Privacy: randomized coin selection (BnB changeless + single random draw) (#3408)

* Randomize coin selection with single random draw

The greedy selection walked the unspent pool in a predictable order (address generation order, then per-address server order), a fingerprint an analyst can exploit. Shuffle the pool before the accumulate-until-covered loop so the input set is chosen non-deterministically (single random draw). MWEB coins are still kept last.

Branch-and-bound (changeless exact match) is a larger follow-up.

* Add BnB + SRD coin selection primitives

Pure, wallet-independent coin selector: branch-and-bound for an exact
changeless match within the cost-of-change window, single-random-draw
fallback (shuffled, injectable RNG) when no exact match exists, and
selectCoins tying them together over effective values.

This is the basis for replacing the greedy accumulation in _createUTXOS
so sends produce no change when possible and a non-deterministic
selection otherwise. Validated with dart test (9 cases); wiring into
_createUTXOS is a separate step.

* Use BnB changeless matching in coin selection

Before the shuffled greedy walk, run branch-and-bound over effective
values (value minus per-input fee cost) looking for an input set whose
excess over amount plus fee stays below dust. When found, order those
inputs first and cap the walk at their count: the caller then computes
a change below dust, drops the change output, and absorbs the residue
into the fee, producing a changeless transaction with no residual
change fingerprint.

When no match exists, selection falls back to the shuffled pool, which
the greedy walk turns into a single random draw. BnB is skipped for
sendAll, forced input counts and pools holding MWEB coins.

changelessMatch filters non-positive effective values and maps indices
back to the original pool.

* Cover changeless fee bounds and BnB termination

Assert the end-to-end arithmetic the wallet performs around a
branch-and-bound match: with the 68/34/10 vBytes model, the leftover
the caller absorbs into the fee is never negative (no re-selection
loop) and never exceeds the dust limit (bounded fee overpay).

Also pin termination: a large pool with no possible match returns null
through the maxTries cap instead of exploring the full search tree.

* Use a secure RNG for coin selection randomness

The selection shuffle and the single-random-draw fallback exist to be
unpredictable, so seed them from Random.secure() instead of the default
PRNG, matching what Core and bdk use for coin selection. Pool sizes are
small, so the cost is negligible. Tests keep injecting a seeded Random
for determinism.

* Randomize RBF and payjoin input candidate order

Two secondary paths still consumed unspentCoins in wallet scan order
(address generation order, then per-address age), the same predictable
order removed from the main selection path:

- replaceByFee walked the unused-UTXO list in scan order when the fee
  bump needed extra inputs
- the payjoin receiver handed input candidates to the payjoin library
  in scan order, letting ties inside its selection mirror that order

Shuffle both with a secure RNG so no input-selection path exposes the
wallet's address or coin age ordering.

* ci: skip Linux PR build on forks (no secrets access)

