crypto: torsion clearing for FCMP++

diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 85116ae..8217a2c 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -83,6 +83,7 @@ monero_add_library(version SOURCES ${CMAKE_BINARY_DIR}/version.cpp DEPENDS genve
 
 add_subdirectory(common)
 add_subdirectory(crypto)
+add_subdirectory(fcmp_pp)
 add_subdirectory(ringct)
 add_subdirectory(checkpoints)
 add_subdirectory(cryptonote_basic)
diff --git a/src/crypto/crypto.h b/src/crypto/crypto.h
index 1145192..4a6b20a 100644
--- a/src/crypto/crypto.h
+++ b/src/crypto/crypto.h
@@ -320,6 +320,9 @@ namespace crypto {
   inline std::ostream &operator <<(std::ostream &o, const crypto::view_tag &v) {
     epee::to_hex::formatted(o, epee::as_byte_span(v)); return o;
   }
+  inline std::ostream &operator <<(std::ostream &o, const crypto::ec_point &v) {
+    epee::to_hex::formatted(o, epee::as_byte_span(v)); return o;
+  }
 
   const extern crypto::public_key null_pkey;
   const extern crypto::secret_key null_skey;
@@ -336,6 +339,7 @@ inline const unsigned char* to_bytes(const crypto::ec_scalar &scalar) { return &
 inline unsigned char* to_bytes(crypto::ec_point &point) { return &reinterpret_cast<unsigned char&>(point); }
 inline const unsigned char* to_bytes(const crypto::ec_point &point) { return &reinterpret_cast<const unsigned char&>(point); }
 
