crypto: derive key image generator & separate {un}biased hash to ec https://github.com/monero-project/research-lab/issues/142
What changed, and why it matters
This commit adds new cryptographic routines to Monero and renames an existing one. It introduces a new way to derive 'key image generators' (used to prove a coin hasn't been spent twice) and a new 'unbiased' method for hashing data to an elliptic-curve point. The old method is now explicitly labeled 'biased' but remains in use for existing ring signatures. The changes are presented as a research-driven cryptographic improvement, not as a fix for an active bug or vulnerability.
Treat this as a cryptographic hardening and API-extension change rather than an urgent security fix. Review the new `unbiased_hash_to_ec` and `blake2b_monero` implementations for correctness, constant-time behavior where required, and proper handling of hash-function error codes. Ensure that future protocol upgrades (e.g., FCMP++/Carrot) correctly select the unbiased path and that the biased path is not accidentally used where unbiased is required.
Security signals we found
New keyed hash primitive with domain separation (BLAKE2b personalization 'Monero')
Introduction of an unbiased hash-to-curve construction alongside the existing biased one
Renaming of legacy hash-to-ec to 'biased_hash_to_ec' to flag its non-uniform distribution
Key image generator derivation split into biased/unbiased variants
No removal or change to existing ring-signature/key-image logic; backward-compatible path retained
Evidence from the diff
The patch adds blake2b_monero, a keyed BLAKE2b variant with a fixed ‘Monero’ personalization string, and exposes it in crypto.h. It renames the existing hash_to_ec to biased_hash_to_ec and adds a new unbiased_hash_to_ec that uses a 64-byte BLAKE2b output split into two 32-byte field elements, maps each to a curve point via ge_fromfe_frombytes_vartime, multiplies by the cofactor, and adds the results. A new derive_key_image_generator API is introduced with biased and unbiased variants. Existing generate_key_image and ring-signature code continue to use the biased path, preserving backward compatibility. Tests and test vectors are updated accordingly.
Changed components
src/crypto/blake2b.csrc/crypto/blake2b.hsrc/crypto/crypto.cppsrc/crypto/crypto.htests/crypto/crypto-tests.htests/crypto/crypto.cpptests/crypto/main.cpptests/crypto/tests.txtInspect captured patch +612 / −267
diff --git a/src/crypto/blake2b.c b/src/crypto/blake2b.c
index 6c0d78e..00f4add 100644
--- a/src/crypto/blake2b.c
+++ b/src/crypto/blake2b.c
@@ -36,6 +36,7 @@ OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#include "memwipe.h"
+#include <assert.h>
#include <stdint.h>
#include <string.h>
#include <stdio.h>
@@ -280,9 +281,12 @@ int blake2b_init_key(blake2b_state *S, size_t outlen, const void *key, size_t ke
uint8_t block[BLAKE2B_BLOCKBYTES];
memset(block, 0, BLAKE2B_BLOCKBYTES);
memcpy(block, key, keylen);
- blake2b_update(S, block, BLAKE2B_BLOCKBYTES);
+ int r = blake2b_update(S, block, BLAKE2B_BLOCKBYTES);
/* Burn the key from stack */
clear_internal_memory(block, BLAKE2B_BLOCKBYTES);
+ if (r < 0) {
+ return -1;
+ }
}
return 0;
}
@@ -515,4 +519,73 @@ fail:
}
/* Argon2 Team - End Code */
+int blake2b_monero(void *out, size_t outlen, const void *in, size_t inlen,
+ const void *key, size_t keylen) {
+ // At this time, we expect all Monero-based callers to use a keylen=32
+ // if a key is included. If a caller wants to use a key and keylen != 32,
+ // just remove this assert (and #include <assert.h>).