* Account for script-type sizes in changeless matching

* Keep coin selection order stable within a transaction build

cw_bitcoin/lib/coin_selection.dart

@@ -0,0 +1,88 @@
+import 'dart:math';
+
+int effectiveValue(int value, int inputCost) => value - inputCost;
+
+class SelectedCoins {
+  final List<int> indices;
+  final bool hasChange;
+  const SelectedCoins(this.indices, this.hasChange);
+}
+
+SelectedCoins? branchAndBound(List<int> effValues, int target, int costOfChange,
+    {int maxTries = 100000}) {
+  final n = effValues.length;
+  final order = List<int>.generate(n, (i) => i)
+    ..sort((a, b) => effValues[b].compareTo(effValues[a]));
+  final sorted = [for (final i in order) effValues[i]];
+  final suffix = List<int>.filled(n + 1, 0);
+  for (var i = n - 1; i >= 0; i--) suffix[i] = suffix[i + 1] + sorted[i];
+  final upper = target + costOfChange;
+  List<int>? best;
+  final picked = <int>[];
+  var tries = 0;
+  void dfs(int i, int sum) {
+    if (best != null || tries++ >= maxTries) return;
+    if (sum > upper) return;
+    if (sum >= target) { best = List.of(picked); return; }
+    if (i >= n || sum + suffix[i] < target) return;
+    picked.add(order[i]); dfs(i + 1, sum + sorted[i]); picked.removeLast();
+    dfs(i + 1, sum);
+  }
+  dfs(0, 0);
+  return best == null ? null : SelectedCoins(best!, false);
+}
+
+SelectedCoins? singleRandomDraw(List<int> effValues, int target, int minChange, Random rng) {
+  final order = List<int>.generate(effValues.length, (i) => i)..shuffle(rng);
+  final picked = <int>[]; var sum = 0;
+  for (final i in order) {
+    picked.add(i); sum += effValues[i];
+    if (sum >= target + minChange) return SelectedCoins(picked, true);
+  }
+  return null;
+}
+
+/// Branch-and-bound over effective values (value minus the cost of spending the
+/// input at the current fee rate). [inputCosts] is parallel to [values] so each
+/// input pays for its own script type's size. A match means the excess over
+/// [target] stays within [window], so the remainder can be absorbed into the fee
+/// instead of creating a change output. Returns null when no such subset exists.
+SelectedCoins? changelessMatch({
+  required List<int> values,
+  required int target,
+  required List<int> inputCosts,
+  required int window,
+  int maxTries = 100000,
+}) {
+  assert(values.length == inputCosts.length);
+  final keep = <int>[];
+  final eff = <int>[];
+  for (var i = 0; i < values.length; i++) {
+    final e = effectiveValue(values[i], inputCosts[i]);
+    if (e > 0) {
+      keep.add(i);
+      eff.add(e);
+    }
+  }
+  final match = branchAndBound(eff, target, window, maxTries: maxTries);
+  if (match == null) return null;
+  return SelectedCoins([for (final i in match.indices) keep[i]], false);
+}
+
+class InsufficientFundsException implements Exception { const InsufficientFundsException(); }
+
+SelectedCoins selectCoins({required List<int> values, required int target,
+    required int inputCost, required int costOfChange, required int minChange, Random? rng}) {
+  final keep = <int>[]; final eff = <int>[];
+  for (var i = 0; i < values.length; i++) {
+    final e = effectiveValue(values[i], inputCost);
+    if (e > 0) { keep.add(i); eff.add(e); }
+  }
+  SelectedCoins? map(SelectedCoins? s) =>
+      s == null ? null : SelectedCoins([for (final i in s.indices) keep[i]], s.hasChange);
+  final bnb = map(branchAndBound(eff, target, costOfChange));
+  if (bnb != null) return bnb;
+  final srd = map(singleRandomDraw(eff, target, minChange, rng ?? Random.secure()));
+  if (srd != null) return srd;
+  throw const InsufficientFundsException();
+}

cw_bitcoin/lib/electrum_wallet.dart

@@ -1,6 +1,7 @@
 import 'dart:async';
 import 'dart:convert';
 import 'dart:isolate';
+import 'dart:math' show Random;
 
 import 'package:bitcoin_base/bitcoin_base.dart';
 import 'package:cw_bitcoin/lightning/lightning_wallet.dart';
@@ -10,6 +11,7 @@ import 'package:cw_core/root_dir.dart';
 import 'package:cw_core/utils/proxy_wrapper.dart';
 import 'package:cw_core/utils/print_verbose.dart';
 import 'package:cw_bitcoin/bitcoin_wallet.dart';
+import 'package:cw_bitcoin/coin_selection.dart';
 import 'package:cw_bitcoin/litecoin_wallet.dart';
 import 'package:shared_preferences/shared_preferences.dart';
 import 'package:blockchain_utils/blockchain_utils.dart';
@@ -261,6 +263,29 @@ abstract class ElectrumWalletBase
   static int estimatedTransactionSize(int inputsCount, int outputsCounts) =>
       inputsCount * 68 + outputsCounts * 34 + 10;
 
