bulletproofs: reject points not in the main subgroup

src/ringct/bulletproofs.cc

@@ -922,6 +922,19 @@ bool bulletproof_VERIFY(const std::vector<const Bulletproof*> &proofs)
   for (const Bulletproof *p: proofs)
   {
     const Bulletproof &proof = *p;
+
+    // check subgroup
+    for (const rct::key &k: proof.V)
+      CHECK_AND_ASSERT_MES(rct::isInMainSubgroup(k), false, "Input point not in subgroup");
+    for (const rct::key &k: proof.L)
+      CHECK_AND_ASSERT_MES(rct::isInMainSubgroup(k), false, "Input point not in subgroup");
+    for (const rct::key &k: proof.R)
+      CHECK_AND_ASSERT_MES(rct::isInMainSubgroup(k), false, "Input point not in subgroup");
+    CHECK_AND_ASSERT_MES(rct::isInMainSubgroup(proof.A), false, "Input point not in subgroup");
+    CHECK_AND_ASSERT_MES(rct::isInMainSubgroup(proof.S), false, "Input point not in subgroup");
+    CHECK_AND_ASSERT_MES(rct::isInMainSubgroup(proof.T1), false, "Input point not in subgroup");
+    CHECK_AND_ASSERT_MES(rct::isInMainSubgroup(proof.T2), false, "Input point not in subgroup");
+
     CHECK_AND_ASSERT_MES(proof.V.size() >= 1, false, "V does not have at least one element");
     CHECK_AND_ASSERT_MES(proof.L.size() == proof.R.size(), false, "Mismatched L and R sizes");
     CHECK_AND_ASSERT_MES(proof.L.size() > 0, false, "Empty proof");

src/ringct/rctOps.cpp

@@ -60,6 +60,17 @@ namespace rct {
 
     //Various key generation functions
 
+    bool toPointCheckOrder(ge_p3 *P, const unsigned char *data)
+    {
+        if (ge_frombytes_vartime(P, data))
+            return false;
+        ge_p2 R;
+        ge_scalarmult(&R, curveOrder().bytes, P);
+        key tmp;
+        ge_tobytes(tmp.bytes, &R);
+        return tmp == identity();
+    }
+
     //generates a random scalar which can be used as a secret key or mask
     void skGen(key &sk) {
         random32_unbiased(sk.bytes);
@@ -200,6 +211,12 @@ namespace rct {
         return aP;
     }
 
+    //Computes aL where L is the curve order
+    bool isInMainSubgroup(const key & a) {
+        ge_p3 p3;
+        return toPointCheckOrder(&p3, a.bytes);
+    }
+
     //Curve addition / subtractions
 
     //for curve points: AB = A + B

src/ringct/rctOps.h

@@ -83,6 +83,7 @@ namespace rct {
     keyM keyMInit(size_t rows, size_t cols);
 
     //Various key generation functions        
+    bool toPointCheckOrder(ge_p3 *P, const unsigned char *data);
 
     //generates a random scalar which can be used as a secret key or mask
     key skGen();
@@ -119,6 +120,8 @@ namespace rct {
     key scalarmultKey(const key &P, const key &a);
     //Computes aH where H= toPoint(cn_fast_hash(G)), G the basepoint
     key scalarmultH(const key & a);
+    // checks a is in the main subgroup (ie, not a small one)
+    bool isInMainSubgroup(const key & a);
 