+ assert(keylen == 0 || keylen == 32);
+
+ static const uint8_t PERSONAL[BLAKE2B_PERSONALBYTES] = {'M', 'o', 'n', 'e', 'r', 'o'};
+
+ blake2b_param P;
+ blake2b_state S;
+ int ret = -1;
+
+ /* Verify parameters */
+ if (NULL == in && inlen > 0) {
+ goto fail;
+ }
+
+ if (NULL == out || outlen == 0 || outlen > BLAKE2B_OUTBYTES) {
+ goto fail;
+ }
+
+ if ((NULL == key && keylen > 0) || keylen > BLAKE2B_KEYBYTES) {
+ goto fail;
+ }
+
+ if (NULL != key && keylen == 0) {
+ goto fail;
+ }
+
+ /* Setup Parameter Block */
+ P.digest_length = (uint8_t)outlen;
+ P.key_length = (uint8_t)keylen;
+ P.fanout = 1;
+ P.depth = 1;
+ P.leaf_length = 0;
+ P.node_offset = 0;
+ P.node_depth = 0;
+ P.inner_length = 0;
+ memset(P.reserved, 0, sizeof(P.reserved));
+ memset(P.salt, 0, sizeof(P.salt));
+ memcpy(P.personal, PERSONAL, sizeof(PERSONAL));
+
+ if (blake2b_init_param(&S, &P) < 0) {
+ goto fail;
+ }
+
+ if (NULL != key) {
+ uint8_t block[BLAKE2B_BLOCKBYTES];
+ memset(block, 0, BLAKE2B_BLOCKBYTES);
+ memcpy(block, key, keylen);
+ int r = blake2b_update(&S, block, BLAKE2B_BLOCKBYTES);
+ /* Burn the key from stack */
+ clear_internal_memory(block, BLAKE2B_BLOCKBYTES);
+ if (r < 0) {
+ goto fail;
+ }
+ }
+
+ if (blake2b_update(&S, in, inlen) < 0) {
+ goto fail;
+ }
+ ret = blake2b_final(&S, out, outlen);
+
+fail:
+ clear_internal_memory(&S, sizeof(S));
+ return ret;
+}
+
/// END: blake2b.c
diff --git a/src/crypto/blake2b.h b/src/crypto/blake2b.h
index ea00f38..da2b0ad 100644
--- a/src/crypto/blake2b.h
+++ b/src/crypto/blake2b.h
@@ -111,6 +111,9 @@ extern "C" {
int blake2b_long(void *out, size_t outlen, const void *in, size_t inlen);
/* Argon2 Team - End Code */
+ int blake2b_monero(void *out, size_t outlen, const void *in, size_t inlen,
+ const void *key, size_t keylen);
+
#if defined(__cplusplus)
}
#endif
diff --git a/src/crypto/crypto.cpp b/src/crypto/crypto.cpp
index f6c94fa..4997ea8 100644
--- a/src/crypto/crypto.cpp
+++ b/src/crypto/crypto.cpp
@@ -42,6 +42,7 @@
#include "warnings.h"
#include "crypto.h"
#include "hash.h"
+#include "blake2b.h"
#include "cryptonote_config.h"
@@ -608,7 +609,7 @@ namespace crypto {
return sc_isnonzero(&c2) == 0;
}
- static void hash_to_ec(const public_key &key, ge_p3 &res) {
+ static void biased_hash_to_ec(const public_key &key, ge_p3 &res) {
hash h;
ge_p2 point;
ge_p1p1 point2;
@@ -618,11 +619,58 @@ namespace crypto {
ge_p1p1_to_p3(&res, &point2);
}
+ void crypto_ops::unbiased_hash_to_ec(const unsigned char *preimage, const std::size_t length, ec_point &res) {
+ unsigned char hash[64];
+ if (blake2b_monero(std::addressof(hash), 64, preimage, length, NULL, 0) != 0)
+ throw std::runtime_error("Failed blake2b");
+
+ ge_p2 first;
+ ge_fromfe_frombytes_vartime(&first, hash);
+ ge_p1p1 first_p1p1;
+ ge_mul8(&first_p1p1, &first);
+ ge_p3 first_p3;
+ ge_p1p1_to_p3(&first_p3, &first_p1p1);
+
+ ge_p2 second;
+ ge_fromfe_frombytes_vartime(&second, hash + 32);
+ ge_p1p1 second_p1p1;
+ ge_mul8(&second_p1p1, &second);
+ ge_p3 second_p3;
+ ge_p1p1_to_p3(&second_p3, &second_p1p1);
+ ge_cached second_cached;
+ ge_p3_to_cached(&second_cached, &second_p3);
+
+ ge_p1p1 point;
+ ge_add(&point, &first_p3, &second_cached);
+
+ ge_p3 res_ge_p3;
+ ge_p1p1_to_p3(&res_ge_p3, &point);
+ ge_p3_tobytes(&res, &res_ge_p3);
+ }
+
+ static void biased_derive_key_image_generator(const public_key &pub, ec_point &ki_gen) {
+ ge_p3 point;
+ biased_hash_to_ec(pub, point);
+ ge_p3_tobytes(&ki_gen, &point);
