miniscript: check maximum stack size during execution

Under Tapscript, due to the lifting of some standardness and consensus
limits, scripts can now run into the maximum stack size during
execution. Any Miniscript that may hit the limit on any of its spending
paths must be marked as unsafe.

Co-Authored-By: Pieter Wuille <[email protected]>

Author: darosior

src/script/miniscript.h

@@ -373,13 +373,112 @@ struct Ops {
     Ops(uint32_t in_count, MaxInt<uint32_t> in_sat, MaxInt<uint32_t> in_dsat) : count(in_count), sat(in_sat), dsat(in_dsat) {};
 };
 
+/** A data structure to help the calculation of stack size limits.
+ *
+ * Conceptually, every SatInfo object corresponds to a (possibly empty) set of script execution
+ * traces (sequences of opcodes).
+ * - SatInfo{} corresponds to the empty set.
+ * - SatInfo{n, e} corresponds to a single trace whose net effect is removing n elements from the
+ *   stack (may be negative for a net increase), and reaches a maximum of e stack elements more
+ *   than it ends with.
+ * - operator| is the union operation: (a | b) corresponds to the union of the traces in a and the
+ *   traces in b.
+ * - operator+ is the concatenation operator: (a + b) corresponds to the set of traces formed by
+ *   concatenating any trace in a with any trace in b.
+ *
+ * Its fields are:
+ * - valid is true if the set is non-empty.
+ * - netdiff (if valid) is the largest difference between stack size at the beginning and at the
+ *   end of the script across all traces in the set.
+ * - exec (if valid) is the largest difference between stack size anywhere during execution and at
+ *   the end of the script, across all traces in the set (note that this is not necessarily due
+ *   to the same trace as the one that resulted in the value for netdiff).
+ *
+ * This allows us to build up stack size limits for any script efficiently, by starting from the
+ * individual opcodes miniscripts correspond to, using concatenation to construct scripts, and
+ * using the union operation to choose between execution branches. Since any top-level script
+ * satisfaction ends with a single stack element, we know that for a full script:
+ * - netdiff+1 is the maximal initial stack size (relevant for P2WSH stack limits).
+ * - exec+1 is the maximal stack size reached during execution (relevant for P2TR stack limits).
+ *
+ * Mathematically, SatInfo forms a semiring:
+ * - operator| is the semiring addition operator, with identity SatInfo{}, and which is commutative
+ *   and associative.
+ * - operator+ is the semiring multiplication operator, with identity SatInfo{0}, and which is
+ *   associative.
+ * - operator+ is distributive over operator|, so (a + (b | c)) = (a+b | a+c). This means we do not
+ *   need to actually materialize all possible full execution traces over the whole script (which
+ *   may be exponential in the length of the script); instead we can use the union operation at the
+ *   individual subexpression level, and concatenate the result with subexpressions before and
+ *   after it.
+ * - It is not a commutative semiring, because a+b can differ from b+a. For example, "OP_1 OP_DROP"
+ *   has exec=1, while "OP_DROP OP_1" has exec=0.
+ */
+struct SatInfo {
+    //! Whether a canonical satisfaction/dissatisfaction is possible at all.
+    const bool valid;
+    //! How much higher the stack size at start of execution can be compared to at the end.
+    const int32_t netdiff;
+    //! Mow much higher the stack size can be during execution compared to at the end.
+    const int32_t exec;
+
+    /** Empty script set. */
+    constexpr SatInfo() noexcept : valid(false), netdiff(0), exec(0) {}
+
+    /** Script set with a single script in it, with specified netdiff and exec. */
+    constexpr SatInfo(int32_t in_netdiff, int32_t in_exec) noexcept :
+        valid{true}, netdiff{in_netdiff}, exec{in_exec} {}
+
+    /** Script set union. */
+    constexpr friend SatInfo operator|(const SatInfo& a, const SatInfo& b) noexcept
+    {
+        // Union with an empty set is itself.
+        if (!a.valid) return b;
+        if (!b.valid) return a;
+        // Otherwise the netdiff and exec of the union is the maximum of the individual values.
+        return {std::max(a.netdiff, b.netdiff), std::max(a.exec, b.exec)};
+    }
+
+    /** Script set concatenation. */
+    constexpr friend SatInfo operator+(const SatInfo& a, const SatInfo& b) noexcept
+    {
+        // Concatenation with an empty set yields an empty set.
+        if (!a.valid || !b.valid) return {};
+        // Otherwise, the maximum stack size difference for the combined scripts is the sum of the
+        // netdiffs, and the maximum stack size difference anywhere is either b.exec (if the
+        // maximum occurred in b) or b.netdiff+a.exec (if the maximum occurred in a).
+        return {a.netdiff + b.netdiff, std::max(b.exec, b.netdiff + a.exec)};
+    }
+
+    /** The empty script. */
+    static constexpr SatInfo Empty() noexcept { return {0, 0}; }
+    /** A script consisting of a single push opcode. */
+    static constexpr SatInfo Push() noexcept { return {-1, 0}; }
+    /** A script consisting of a single hash opcode. */
+    static constexpr SatInfo Hash() noexcept { return {0, 0}; }
+    /** A script consisting of just a repurposed nop (OP_CHECKLOCKTIMEVERIFY, OP_CHECKSEQUENCEVERIFY). */
+    static constexpr SatInfo Nop() noexcept { return {0, 0}; }
+    /** A script consisting of just OP_IF or OP_NOTIF. Note that OP_ELSE and OP_ENDIF have no stack effect. */
+    static constexpr SatInfo If() noexcept { return {1, 1}; }
+    /** A script consisting of just a binary operator (OP_BOOLAND, OP_BOOLOR, OP_ADD). */
+    static constexpr SatInfo BinaryOp() noexcept { return {1, 1}; }
+
+    // Scripts for specific individual opcodes.
+    static constexpr SatInfo OP_DUP() noexcept { return {-1, 0}; }
+    static constexpr SatInfo OP_IFDUP(bool nonzero) noexcept { return {nonzero ? -1 : 0, 0}; }
+    static constexpr SatInfo OP_EQUALVERIFY() noexcept { return {2, 2}; }
+    static constexpr SatInfo OP_EQUAL() noexcept { return {1, 1}; }
+    static constexpr SatInfo OP_SIZE() noexcept { return {-1, 0}; }
+    static constexpr SatInfo OP_CHECKSIG() noexcept { return {1, 1}; }
+    static constexpr SatInfo OP_0NOTEQUAL() noexcept { return {0, 0}; }
+    static constexpr SatInfo OP_VERIFY() noexcept { return {1, 1}; }
+};
+
 struct StackSize {
-    //! Maximum stack size to satisfy;
-    MaxInt<uint32_t> sat;
-    //! Maximum stack size to dissatisfy;
-    MaxInt<uint32_t> dsat;
+    const SatInfo sat, dsat;
 