     //Curve addition / subtractions
 

tests/performance_tests/crypto_ops.h

@@ -51,6 +51,7 @@ enum test_op
   op_addKeys2,
   op_addKeys3,
   op_addKeys3_2,
+  op_isInMainSubgroup,
 };
 
 template<test_op op>
@@ -102,6 +103,7 @@ public:
       case op_addKeys2: rct::addKeys2(key, scalar0, scalar1, point0); break;
       case op_addKeys3: rct::addKeys3(key, scalar0, point0, scalar1, precomp1); break;
       case op_addKeys3_2: rct::addKeys3(key, scalar0, precomp0, scalar1, precomp1); break;
+      case op_isInMainSubgroup: rct::isInMainSubgroup(point0); break;
       default: return false;
     }
     return true;

tests/performance_tests/main.cpp

@@ -237,6 +237,7 @@ int main(int argc, char** argv)
   TEST_PERFORMANCE1(filter, p, test_crypto_ops, op_addKeys2);
   TEST_PERFORMANCE1(filter, p, test_crypto_ops, op_addKeys3);
   TEST_PERFORMANCE1(filter, p, test_crypto_ops, op_addKeys3_2);
+  TEST_PERFORMANCE1(filter, p, test_crypto_ops, op_isInMainSubgroup);
 
   TEST_PERFORMANCE2(filter, p, test_multiexp, multiexp_bos_coster, 2);
   TEST_PERFORMANCE2(filter, p, test_multiexp, multiexp_bos_coster, 4);

tests/unit_tests/bulletproofs.cpp

@@ -30,6 +30,7 @@
 
 #include "gtest/gtest.h"
 
+#include "string_tools.h"
 #include "ringct/rctOps.h"
 #include "ringct/rctSigs.h"
 #include "ringct/bulletproofs.h"
@@ -193,3 +194,63 @@ TEST(bulletproofs, invalid_gamma_ff)
   rct::Bulletproof proof = bulletproof_PROVE(invalid_amount, gamma);
   ASSERT_FALSE(rct::bulletproof_VERIFY(proof));
 }
+
+static const char * const torsion_elements[] =
+{
+  "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa",
+  "0000000000000000000000000000000000000000000000000000000000000000",
+  "26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc85",
+  "ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f",
+  "26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05",
+  "0000000000000000000000000000000000000000000000000000000000000080",
+  "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a",
+};
+
+TEST(bulletproofs, invalid_torsion)
+{
+  rct::Bulletproof proof = bulletproof_PROVE(7329838943733, rct::skGen());
+  ASSERT_TRUE(rct::bulletproof_VERIFY(proof));
+  for (const auto &xs: torsion_elements)
+  {
+    rct::key x;
+    ASSERT_TRUE(epee::string_tools::hex_to_pod(xs, x));
+    ASSERT_FALSE(rct::isInMainSubgroup(x));
+    for (auto &k: proof.V)
+    {
+      const rct::key org_k = k;
+      rct::addKeys(k, org_k, x);
+      ASSERT_FALSE(rct::bulletproof_VERIFY(proof));
+      k = org_k;
+    }
+    for (auto &k: proof.L)
+    {
+      const rct::key org_k = k;
+      rct::addKeys(k, org_k, x);
+      ASSERT_FALSE(rct::bulletproof_VERIFY(proof));
+      k = org_k;
+    }
+    for (auto &k: proof.R)
+    {
+      const rct::key org_k = k;
+      rct::addKeys(k, org_k, x);
+      ASSERT_FALSE(rct::bulletproof_VERIFY(proof));
+      k = org_k;
+    }
+    const rct::key org_A = proof.A;
+    rct::addKeys(proof.A, org_A, x);
+    ASSERT_FALSE(rct::bulletproof_VERIFY(proof));
+    proof.A = org_A;
+    const rct::key org_S = proof.S;
+    rct::addKeys(proof.S, org_S, x);
+    ASSERT_FALSE(rct::bulletproof_VERIFY(proof));
+    proof.S = org_S;
+    const rct::key org_T1 = proof.T1;
+    rct::addKeys(proof.T1, org_T1, x);
+    ASSERT_FALSE(rct::bulletproof_VERIFY(proof));
+    proof.T1 = org_T1;
+    const rct::key org_T2 = proof.T2;
+    rct::addKeys(proof.T2, org_T2, x);
+    ASSERT_FALSE(rct::bulletproof_VERIFY(proof));
+    proof.T2 = org_T2;
+  }
+}