+ }
+
+ static void unbiased_derive_key_image_generator(const public_key &pub, ec_point &ki_gen) {
+ unbiased_hash_to_ec(&pub, sizeof(public_key), ki_gen);
+ }
+
+ void crypto_ops::derive_key_image_generator(const public_key &pub, const bool biased, ec_point &ki_gen) {
+ if (biased)
+ biased_derive_key_image_generator(pub, ki_gen);
+ else
+ unbiased_derive_key_image_generator(pub, ki_gen);
+ }
+
+ // key image derivation used before FCMP++/Carrot
void crypto_ops::generate_key_image(const public_key &pub, const secret_key &sec, key_image &image) {
ge_p3 point;
ge_p2 point2;
assert(sc_check(&sec) == 0);
- hash_to_ec(pub, point);
+ biased_hash_to_ec(pub, point);
ge_scalarmult(&point2, &unwrap(sec), &point);
ge_tobytes(&image, &point2);
}
@@ -683,7 +731,7 @@ POP_WARNINGS
random_scalar(k);
ge_scalarmult_base(&tmp3, &k);
ge_p3_tobytes(&buf->ab[i].a, &tmp3);
- hash_to_ec(*pubs[i], tmp3);
+ biased_hash_to_ec(*pubs[i], tmp3);
ge_scalarmult(&tmp2, &k, &tmp3);
ge_tobytes(&buf->ab[i].b, &tmp2);
} else {
@@ -695,7 +743,7 @@ POP_WARNINGS
}
ge_double_scalarmult_base_vartime(&tmp2, &sig[i].c, &tmp3, &sig[i].r);
ge_tobytes(&buf->ab[i].a, &tmp2);
- hash_to_ec(*pubs[i], tmp3);
+ biased_hash_to_ec(*pubs[i], tmp3);
ge_double_scalarmult_precomp_vartime(&tmp2, &sig[i].r, &tmp3, &sig[i].c, image_pre);
ge_tobytes(&buf->ab[i].b, &tmp2);
sc_add(&sum, &sum, &sig[i].c);
@@ -740,7 +788,7 @@ POP_WARNINGS
}
ge_double_scalarmult_base_vartime(&tmp2, &sig[i].c, &tmp3, &sig[i].r);
ge_tobytes(&buf->ab[i].a, &tmp2);
- hash_to_ec(*pubs[i], tmp3);
+ biased_hash_to_ec(*pubs[i], tmp3);
ge_double_scalarmult_precomp_vartime(&tmp2, &sig[i].r, &tmp3, &sig[i].c, image_pre);
ge_tobytes(&buf->ab[i].b, &tmp2);
sc_add(&sum, &sum, &sig[i].c);
diff --git a/src/crypto/crypto.h b/src/crypto/crypto.h
index da3ae13..92092d9 100644
--- a/src/crypto/crypto.h
+++ b/src/crypto/crypto.h
@@ -133,6 +133,10 @@ namespace crypto {
friend void generate_tx_proof_v1(const hash &, const public_key &, const public_key &, const boost::optional<public_key> &, const public_key &, const secret_key &, signature &);
static bool check_tx_proof(const hash &, const public_key &, const public_key &, const boost::optional<public_key> &, const public_key &, const signature &, const int);
friend bool check_tx_proof(const hash &, const public_key &, const public_key &, const boost::optional<public_key> &, const public_key &, const signature &, const int);
+ static void unbiased_hash_to_ec(const unsigned char *, const std::size_t, ec_point &);
+ friend void unbiased_hash_to_ec(const unsigned char *, const std::size_t, ec_point &);
+ static void derive_key_image_generator(const public_key &, const bool biased, ec_point &);
+ friend void derive_key_image_generator(const public_key &, const bool biased, ec_point &);
static void generate_key_image(const public_key &, const secret_key &, key_image &);
friend void generate_key_image(const public_key &, const secret_key &, key_image &);
static void generate_ring_signature(const hash &, const key_image &,
@@ -258,6 +262,10 @@ namespace crypto {
return crypto_ops::check_tx_proof(prefix_hash, R, A, B, D, sig, version);
}
+ inline void derive_key_image_generator(const public_key &pub, const bool biased, ec_point &ki_gen) {
+ crypto_ops::derive_key_image_generator(pub, biased, ki_gen);
+ }
+
/* To send money to a key:
* * The sender generates an ephemeral key and includes it in transaction output.