-    StackSize(MaxInt<uint32_t> in_sat, MaxInt<uint32_t> in_dsat) : sat(in_sat), dsat(in_dsat) {};
+    constexpr StackSize(SatInfo in_sat, SatInfo in_dsat) noexcept : sat(in_sat), dsat(in_dsat) {};
+    constexpr StackSize(SatInfo in_both) noexcept : sat(in_both), dsat(in_both) {};
 };
 
 struct WitnessSize {
@@ -878,51 +977,115 @@ struct Node {
     }
 
     internal::StackSize CalcStackSize() const {
+        using namespace internal;
         switch (fragment) {
-            case Fragment::JUST_0: return {{}, 0};
-            case Fragment::JUST_1:
+            case Fragment::JUST_0: return {{}, SatInfo::Push()};
+            case Fragment::JUST_1: return {SatInfo::Push(), {}};
             case Fragment::OLDER:
-            case Fragment::AFTER: return {0, {}};
-            case Fragment::PK_K: return {0, 0};
-            case Fragment::PK_H: return {1, 1};
+            case Fragment::AFTER: return {SatInfo::Push() + SatInfo::Nop(), {}};
+            case Fragment::PK_K: return {SatInfo::Push()};
+            case Fragment::PK_H: return {SatInfo::OP_DUP() + SatInfo::Hash() + SatInfo::Push() + SatInfo::OP_EQUALVERIFY()};
             case Fragment::SHA256:
             case Fragment::RIPEMD160:
             case Fragment::HASH256:
-            case Fragment::HASH160: return {1, {}};
+            case Fragment::HASH160: return {
+                SatInfo::OP_SIZE() + SatInfo::Push() + SatInfo::OP_EQUALVERIFY() + SatInfo::Hash() + SatInfo::Push() + SatInfo::OP_EQUAL(),
+                {}
+            };
             case Fragment::ANDOR: {
-                const auto sat{(subs[0]->ss.sat + subs[1]->ss.sat) | (subs[0]->ss.dsat + subs[2]->ss.sat)};
-                const auto dsat{subs[0]->ss.dsat + subs[2]->ss.dsat};
-                return {sat, dsat};
+                const auto& x{subs[0]->ss};
+                const auto& y{subs[1]->ss};
+                const auto& z{subs[2]->ss};
+                return {
+                    (x.sat + SatInfo::If() + y.sat) | (x.dsat + SatInfo::If() + z.sat),
+                    x.dsat + SatInfo::If() + z.dsat
+                };
+            }
+            case Fragment::AND_V: {
+                const auto& x{subs[0]->ss};
+                const auto& y{subs[1]->ss};
+                return {x.sat + y.sat, {}};
+            }
+            case Fragment::AND_B: {
+                const auto& x{subs[0]->ss};
+                const auto& y{subs[1]->ss};
+                return {x.sat + y.sat + SatInfo::BinaryOp(), x.dsat + y.dsat + SatInfo::BinaryOp()};
             }
-            case Fragment::AND_V: return {subs[0]->ss.sat + subs[1]->ss.sat, {}};
-            case Fragment::AND_B: return {subs[0]->ss.sat + subs[1]->ss.sat, subs[0]->ss.dsat + subs[1]->ss.dsat};
             case Fragment::OR_B: {
-                const auto sat{(subs[0]->ss.dsat + subs[1]->ss.sat) | (subs[0]->ss.sat + subs[1]->ss.dsat)};
-                const auto dsat{subs[0]->ss.dsat + subs[1]->ss.dsat};
-                return {sat, dsat};
+                const auto& x{subs[0]->ss};
+                const auto& y{subs[1]->ss};
+                return {
+                    ((x.sat + y.dsat) | (x.dsat + y.sat)) + SatInfo::BinaryOp(),
+                    x.dsat + y.dsat + SatInfo::BinaryOp()
+                };
+            }
+            case Fragment::OR_C: {
+                const auto& x{subs[0]->ss};
+                const auto& y{subs[1]->ss};
+                return {(x.sat + SatInfo::If()) | (x.dsat + SatInfo::If() + y.sat), {}};
+            }
+            case Fragment::OR_D: {
+                const auto& x{subs[0]->ss};
+                const auto& y{subs[1]->ss};
+                return {
+                    (x.sat + SatInfo::OP_IFDUP(true) + SatInfo::If()) | (x.dsat + SatInfo::OP_IFDUP(false) + SatInfo::If() + y.sat),
+                    x.dsat + SatInfo::OP_IFDUP(false) + SatInfo::If() + y.dsat
+                };
+            }
+            case Fragment::OR_I: {
+                const auto& x{subs[0]->ss};
+                const auto& y{subs[1]->ss};
+                return {SatInfo::If() + (x.sat | y.sat), SatInfo::If() + (x.dsat | y.dsat)};
             }
-            case Fragment::OR_C: return {subs[0]->ss.sat | (subs[0]->ss.dsat + subs[1]->ss.sat), {}};
-            case Fragment::OR_D: return {subs[0]->ss.sat | (subs[0]->ss.dsat + subs[1]->ss.sat), subs[0]->ss.dsat + subs[1]->ss.dsat};