+CRYPTO_MAKE_HASHABLE(ec_point)
 CRYPTO_MAKE_HASHABLE(public_key)
 CRYPTO_MAKE_HASHABLE_CONSTANT_TIME(secret_key)
 CRYPTO_MAKE_HASHABLE_CONSTANT_TIME(public_key_memsafe)
diff --git a/src/fcmp_pp/CMakeLists.txt b/src/fcmp_pp/CMakeLists.txt
new file mode 100644
index 0000000..32ca1b4
--- /dev/null
+++ b/src/fcmp_pp/CMakeLists.txt
@@ -0,0 +1,42 @@
+# Copyright (c) 2024, The Monero Project
+#
+# All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without modification, are
+# permitted provided that the following conditions are met:
+#
+# 1. Redistributions of source code must retain the above copyright notice, this list of
+#    conditions and the following disclaimer.
+#
+# 2. Redistributions in binary form must reproduce the above copyright notice, this list
+#    of conditions and the following disclaimer in the documentation and/or other
+#    materials provided with the distribution.
+#
+# 3. Neither the name of the copyright holder nor the names of its contributors may be
+#    used to endorse or promote products derived from this software without specific
+#    prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
+# EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+# MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
+# THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+# STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
+# THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+set(fcmp_pp_sources
+  fcmp_pp_crypto.cpp)
+
+monero_find_all_headers(fcmp_pp_headers "${CMAKE_CURRENT_SOURCE_DIR}")
+
+monero_add_library(fcmp_pp
+  ${fcmp_pp_sources}
+  ${fcmp_pp_headers})
+
+target_link_libraries(fcmp_pp
+  PUBLIC
+    cncrypto
+  PRIVATE
+    ${EXTRA_LIBRARIES})
diff --git a/src/fcmp_pp/fcmp_pp_crypto.cpp b/src/fcmp_pp/fcmp_pp_crypto.cpp
new file mode 100644
index 0000000..39b95db
--- /dev/null
+++ b/src/fcmp_pp/fcmp_pp_crypto.cpp
@@ -0,0 +1,68 @@
+// Copyright (c) 2024, The Monero Project
+// 
+// All rights reserved.
+// 
+// Redistribution and use in source and binary forms, with or without modification, are
+// permitted provided that the following conditions are met:
+// 
+// 1. Redistributions of source code must retain the above copyright notice, this list of
+//    conditions and the following disclaimer.
+// 
+// 2. Redistributions in binary form must reproduce the above copyright notice, this list
+//    of conditions and the following disclaimer in the documentation and/or other
+//    materials provided with the distribution.
+// 
+// 3. Neither the name of the copyright holder nor the names of its contributors may be
+//    used to endorse or promote products derived from this software without specific
+//    prior written permission.
+// 
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
+// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
+// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
+// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#include "fcmp_pp_crypto.h"
+
+namespace fcmp_pp
+{
+//----------------------------------------------------------------------------------------------------------------------
+bool mul8_is_identity_vartime(const ge_p3 &point) {
+    ge_p2 point_ge_p2;
+    ge_p3_to_p2(&point_ge_p2, &point);
+    ge_p1p1 point_mul8;
+    ge_mul8(&point_mul8, &point_ge_p2);
+    ge_p3 point_mul8_p3;
+    ge_p1p1_to_p3(&point_mul8_p3, &point_mul8);
+    return ge_p3_is_point_at_infinity_vartime(&point_mul8_p3);
+}
+//----------------------------------------------------------------------------------------------------------------------
+crypto::ec_point clear_torsion_vartime(const ge_p3 &point) {
+    // mul by inv 8, then mul by 8
+    ge_p2 point_inv_8;
+    ge_scalarmult(&point_inv_8, to_bytes(EC_INV_EIGHT), &point);
+    ge_p1p1 point_inv_8_mul_8;
+    ge_mul8(&point_inv_8_mul_8, &point_inv_8);
+    ge_p3 torsion_cleared_point;
+    ge_p1p1_to_p3(&torsion_cleared_point, &point_inv_8_mul_8);
+    crypto::ec_point k_out;
+    ge_p3_tobytes(to_bytes(k_out), &torsion_cleared_point);
+    return k_out;
+}
+//----------------------------------------------------------------------------------------------------------------------
+bool get_valid_torsion_cleared_point_vartime(const crypto::ec_point &point, crypto::ec_point &torsion_cleared_out) {
+    ge_p3 p3;
+    if (ge_frombytes_vartime(&p3, to_bytes(point)) != 0)
+        return false;
+    torsion_cleared_out = fcmp_pp::clear_torsion_vartime(p3);
+    if (torsion_cleared_out == EC_I)
+        return false;
+    return true;
+}
+//----------------------------------------------------------------------------------------------------------------------
+//----------------------------------------------------------------------------------------------------------------------
+}//namespace fcmp_pp
diff --git a/src/fcmp_pp/fcmp_pp_crypto.h b/src/fcmp_pp/fcmp_pp_crypto.h
new file mode 100644
index 0000000..d1d2b1b
--- /dev/null
+++ b/src/fcmp_pp/fcmp_pp_crypto.h
@@ -0,0 +1,68 @@
+// Copyright (c) 2024, The Monero Project
+// 
+// All rights reserved.
+// 
+// Redistribution and use in source and binary forms, with or without modification, are
+// permitted provided that the following conditions are met:
+// 
+// 1. Redistributions of source code must retain the above copyright notice, this list of
+//    conditions and the following disclaimer.
+// 
+// 2. Redistributions in binary form must reproduce the above copyright notice, this list
+//    of conditions and the following disclaimer in the documentation and/or other
+//    materials provided with the distribution.
+// 
+// 3. Neither the name of the copyright holder nor the names of its contributors may be
+//    used to endorse or promote products derived from this software without specific
+//    prior written permission.
+// 
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
+// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
+// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
+// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#pragma once
+
+extern "C"
+{
+#include "crypto/crypto-ops.h"
+}
+#include "crypto/crypto.h"
+
+namespace fcmp_pp
+{
+//----------------------------------------------------------------------------------------------------------------------
+//----------------------------------------------------------------------------------------------------------------------
+static const crypto::ec_point EC_I = {1};
+
+static const crypto::ec_scalar EC_INV_EIGHT = {{
+    static_cast<char>(static_cast<signed char>(121)), static_cast<char>(static_cast<signed char>(47)),
+    static_cast<char>(static_cast<signed char>(-36)), static_cast<char>(static_cast<signed char>(-30)),
+    static_cast<char>(static_cast<signed char>(41)),  static_cast<char>(static_cast<signed char>(-27)),
+    static_cast<char>(static_cast<signed char>(6)),   static_cast<char>(static_cast<signed char>(97)),
+    static_cast<char>(static_cast<signed char>(-48)), static_cast<char>(static_cast<signed char>(-38)),
+    static_cast<char>(static_cast<signed char>(28)),  static_cast<char>(static_cast<signed char>(125)),
+    static_cast<char>(static_cast<signed char>(-77)), static_cast<char>(static_cast<signed char>(-99)),
+    static_cast<char>(static_cast<signed char>(-45)), static_cast<char>(static_cast<signed char>(7)),
+    static_cast<char>(static_cast<signed char>(0)),   static_cast<char>(static_cast<signed char>(0)),
+    static_cast<char>(static_cast<signed char>(0)),   static_cast<char>(static_cast<signed char>(0)),
+    static_cast<char>(static_cast<signed char>(0)),   static_cast<char>(static_cast<signed char>(0)),
+    static_cast<char>(static_cast<signed char>(0)),   static_cast<char>(static_cast<signed char>(0)),
+    static_cast<char>(static_cast<signed char>(0)),   static_cast<char>(static_cast<signed char>(0)),
+    static_cast<char>(static_cast<signed char>(0)),   static_cast<char>(static_cast<signed char>(0)),
+    static_cast<char>(static_cast<signed char>(0)),   static_cast<char>(static_cast<signed char>(0)),
+    static_cast<char>(static_cast<signed char>(0)),   static_cast<char>(static_cast<signed char>(6))
+  }};
+//----------------------------------------------------------------------------------------------------------------------
+//----------------------------------------------------------------------------------------------------------------------
+bool mul8_is_identity_vartime(const ge_p3 &point);
+crypto::ec_point clear_torsion_vartime(const ge_p3 &point);
+bool get_valid_torsion_cleared_point_vartime(const crypto::ec_point &point, crypto::ec_point &torsion_cleared_out);
+//----------------------------------------------------------------------------------------------------------------------
+//----------------------------------------------------------------------------------------------------------------------
+}//namespace fcmp_pp
diff --git a/src/ringct/CMakeLists.txt b/src/ringct/CMakeLists.txt
index 8a6ed9f..c1a6d14 100644
--- a/src/ringct/CMakeLists.txt
+++ b/src/ringct/CMakeLists.txt
@@ -70,6 +70,7 @@ target_link_libraries(ringct
     common
     cncrypto
     device
+    fcmp_pp
   PRIVATE
     ${OPENSSL_LIBRARIES}
     ${EXTRA_LIBRARIES})
diff --git a/src/ringct/rctSigs.cpp b/src/ringct/rctSigs.cpp
index 6a2e32a..90e3c3a 100644
--- a/src/ringct/rctSigs.cpp
+++ b/src/ringct/rctSigs.cpp
@@ -30,6 +30,8 @@
 