* * To spend the money, the receiver generates a key image from it.
@@ -301,6 +309,10 @@ namespace crypto {
crypto_ops::derive_view_tag(derivation, output_index, vt);
}
+ inline void unbiased_hash_to_ec(const unsigned char *preimage, const std::size_t length, ec_point &res) {
+ crypto_ops::unbiased_hash_to_ec(preimage, length, res);
+ }
+
inline std::ostream &operator <<(std::ostream &o, const crypto::public_key &v) {
epee::to_hex::formatted(o, epee::as_byte_span(v)); return o;
}
diff --git a/tests/crypto/crypto-tests.h b/tests/crypto/crypto-tests.h
index ed57317..636dc86 100644
--- a/tests/crypto/crypto-tests.h
+++ b/tests/crypto/crypto-tests.h
@@ -45,7 +45,7 @@ bool check_scalar(const crypto::ec_scalar &scalar);
void random_scalar(crypto::ec_scalar &res);
void hash_to_scalar(const void *data, std::size_t length, crypto::ec_scalar &res);
void hash_to_point(const crypto::hash &h, crypto::ec_point &res);
-void hash_to_ec(const crypto::public_key &key, crypto::ec_point &res);
+void biased_hash_to_ec(const crypto::public_key &key, crypto::ec_point &res);
bool check_ge_p3_identity_failure(const crypto::public_key &point);
bool check_ge_p3_identity_success(const crypto::public_key &point);
#endif
diff --git a/tests/crypto/crypto.cpp b/tests/crypto/crypto.cpp
index aeca2d7..b3f2a11 100644
--- a/tests/crypto/crypto.cpp
+++ b/tests/crypto/crypto.cpp
@@ -80,9 +80,9 @@ void hash_to_point(const crypto::hash &h, crypto::ec_point &res) {
crypto::ge_tobytes(crypto::operator &(res), &point);
}
-void hash_to_ec(const crypto::public_key &key, crypto::ec_point &res) {
+void biased_hash_to_ec(const crypto::public_key &key, crypto::ec_point &res) {
crypto::ge_p3 tmp;
- crypto::hash_to_ec(key, tmp);
+ crypto::biased_hash_to_ec(key, tmp);
crypto::ge_p3_tobytes(crypto::operator &(res), &tmp);
}
diff --git a/tests/crypto/main.cpp b/tests/crypto/main.cpp
index ff644e1..815d742 100644
--- a/tests/crypto/main.cpp
+++ b/tests/crypto/main.cpp
@@ -194,11 +194,11 @@ int main(int argc, char *argv[]) {
if (expected != actual) {
goto error;
}
- } else if (cmd == "hash_to_ec") {
+ } else if (cmd == "biased_hash_to_ec") {
public_key key;
ec_point expected, actual;
get(input, key, expected);
- hash_to_ec(key, actual);
+ biased_hash_to_ec(key, actual);
if (expected != actual) {
goto error;
}
@@ -287,6 +287,15 @@ int main(int argc, char *argv[]) {
if (expected_wei_x != actual_wei_x || expected_wei_y != actual_wei_y) {
goto error;
}
+ } else if (cmd == "derive_key_image_generator") {
+ public_key point;
+ bool biased;
+ ec_point expected_result, actual_result;
+ get(input, point, biased, expected_result);
+ crypto::derive_key_image_generator(point, biased, actual_result);
+ if (expected_result != actual_result) {
+ goto error;
+ }
} else {
throw ios_base::failure("Unknown function: " + cmd);
}