-            case Fragment::OR_I: return {(subs[0]->ss.sat + 1) | (subs[1]->ss.sat + 1), (subs[0]->ss.dsat + 1) | (subs[1]->ss.dsat + 1)};
-            case Fragment::MULTI: return {k + 1, k + 1};
-            case Fragment::MULTI_A: return {keys.size(), keys.size()};
+            // multi(k, key1, key2, ..., key_n) starts off with k+1 stack elements (a 0, plus k
+            // signatures), then reaches n+k+3 stack elements after pushing the n keys, plus k and
+            // n itself, and ends with 1 stack element (success or failure). Thus, it net removes
+            // k elements (from k+1 to 1), while reaching k+n+2 more than it ends with.
+            case Fragment::MULTI: return {SatInfo(k, k + keys.size() + 2)};
+            // multi_a(k, key1, key2, ..., key_n) starts off with n stack elements (the
+            // signatures), reaches 1 more (after the first key push), and ends with 1. Thus it net
+            // removes n-1 elements (from n to 1) while reaching n more than it ends with.
+            case Fragment::MULTI_A: return {SatInfo(keys.size() - 1, keys.size())};
             case Fragment::WRAP_A:
             case Fragment::WRAP_N:
             case Fragment::WRAP_S: return subs[0]->ss;
-            case Fragment::WRAP_C: return {subs[0]->ss.sat + 1, subs[0]->ss.dsat + 1};
-            case Fragment::WRAP_D: return {1 + subs[0]->ss.sat, 1};
-            case Fragment::WRAP_V: return {subs[0]->ss.sat, {}};
-            case Fragment::WRAP_J: return {subs[0]->ss.sat, 1};
+            case Fragment::WRAP_C: return {
+                subs[0]->ss.sat + SatInfo::OP_CHECKSIG(),
+                subs[0]->ss.dsat + SatInfo::OP_CHECKSIG()
+            };
+            case Fragment::WRAP_D: return {
+                SatInfo::OP_DUP() + SatInfo::If() + subs[0]->ss.sat,
+                SatInfo::OP_DUP() + SatInfo::If()
+            };
+            case Fragment::WRAP_V: return {subs[0]->ss.sat + SatInfo::OP_VERIFY(), {}};
+            case Fragment::WRAP_J: return {
+                SatInfo::OP_SIZE() + SatInfo::OP_0NOTEQUAL() + SatInfo::If() + subs[0]->ss.sat,
+                SatInfo::OP_SIZE() + SatInfo::OP_0NOTEQUAL() + SatInfo::If()
+            };
             case Fragment::THRESH: {
-                auto sats = Vector(internal::MaxInt<uint32_t>(0));
-                for (const auto& sub : subs) {
-                    auto next_sats = Vector(sats[0] + sub->ss.dsat);
-                    for (size_t j = 1; j < sats.size(); ++j) next_sats.push_back((sats[j] + sub->ss.dsat) | (sats[j - 1] + sub->ss.sat));
-                    next_sats.push_back(sats[sats.size() - 1] + sub->ss.sat);
+                // sats[j] is the SatInfo corresponding to all traces reaching j satisfactions.
+                auto sats = Vector(SatInfo::Empty());
+                for (size_t i = 0; i < subs.size(); ++i) {
+                    // Loop over the subexpressions, processing them one by one. After adding
+                    // element i we need to add OP_ADD (if i>0).
+                    auto add = i ? SatInfo::BinaryOp() : SatInfo::Empty();
+                    // Construct a variable that will become the next sats, starting with index 0.
+                    auto next_sats = Vector(sats[0] + subs[i]->ss.dsat + add);
+                    // Then loop to construct next_sats[1..i].
+                    for (size_t j = 1; j < sats.size(); ++j) {
+                        next_sats.push_back(((sats[j] + subs[i]->ss.dsat) | (sats[j - 1] + subs[i]->ss.sat)) + add);
+                    }
+                    // Finally construct next_sats[i+1].
+                    next_sats.push_back(sats[sats.size() - 1] + subs[i]->ss.sat + add);
+                    // Switch over.
                     sats = std::move(next_sats);
                 }
-                assert(k <= sats.size());
-                return {sats[k], sats[0]};
+                // To satisfy thresh we need k satisfactions; to dissatisfy we need 0. In both
+                // cases a push of k and an OP_EQUAL follow.
+                return {
+                    sats[k] + SatInfo::Push() + SatInfo::OP_EQUAL(),
+                    sats[0] + SatInfo::Push() + SatInfo::OP_EQUAL()
+                };
             }
         }
         assert(false);
@@ -1310,17 +1473,32 @@ struct Node {
         return true;
     }
 