 #include "rctSigs.h"
 
+#include <atomic>
+
 #include "misc_log_ex.h"
 #include "misc_language.h"
 #include "common/perf_timer.h"
@@ -39,6 +41,7 @@
 #include "bulletproofs_plus.h"
 #include "cryptonote_config.h"
 #include "device/device.hpp"
+#include "fcmp_pp/fcmp_pp_crypto.h"
 #include "serialization/crypto.h"
 
 using namespace crypto;
@@ -1574,4 +1577,33 @@ namespace rct {
       key mask;
       return decodeRct(rv, sk, i, mask, hwdev);
     }
+
+    bool verPointsForTorsion(const std::vector<key> & pts) {
+      if (pts.empty())
+        return true;
+
+      tools::threadpool& tpool = tools::threadpool::getInstanceForCompute();
+      tools::threadpool::waiter waiter(tpool);
+
+      std::atomic<bool> all_valid{true};
+      for (std::size_t i = 0; i < pts.size(); ++i)
+      {
+        tpool.submit(&waiter, [&pts, &all_valid, i]
+          {
+            const crypto::ec_point &point = rct::rct2pt(pts[i]);
+            crypto::ec_point torsion_cleared_point;
+            if (fcmp_pp::get_valid_torsion_cleared_point_vartime(point, torsion_cleared_point)
+                && point == torsion_cleared_point)
+            {
+              // Point is torsion free if it's equal to itself after clearing torsion
+              return;
+            }
+            all_valid.store(false);
+          });
+      }
+
+      CHECK_AND_ASSERT_MES(waiter.wait(), false, "threadpool waiter failed in torsion check");
+      CHECK_AND_ASSERT_MES(all_valid.load(), false, "Torsion check failed");
+      return true;
+    }
 }
diff --git a/src/ringct/rctSigs.h b/src/ringct/rctSigs.h
index 6cc7e74..3b9fe09 100644
--- a/src/ringct/rctSigs.h
+++ b/src/ringct/rctSigs.h
@@ -136,6 +136,9 @@ namespace rct {
     xmr_amount decodeRct(const rctSig & rv, const key & sk, unsigned int i, key & mask, hw::device &hwdev);
     xmr_amount decodeRct(const rctSig & rv, const key & sk, unsigned int i, hw::device &hwdev);
     key get_pre_mlsag_hash(const rctSig &rv, hw::device &hwdev);
+
+    // Make sure points are valid points, don't have torsion, and are not equal to identity
+    bool verPointsForTorsion(const std::vector<key> & pts);
 }
 #endif  /* RCTSIGS_H */
 