diff --git a/tests/crypto/tests.txt b/tests/crypto/tests.txt
index 2331e33..1291f91 100644
--- a/tests/crypto/tests.txt
+++ b/tests/crypto/tests.txt
@@ -3675,262 +3675,262 @@ hash_to_point fcffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 4
hash_to_point fdffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 9b238c928fe8993e63543b87c83d6cf17bc0524dc149b080102671bbcd3cfb8f
hash_to_point feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 123a5287f4de990b3dcf9c32456a57349fb40bcf0963912c604770a8fb9e9a41
hash_to_point ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 80c90f3f23af8763b058cf5029e42f6a78a3e48dc0eeb38f31b3a6419e64fdbf
-hash_to_ec da66e9ba613919dec28ef367a125bb310d6d83fb9052e71034164b6dc4f392d0 52b3f38753b4e13b74624862e253072cf12f745d43fcfafbe8c217701a6e5875
-hash_to_ec a7fbdeeccb597c2d5fdaf2ea2e10cbfcd26b5740903e7f6d46bcbf9a90384fc6 f055ba2d0d9828ce2e203d9896bfda494d7830e7e3a27fa27d5eaa825a79a19c
-hash_to_ec ed6e6579368caba2cc4851672972e949c0ee586fee4d6d6a9476d4a908f64070 da3ceda9a2ef6316bf9272566e6dffd785ac71f57855c0202f422bbb86af4ec0
-hash_to_ec 9ae78e5620f1c4e6b29d03da006869465b3b16dae87ab0a51f4e1b74bc8aa48b 72d8720da66f797f55fbb7fa538af0b4a4f5930c8289c991472c37dc5ec16853
-hash_to_ec ab49eb4834d24db7f479753217b763f70604ecb79ed37e6c788528720f424e5b 45914ba926a1a22c8146459c7f050a51ef5f560f5b74bae436b93a379866e6b8
-hash_to_ec 5b79158ef2341180b8327b976efddbf364620b7e88d2e0707fa56f3b902c34b3 eac991dcbba39cb3bd166906ab48e2c3c3f4cd289a05e1c188486d348ede7c2e
-hash_to_ec f21daa7896c81d3a7a2e9df721035d3c3902fe546c9d739d0c334ed894fb1d21 a6bedc5ffcc867d0c13a88a03360c8c83a9e4ddf339851bd3768c53a124378ec
-hash_to_ec 3dae79aaca1abe6aecea7b0d38646c6b013d40053c7cdde2bed094497d925d2b 1a442546a35860a4ab697a36b158ded8e001bbfe20aef1c63e2840e87485c613
-hash_to_ec 3d219463a55c24ac6f55706a6e46ade3fcd1edc87bade7b967129372036aca63 b252922ab64e32968735b8ade861445aa8dc02b763bd249bff121d10829f7c52
-hash_to_ec bc5db69aced2b3197398eaf7cf60fd782379874b5ca27cb21bd23692c3c885cc ae072a43f78a0f29dc9822ae5e70865bbd151236a6d7fe4ae3e8f8961e19b0e5
-hash_to_ec 98a6ed760b225976f8ada0579540e35da643089656695b5d0b8c7265a37e2342 6a99dbfa8ead6228910498cc3ff3fb18cb8627c5735e4b8657da846c16d2dcad
-hash_to_ec e9cdc9fd9425a4a2389a5d60f76a2d839f0afbf66330f079a88fe23d73eae930 8aa518d091928668f3ca40e71e14b2698f6cae097b8120d7f6ae9afba8fd3d60
-hash_to_ec a50c026c0af2f9f9884c2e9b8464724ac83bef546fec2c86b7de0880980d24fb b07433f8df39da2453a1e13fd413123a158feae602d822b724d42ef6c8e443bf
-hash_to_ec bf180e20d160fa23ccfa6993febe22b920160efc5a9614245f1a3a360076e87a 9d6454ff69779ce978ea5fb3be88576dc8feaedf151e93b70065f92505f2e800
-hash_to_ec b2b64dfeb1d58c6afbf5a56d8c0c42012175ebb4b7df30f26a67b66be8c34614 0523b22e7f220c939b604a15780abc5816709b91b81d9ee1541d44bd2586bbd8