+  // vbytes an input of the given script type adds to a transaction. The generic
+  // estimate above assumes P2WPKH (68); legacy and taproot inputs differ enough
+  // to break changeless-match arithmetic if not accounted for.
+  static int estimatedInputSize(BitcoinAddressType type) {
+    if (type == P2pkhAddressType.p2pkh) return 148;
+    if (type == P2shAddressType.p2wpkhInP2sh) return 91;
+    if (type == SegwitAddresType.p2tr) return 58;
+    if (type == SegwitAddresType.p2wsh) return 105;
+    if (type == SilentPaymentsAddresType.p2sp) return 58; // spent via taproot
+    return 68;
+  }
+
+  // vbytes an output of the given script type adds to a transaction. Silent
+  // payment outputs are delivered as taproot.
+  static int estimatedOutputSize(BitcoinAddressType type) {
+    if (type == P2pkhAddressType.p2pkh) return 34;
+    if (type == P2shAddressType.p2wpkhInP2sh) return 32;
+    if (type == SegwitAddresType.p2tr) return 43;
+    if (type == SegwitAddresType.p2wsh) return 43;
+    if (type == SilentPaymentsAddresType.p2sp) return 43;
+    return 31;
+  }
+
   // Parses the account index from a BIP-44/49/84/86 derivation path.
   // e.g. "m/84'/0'/1'" → 1.  Returns 0 for unrecognised formats.
   static int _parseAccountIndex(String? derivationPath) {
@@ -881,11 +906,23 @@ abstract class ElectrumWalletBase
   bool _isBelowDust(BigInt amount) =>
       amount <= networkDustAmount && network != BitcoinNetwork.testnet;
 
+  // Random draw priority per outpoint. Assigned lazily with a secure RNG and kept
+  // until the next createTransaction call, so the recursive estimate passes of one
+  // transaction build all see the same input order (reshuffling between passes made
+  // fee estimation unstable). Cleared per transaction so each send is a fresh draw.
+  final Random _coinSelectionRng = Random.secure();
+  final Map<String, int> _coinSelectionOrder = {};
+
+  int _coinSelectionPriority(BitcoinUnspent utx) => _coinSelectionOrder.putIfAbsent(
+      '${utx.hash}:${utx.vout}', () => _coinSelectionRng.nextInt(1 << 32));
+
   UtxoDetails _createUTXOS({
     required bool sendAll,
     required bool paysToSilentPayment,
     int credentialsAmount = 0,
     int? inputsCount,
+    int feeRate = 0,
+    int? outputsVBytes,
     UnspentCoinType coinTypeToSpendFrom = UnspentCoinType.any,
   }) {
     List<UtxoWithAddress> utxos = [];
@@ -914,8 +951,52 @@ abstract class ElectrumWalletBase
     }).toList();
     final unconfirmedCoins = availableInputs.where((utx) => utx.confirmations == 0).toList();
 
-    // sort the unconfirmed coins so that mweb coins are last:
-    availableInputs.sort((a, b) => a.bitcoinAddressRecord.type == SegwitAddresType.mweb ? 1 : -1);
+    // Single Random Draw: order the pool by each coin's random priority so selection is
+    // non-deterministic, removing the predictable address/scan order (a fingerprint).
+    // The priority is stable across the repeated calls of one transaction build.
+    // MWEB coins are kept last afterwards.
+    availableInputs.sort((a, b) {
+      final byPriority = _coinSelectionPriority(a).compareTo(_coinSelectionPriority(b));
+      if (byPriority != 0) return byPriority;
+      return '${a.hash}:${a.vout}'.compareTo('${b.hash}:${b.vout}');
+    });
+    availableInputs = [
+      ...availableInputs.where((u) => u.bitcoinAddressRecord.type != SegwitAddresType.mweb),
+      ...availableInputs.where((u) => u.bitcoinAddressRecord.type == SegwitAddresType.mweb),
+    ];
+
+    // Branch-and-bound: prefer an input set whose excess over the amount plus its own fee
+    // stays below dust, so the caller drops the change output and the send is changeless.
+    // When no such set exists, the shuffled pool below acts as a single random draw.
+    final canTryChangeless = !sendAll &&
+        inputsCount == null &&
+        credentialsAmount > 0 &&
+        feeRate > 0 &&
+        outputsVBytes != null &&
+        outputsVBytes > 0 &&
+        !availableInputs.any((u) => u.bitcoinAddressRecord.type == SegwitAddresType.mweb);
+    if (canTryChangeless) {
+      final match = changelessMatch(
+        values: [for (final u in availableInputs) u.value],
+        // estimatedTransactionSize(0, 0) is the fixed tx overhead (version,
+        // counters, locktime); the outputs' own vbytes come pre-computed per type.
+        target: credentialsAmount + (estimatedTransactionSize(0, 0) + outputsVBytes!) * feeRate,
+        inputCosts: [
+          for (final u in availableInputs)
+            estimatedInputSize(u.bitcoinAddressRecord.type) * feeRate
+        ],
+        window: networkDustAmount.toInt(),
+      );
+      if (match != null) {
+        final chosen = match.indices.toSet();
+        availableInputs = [
+          for (final i in match.indices) availableInputs[i],
+          for (var i = 0; i < availableInputs.length; i++)
+            if (!chosen.contains(i)) availableInputs[i],
+        ];
+        inputsCount = match.indices.length;
+      }
+    }
 
     for (int i = 0; i < availableInputs.length; i++) {
       final utx = availableInputs[i];
@@ -1131,10 +1212,25 @@ abstract class ElectrumWalletBase
       }
     }
 