diff --git a/src/ringct/rctTypes.h b/src/ringct/rctTypes.h
index 038c2e1..608aa5b 100644
--- a/src/ringct/rctTypes.h
+++ b/src/ringct/rctTypes.h
@@ -741,10 +741,12 @@ namespace rct {
     static inline const rct::key &sk2rct(const crypto::secret_key &sk) { return (const rct::key&)sk; }
     static inline const rct::key &ki2rct(const crypto::key_image &ki) { return (const rct::key&)ki; }
     static inline const rct::key &hash2rct(const crypto::hash &h) { return (const rct::key&)h; }
+    static inline const rct::key &pt2rct(const crypto::ec_point &pt) { return (const rct::key&)pt; }
     static inline const crypto::public_key &rct2pk(const rct::key &k) { return (const crypto::public_key&)k; }
     static inline const crypto::secret_key &rct2sk(const rct::key &k) { return (const crypto::secret_key&)k; }
     static inline const crypto::key_image &rct2ki(const rct::key &k) { return (const crypto::key_image&)k; }
     static inline const crypto::hash &rct2hash(const rct::key &k) { return (const crypto::hash&)k; }
+    static inline const crypto::ec_point &rct2pt(const rct::key &k) { return (const crypto::ec_point&)k; }
     static inline bool operator==(const rct::key &k0, const crypto::public_key &k1) { return !crypto_verify_32(k0.bytes, (const unsigned char*)&k1); }
     static inline bool operator!=(const rct::key &k0, const crypto::public_key &k1) { return crypto_verify_32(k0.bytes, (const unsigned char*)&k1); }
 }
diff --git a/tests/crypto/main.cpp b/tests/crypto/main.cpp
index 668c04e..913f8ab 100644
--- a/tests/crypto/main.cpp
+++ b/tests/crypto/main.cpp
@@ -49,10 +49,6 @@ bool operator !=(const ec_scalar &a, const ec_scalar &b) {
   return 0 != memcmp(&a, &b, sizeof(ec_scalar));
 }
 
-bool operator !=(const ec_point &a, const ec_point &b) {
-  return 0 != memcmp(&a, &b, sizeof(ec_point));
-}
-
 bool operator !=(const key_derivation &a, const key_derivation &b) {
   return 0 != memcmp(&a, &b, sizeof(key_derivation));
 }
diff --git a/tests/unit_tests/CMakeLists.txt b/tests/unit_tests/CMakeLists.txt
index dc30a24..00e4259 100644
--- a/tests/unit_tests/CMakeLists.txt
+++ b/tests/unit_tests/CMakeLists.txt
@@ -121,6 +121,7 @@ target_link_libraries(unit_tests
     daemon_messages
     daemon_rpc_server
     blockchain_db
+    fcmp_pp
     lmdb_lib
     rpc
     net
diff --git a/tests/unit_tests/crypto.cpp b/tests/unit_tests/crypto.cpp
index 8583185..2cd260c 100644
--- a/tests/unit_tests/crypto.cpp
+++ b/tests/unit_tests/crypto.cpp
@@ -39,8 +39,11 @@ extern "C"
 }
 #include "crypto/generators.h"
 #include "cryptonote_basic/merge_mining.h"
+#include "fcmp_pp/fcmp_pp_crypto.h"
 #include "ringct/rctOps.h"
+#include "ringct/rctSigs.h"
 #include "ringct/rctTypes.h"
+#include "string_tools.h"
 