-hash_to_ec 463fc877f4279740020d10652c950f088ebdebeae34aa7a366c92c9c8773f63a daa5fa72e70c4d3af407b8f2f3364708029b2d4863bbdde54bd67bd08db0fcad
-hash_to_ec 721842f3809982e7b96a806ae1f162d98ae6911d476307ad1e4f24522fd26f55 4397c300a8cfcb42e7cc310bc975dc975ec2d191eaa7e0462998eb2830c34126
-hash_to_ec 384da8d9b83972af8cbefc2da5efc744037c8ef40efa4b3bacc3238a6232963d 3c80f107e6868f73ef600ab9229a3f4bbe24f4adce52e6ab3a66d5d510e0670d
-hash_to_ec e26f8adef5b6fe5bb01466bff0455ca23fda07e200133697b3b6430ca3332bde e262a58bcc1f8baf1980e00d5d40ba00803690174d14fb4c0f608429ce3df773
-hash_to_ec 6e275b4ea4f085a5d3151aa08cf16a8c60b078e70be7ce5dac75b5d7b0eebe7c cb21b5a7744b4fcdc92ead4be0b04bcb9145e7bb4b06eff3bb2f0fe429b85108
-hash_to_ec a0dde4561ad9daa796d9cd8a3c34fd41687cee76d128bf2e2252466e3ef3b068 79a2eb06bb7647f5d0aae5da7cf2e2b2d2ce890f25f2b1f81bfc5fef8c87a7d3
-hash_to_ec dbaf63830e037b4c329969d1d85e58cb6c4f56014fd08eb38219bd20031ae27c 079c93ae27cd98075a487fd3f7457ad2fb57cdf12ec8651fedd944d765d07549
-hash_to_ec 1e87ba8a9acf96948bc199ae55c83ab3277be152c6d0b1d68a07955768d81171 5c6339f834116791f9ea22fcc3970346aaeddacf13fbd0a7d4005fbd469492ca
-hash_to_ec 5a544088e63ddf5b9f444ed75a75bc9315c4c50439522f06b4823ecaf5e8a08d e95ca0730d57c6469be3a0f3c94382f8490257e2e546de86c650bdbc6482eaee
-hash_to_ec e4e06d92ebb036a5e4bb547dbaa43fd70db3929eef2702649455c86d7e59aa46 e26210ff8ee28e24ef2613df40aa8a874b5e3c1d07ae14acc59220615aa334dc
-hash_to_ec 5793b8b32dcc0f204501647f2976493c4f8f1fa5132315226f99f29a5a6fdfce 656e390086906d99852c9696e831f62cb56fc8f85f9a5c936c327f23c7faf4fe
-hash_to_ec 84f56fa4d7f12e0efd48b1f7c81c15d6e3843ebb419f4a27ec97028d4f9da19e 0cbd4f0cd288e1e071cce800877de6aef97b63fff867424a4f2b2bab25602608
-hash_to_ec 242683ddf0a9fc55f6585de3aa64ea17c9c544896ff7677cd82c98f833bdf2ca 38c36d52314549213df7c7201ab7749a4724cbea92812f583bb48cabc20816ad
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generate_key_image e46b60ebfe610b8ba761032018471e5719bb77ea1cd945475c4a4abe7224bfd0 981d477fb18897fa1f784c89721a9d600bf283f06b89cb018a077f41dcefef0f a637203ec41eab772532d30420eac80612fce8e44f1758bc7e2cb1bdda815887
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@@ -5743,3 +5743,203 @@ point_to_wei_x_y b40487632d252fb54e86586720f1ccdc581f2a1f71571c1c7e675f6922f3490
point_to_wei_x_y 7b5dc3036612d38132ce6681713431aa3659f805b78fa18e86009e8595aa27d0 549e5dc37037da8155434a7651a0cfb5d1fcda316edddedceda69d8a0c909e6b b9a0e46f4dc12c72f672a99e6eb2885c7d923df0ee3edb119dbe2a19cae82553
point_to_wei_x_y c4092a49ee9a033883c2f2af9588b25bb06faed117dd84f7460adbd8a91734d2 11dd5a8aa1f970acc1c1709ed2d6a8a0718ea455fa243455ab25d3d30304343e b17199f31e269cc490aea95ab3b8be455a6ad45232402e4909fb3a9c17c69d20
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Why this scored 34/100
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