+    // Per-type output sizes for the changeless target. MWEB outputs follow a
+    // different size model entirely, so they disable the changeless path (null).
+    int? outputsVBytes = 0;
+    for (final out in outputs) {
+      final type =
+          out.isSilentPayment == true ? SilentPaymentsAddresType.p2sp : _getScriptType(out.address);
+      if (type == SegwitAddresType.mweb) {
+        outputsVBytes = null;
+        break;
+      }
+      outputsVBytes = outputsVBytes! + estimatedOutputSize(type);
+    }
+
     final utxoDetails = _createUTXOS(
       sendAll: false,
       credentialsAmount: credentialsAmount.amount.toInt(),
       inputsCount: inputsCount,
+      feeRate: feeRate,
+      outputsVBytes: outputsVBytes,
       paysToSilentPayment: hasSilentPayment,
       coinTypeToSpendFrom: coinTypeToSpendFrom,
     );
@@ -1397,6 +1493,10 @@ abstract class ElectrumWalletBase
   @override
   Future<PendingTransaction> createTransaction(Object credentials) async {
     try {
+      // New transaction, new random draw: drop the previous input ordering so this
+      // build gets fresh priorities, then keep them fixed for all estimate passes.
+      _coinSelectionOrder.clear();
+
       // start by updating unspent coins
       await updateAllUnspents();
 
@@ -2220,11 +2320,13 @@ abstract class ElectrumWalletBase
         }
       }
 
-      // If still not enough, add UTXOs until the fee is covered
+      // If still not enough, add UTXOs until the fee is covered, drawing them at
+      // random instead of in the predictable wallet scan order (address, then age).
       if (remainingFee > BigInt.zero) {
         final unusedUtxos = unspentCoins
             .where((utxo) => utxo.isSending && !utxo.isFrozen && utxo.confirmations! > 0)
-            .toList();
+            .toList()
+          ..shuffle(Random.secure());
 
         for (final utxo in unusedUtxos) {
           final address = RegexUtils.addressTypeFromStr(utxo.address, network);

cw_bitcoin/lib/payjoin/manager.dart

@@ -295,6 +295,9 @@ class PayjoinManager {
                 await _wallet.updateAllUnspents();
                 utxos = _wallet.getUtxoWithPrivateKeys(confirmedOnly: true);
               }
+              // Candidates arrive in wallet scan order (address, then age), which is
+              // predictable; shuffle so the receiver's input choice can't mirror it.
+              utxos.shuffle(Random.secure());
               mainToIsolateSendPort?.send({
                 'requestId': message['requestId'],
                 'result': utxos,