 namespace
 {
@@ -429,3 +432,92 @@ TEST(Crypto, fe_equals)
   ASSERT_NE(memcmp(fe_d2_reduced, fe_d2, sizeof(fe)), 0);
   ASSERT_EQ(fe_equals(fe_d2_reduced, fe_d2), 1);
 }
+
+TEST(Crypto, ec_constants_rct_parity)
+{
+  ASSERT_TRUE(memcmp(&fcmp_pp::EC_I,         &rct::I,         32) == 0);
+  ASSERT_TRUE(memcmp(&fcmp_pp::EC_INV_EIGHT, &rct::INV_EIGHT, 32) == 0);
+}
+
+#define CHECK_CLEARED(k, cleared) \
+  crypto::ec_point cleared2; \
+  const bool r = fcmp_pp::get_valid_torsion_cleared_point_vartime(rct::rct2pt(k), cleared2); \
+  ASSERT_TRUE(r); \
+  ASSERT_EQ(cleared, cleared2);
+
+TEST(Crypto, torsion_check_pass_random)
+{
+  std::vector<rct::key> pts;
+  for (int i = 0; i < 1000; ++i)
+  {
+    const rct::key pk = rct::pkGen();
+    ge_p3 x;
+    ASSERT_EQ(ge_frombytes_vartime(&x, pk.bytes), 0);
+    ASSERT_TRUE(rct::isInMainSubgroup(pk));
+    ASSERT_FALSE(fcmp_pp::mul8_is_identity_vartime(x));
+    const crypto::ec_point cleared = fcmp_pp::clear_torsion_vartime(x);
+    ASSERT_EQ(rct::rct2pt(pk), cleared);
+    CHECK_CLEARED(pk, cleared);
+    pts.emplace_back(pk);
+  }
+  ASSERT_TRUE(rct::verPointsForTorsion(pts));
+}
+
+TEST(Crypto, torsion_check_hardcoded)
+{
+  struct TorsionTestPoints { std::string point; bool torsion_free; };
+  static const std::vector<TorsionTestPoints> torsion_test_points = {
+      {"b10ba13e303cbe9abf7d5d44f1d417727abcc14903a74e071abd652ce1bf76dd", false},
+      {"9b2e4c0281c0b02e7c53291a94d1d0cbff8883f8024f5142ee494ffbbd088071", false}, // genesis (see config::GENESIS_TX)
+      {"785eda585dca4f3d27976106008ccfbca13146c8b21b8c7e4909032639a776e1", true},
+      {"9a7b10563aa266032cd075f4e347f348a3841ae4f41572633351a97dd44066b4", true},
+    };
+
+  std::vector<rct::key> all_pts, torsion_free_pts, torsioned_pts, torsion_cleared_pts;
+  for (const auto &point : torsion_test_points)
+  {
+    rct::key k;
+    epee::string_tools::hex_to_pod(point.point, k);
+    ge_p3 x;
+    ASSERT_EQ(ge_frombytes_vartime(&x, k.bytes), 0);
+    ASSERT_EQ(rct::isInMainSubgroup(k), point.torsion_free);
+    ASSERT_FALSE(fcmp_pp::mul8_is_identity_vartime(x));
+    const crypto::ec_point cleared = fcmp_pp::clear_torsion_vartime(x);
+    if (point.torsion_free)
+    {
+      ASSERT_EQ(rct::rct2pt(k), cleared);
+      torsion_free_pts.push_back(k);
+    }
+    else
+    {
+      ASSERT_NE(rct::rct2pt(k), cleared);
+      torsioned_pts.push_back(k);
+    }
+    CHECK_CLEARED(k, cleared);
+    all_pts.emplace_back(k);
+    torsion_cleared_pts.emplace_back(rct::pt2rct(cleared));
+  }
+
+  ASSERT_TRUE(rct::verPointsForTorsion(torsion_free_pts));
+  ASSERT_FALSE(rct::verPointsForTorsion(torsioned_pts));
+  ASSERT_FALSE(rct::verPointsForTorsion(all_pts));
+  ASSERT_TRUE(rct::verPointsForTorsion(torsion_cleared_pts));
+}
+
+TEST(Crypto, mul8_is_identity_vartime)
+{
+  static const std::vector<rct::key> mul8_identity_points = {
+      rct::I,
+      rct::Z
+    };
+
+  for (const auto &point : mul8_identity_points)
+  {
+    ge_p3 x;
+    ASSERT_EQ(ge_frombytes_vartime(&x, point.bytes), 0);
+    ASSERT_TRUE(fcmp_pp::mul8_is_identity_vartime(x));
+
+    crypto::ec_point _;
+    ASSERT_FALSE(fcmp_pp::get_valid_torsion_cleared_point_vartime(rct::rct2pt(point), _));
+  }
+}