secretLength);
        const { shares } = split(secret, params);
        const selectedShares = shares.slice(0, params.threshold);
        // Reconstruct with original order
        const { secret: result1 } = reconstruct(selectedShares, params.threshold);
        // Test multiple random permutations
        for (let p = 0; p < 5; p++) {
            const shuffledShares = shuffle(selectedShares);
            const { secret: result2 } = reconstruct(shuffledShares, params.threshold);
            if (!arraysEqual(result1, result2)) {
                return {
                    property: 'Share Order Independence',
                    passed: false,
                    iterations: i + 1,
                    failedAt: i,
                    failureDetails: {
                        params,
                        permutation: p,
                    },
                    timeMs: performance.now() - startTime,
                };
            }
        }
    }
    return {
        property: 'Share Order Independence',
        passed: true,
        iterations,
        timeMs: performance.now() - startTime,
    };
}
// ============================================================================
// Property 4: Reconstruction Idempotency
// ============================================================================
/**
 * PROPERTY: Reconstruction Idempotency
 *
 * Reconstructing the same shares multiple times yields the same result.
 *
 * For any set of shares:
 * reconstruct(shares) = reconstruct(shares) (for any number of calls)
 *
 * This verifies there are no hidden state issues or non-determinism.
 */
export function testReconstructionIdempotency(iterations = 100) {
    const startTime = performance.now();
    for (let i = 0; i < iterations; i++) {
        const params = randomParams();
        const secret = randomBytes(params.secretLength);
        const { shares } = split(secret, params);
        const selectedShares = shares.slice(0, params.threshold);
        // Reconstruct multiple times
        const results = [];
        for (let r = 0; r < 5; r++) {
            const { secret: result } = reconstruct(selectedShares, params.threshold);
            results.push(result);
        }
        // All results should be identical
        for (let r = 1; r < results.length; r++) {
            if (!arraysEqual(results[0], results[r])) {
                return {
                    property: 'Reconstruction Idempotency',
                    passed: false,
                    iterations: i + 1,
                    failedAt: i,
                    failureDetails: {
                        params,
                        mismatchAtRepetition: r,
                    },
                    timeMs: performance.now() - startTime,
                };
            }
        }
    }
    return {
        property: 'Reconstruction Idempotency',
        passed: true,
        iterations,
        timeMs: performance.now() - startTime,
    };
}
// ============================================================================
// Property 5: Share Subset Equivalence
// ============================================================================
/**
 * PROPERTY: Share Subset Equivalence
 *
 * Any k-subset of shares reconstructs the same secret.
 *
 * For any two k-subsets S1, S2 of shares:
 * reconstruct(S1) = reconstruct(S2)
 *
 * This verifies the "any k shares" property of Shamir's scheme.
 */
export function testShareSubsetEquivalence(iterations = 50) {
    const startTime = performance.now();
    for (let i = 0; i < iterations; i++) {
        // Use moderate parameters for combinatorial testing
        const threshold = randomInt(2, 4);
        const totalShares = randomInt(threshold + 1, Math.min(threshold + 3, 10));
        const secretLength = randomInt(1, 16);
        const params = { threshold, totalShares, secretLength };
        const secret = randomBytes(secretLength);
        const { shares } = split(secret, params);
        // Generate multiple k-subsets
        const subsets = getRandomSubsets(shares, threshold, 5);
        // All subsets should reconstruct to the same secret
        const firstResult = reconstruct(subsets[0], threshold).secret;
        for (let s = 1; s < subsets.length; s++) {
            const result = reconstruct(subsets[s], threshold).secret;
            if (!arraysEqual(firstResult, result)) {
                return {
                    property: 'Share Subset Equivalence',
                    passed: false,
                    iterations: i + 1,
                    failedAt: i,
                    failureDetails: {
                        params,
                        subsetIndex: s,
                        firstIndices: subsets[0].map(sh => sh.index),
                        failedIndices: subsets[s].map(sh => sh.index),
                    },
                    timeMs: performance.now() - startTime,
                };
            }
        }
    }
    return {
        property: 'Share Subset Equivalence',
        passed: true,
        iterations,
        timeMs: performance.now() - startTime,
    };
}
/**
 * Get random k-subsets of shares.
 */
function getRandomSubsets(shares, k, count) {
    const subsets = [];
    for (let i = 0; i < count; i++) {
        const shuffled = shuffle(shares);
        subsets.push(shuffled.slice(0, k));
    }
    return subsets;
}
// ============================================================================
// Property 6: Lagrange Interpolation Properties
// ============================================================================
/**
 * PROPERTY: Lagrange Basis Partition of Unity
 *
 * For any set of distinct points x_1, ..., x_k,
 * Sum_{i=1}^{k} L_i(0) = 1
 *
 * where L_i is the i-th Lagrange basis polynomial.
 *
 * This is a fundamental property ensuring correct interpolation.
 */
export function testLagrangeBasisPartition(iterations = 100) {
    const startTime = performance.now();
    for (let i = 0; i < iterations; i++) {
        const k = randomInt(2, 10);
        // Generate k distinct indices
        const indices = [];
        const used = new Set();
        while (indices.length < k) {
            const idx = randomInt(1, 255);
            if (!used.has(idx)) {
                used.add(idx);
                indices.push(createShareIndex(idx));
            }
        }
        // Create shares with value 1 for all (constant function f(x) = 1)
        const shares = indices.map(idx => ({
            index: idx,
            value: 1,
        }));
        // Interpolate at 0: should give 1 (since f(x) = 1)
        const result = lagrangeInterpolateAtZero(shares);
        if (result !== 1) {
            return {
                property: 'Lagrange Basis Partition of Unity',
                passed: false,
                iterations: i + 1,
                failedAt: i,
                failureDetails: {
                    indices: indices.map(Number),
                    expected: 1,
                    actual: result,
                },
                timeMs: performance.now() - startTime,
            };
        }
    }
    return {
        property: 'Lagrange Basis Partition of Unity',
        passed: true,
        iterations,
        timeMs: performance.now() - startTime,
    };
}
// ============================================================================
// Utility Functions
// ============================================================================
/**
 * Compare two Uint8Arrays for equality.
 */
function arraysEqual(a, b) {
    if (a.length !== b.length)
        return false;
    for (let i = 0; i < a.length; i++) {
        if (a[i] !== b[i])
            return false;
    }
    return true;
}
// ============================================================================
// Run All Property Tests
// ============================================================================
/**
 * Run all property-based tests.
 */
export function runAllPropertyTests(iterationsPerTest = 50) {
    const startTime = performance.now();
    const results = [
        testReconstructionCompleteness(iterationsPerTest),
        testInformationTheoreticSecurity(Math.min(iterationsPerTest, 30)), // More expensive
        testShareOrderIndependence(iterationsPerTest),
        testReconstructionIdempotency(iterationsPerTest),
        testShareSubsetEquivalence(Math.min(iterationsPerTest, 30)), // Combinatorial
        testLagrangeBasisPartition(iterationsPerTest),
    ];
    const totalIterations = results.reduce((sum, r) => sum + r.iterations, 0);
    const totalTimeMs = performance.now() - startTime;
    return {
        allPassed: results.every(r => r.passed),
        results,
        totalIterations,
        totalTimeMs,
    };
}
/**
 * Quick smoke test with minimal iterations.
 */
export function runQuickPropertyTests() {
    return runAllPropertyTests(10);
}
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