cw_bitcoin/test/coin_selection_test.dart

@@ -0,0 +1,100 @@
+import 'dart:math';
+import "package:cw_bitcoin/coin_selection.dart";
+import "package:flutter_test/flutter_test.dart";
+void main() {
+  test('effectiveValue', () {
+    expect(effectiveValue(10000, 136), 9864);
+    expect(effectiveValue(100, 136), -36);
+  });
+  test('BnB finds changeless match in window', () {
+    final r = branchAndBound([200,100,90,80], 300, 50);
+    expect(r, isNotNull); expect(r!.hasChange, isFalse);
+    final vals=[200,100,90,80]; final sum=r.indices.map((i)=>vals[i]).reduce((a,b)=>a+b);
+    expect(sum>=300 && sum<=350, isTrue);
+  });
+  test('BnB null when no subset in window', () {
+    expect(branchAndBound([1000,900], 300, 5), isNull);
+  });
+  test('SRD with change', () {
+    final r = singleRandomDraw([500,500,500,500], 700, 50, Random(1));
+    expect(r, isNotNull); expect(r!.hasChange, isTrue);
+  });
+  test('SRD randomizes across seeds', () {
+    final a = (singleRandomDraw([100,101,102,103,104,105],150,10,Random(1))!.indices..sort());
+    final b = (singleRandomDraw([100,101,102,103,104,105],150,10,Random(9))!.indices..sort());
+    expect(a, isNot(equals(b)));
+  });
+  test('SRD null on insufficient funds', () {
+    expect(singleRandomDraw([100,100], 500, 10, Random(1)), isNull);
+  });
+  test('selectCoins prefers changeless BnB, else SRD', () {
+    expect(selectCoins(values:[200,100,90],target:300,inputCost:0,costOfChange:20,minChange:10).hasChange, isFalse);
+    expect(selectCoins(values:[500,500,500],target:700,inputCost:0,costOfChange:5,minChange:10,rng:Random(1)).hasChange, isTrue);
+  });
+  test('selectCoins drops non-positive effective values', () {
+    // coin of value 50 with inputCost 136 -> effective -86 -> dropped; only the 1000 usable
+    final r = selectCoins(values:[50,1000],target:500,inputCost:136,costOfChange:5,minChange:10,rng:Random(1));
+    expect(r.indices, equals([1]));
+  });
+  test('changelessMatch finds a set whose effective sum lands in the window', () {
+    // inputCost 100: values [50, 400, 300, 200] -> eff [dropped, 300, 200, 100]
+    // target 500, window 46: eff {300, 200} = 500, exact
+    final r = changelessMatch(
+        values: [50, 400, 300, 200], target: 500, inputCosts: [100, 100, 100, 100], window: 46);
+    expect(r, isNotNull);
+    expect(r!.hasChange, isFalse);
+    final effSum = r.indices.map((i) => [50, 400, 300, 200][i] - 100).reduce((a, b) => a + b);
+    expect(effSum >= 500 && effSum <= 546, isTrue);
+    expect(r.indices.contains(0), isFalse); // negative-eff coin never selected
+  });
+  test('changelessMatch returns null when no subset lands in the window', () {
+    expect(
+        changelessMatch(values: [10000, 9000], target: 500, inputCosts: [100, 100], window: 46),
+        isNull);
+  });
+  test('selectCoins throws when insufficient', () {
+    expect(() => selectCoins(values:[100,100],target:500,inputCost:0,costOfChange:5,minChange:10),
+        throwsA(isA<InsufficientFundsException>()));
+  });
+  test('changeless pipeline: leftover absorbed into fee is non-negative and below dust', () {
+    // Mirrors the _createUTXOS / estimateTxForAmount arithmetic with the wallet's
+    // 68*inputs + 34*outputs + 10 vBytes model, at 10 sat/vB with 1 recipient output.
+    const feeRate = 10;
+    const amount = 50000;
+    final values = [60700, 30000, 21800, 9000, 5000];
+    const target = amount + (34 * 1 + 10) * feeRate;
+    final r = changelessMatch(
+        values: values,
+        target: target,
+        inputCosts: List.filled(values.length, 68 * feeRate),
+        window: 546);
+    expect(r, isNotNull);
+    final inAmount = r!.indices.map((i) => values[i]).reduce((a, b) => a + b);
+    final feeNoChange = (68 * r.indices.length + 34 * 1 + 10) * feeRate;
+    final leftover = inAmount - amount - feeNoChange;
+    expect(leftover >= 0, isTrue); // the caller never recurses for more inputs
+    expect(leftover <= 546, isTrue); // fee overpay is bounded by the dust limit
+  });
+  test('BnB terminates and returns null on large pools with no possible match', () {
+    // 300 even effective values, odd target, zero window: no subset can ever match,
+    // so the search must stop at maxTries instead of exploring 2^300 branches.
+    final values = List<int>.generate(300, (i) => 1000000 + i * 2);
+    final r = changelessMatch(
+        values: values, target: 1500001, inputCosts: List.filled(300, 10), window: 0);
+    expect(r, isNull);
+  });
+  test('changelessMatch charges each input its own script-type cost', () {
+    // Legacy input (148 vB) vs segwit input (68 vB) at 10 sat/vB: same value, but
+    // the legacy coin's effective value is 800 lower. Target only reachable when
+    // the cheaper segwit coin is chosen: eff segwit = 10000-680 = 9320.
+    const feeRate = 10;
+    final r = changelessMatch(
+      values: [10000, 10000],
+      target: 9320,
+      inputCosts: [148 * feeRate, 68 * feeRate],
+      window: 0,
+    );
+    expect(r, isNotNull);
+    expect(r!.indices, equals([1]));
+  });
+}