+    /** Whether this node is of type B, K or W. (That is, anything but V.) */
+    bool IsBKW() const {
+        return !((GetType() & "BKW"_mst) == ""_mst);
+    }
+
     /** Return the maximum number of stack elements needed to satisfy this script non-malleably.
      * This does not account for the P2WSH script push. */
     std::optional<uint32_t> GetStackSize() const {
         if (!ss.sat.valid) return {};
-        return ss.sat.value;
+        return ss.sat.netdiff + static_cast<int32_t>(IsBKW());
+    }
+
+    //! Return the maximum size of the stack during execution of this script.
+    std::optional<uint32_t> GetExecStackSize() const {
+        if (!ss.sat.valid) return {};
+        return ss.sat.exec + static_cast<int32_t>(IsBKW());
     }
 
     //! Check the maximum stack size for this script against the policy limit.
     bool CheckStackSize() const {
-        // TODO: MAX_STACK_SIZE during script execution under Tapscript.
-        if (IsTapscript(m_script_ctx)) return true;
+        // Since in Tapscript there is no standardness limit on the script and witness sizes, we may run
+        // into the maximum stack size while executing the script. Make sure it doesn't happen.
+        if (IsTapscript(m_script_ctx)) {
+            if (const auto exec_ss = GetExecStackSize()) return exec_ss <= MAX_STACK_SIZE;
+            return true;
+        }
         if (const auto ss = GetStackSize()) return *ss <= MAX_STANDARD_P2WSH_STACK_ITEMS;
         return true;
     }