[secp256k1] Add secp256k1_ec_pubkey_cmp and `secp256k1_xonly_pubkey…

…_cmp`

Summary:
Allows comparing `secp256k1_pubkey` and `secp256k1_xonly_pubkey` respectively, to establish an order between them.

This is a backport of [[ bitcoin-core/secp256k1#850 | secp256k1#850 ]] and [[ bitcoin-core/secp256k1#926 | secp256k1#926 ]].

We need this for porting `rust-secp256k1` to the secp256k1 library of this repo.

Test Plan: `ninja check-secp256k1`

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D16957

src/secp256k1/include/secp256k1.h

@@ -7,7 +7,9 @@ extern "C" {
 
 #include <stddef.h>
 
-/* These rules specify the order of arguments in API calls:
+/* Unless explicitly stated all pointer arguments must not be NULL.
+ *
+ * The following rules specify the order of arguments in API calls:
  *
  * 1. Context pointers go first, followed by output arguments, combined
  *    output/input arguments, and finally input-only arguments.
@@ -61,8 +63,9 @@ typedef struct secp256k1_scratch_space_struct secp256k1_scratch_space;
  *  The exact representation of data inside is implementation defined and not
  *  guaranteed to be portable between different platforms or versions. It is
  *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
- *  If you need to convert to a format suitable for storage, transmission, or
- *  comparison, use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse.
+ *  If you need to convert to a format suitable for storage or transmission,
+ *  use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse. To
+ *  compare keys, use secp256k1_ec_pubkey_cmp.
  */
 typedef struct {
     unsigned char data[64];
@@ -370,6 +373,21 @@ SECP256K1_API int secp256k1_ec_pubkey_serialize(
     unsigned int flags
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
 
+/** Compare two public keys using lexicographic (of compressed serialization) order
+ *
+ *  Returns: <0 if the first public key is less than the second
+ *           >0 if the first public key is greater than the second
+ *           0 if the two public keys are equal
+ *  Args: ctx:      a secp256k1 context object.
+ *  In:   pubkey1:  first public key to compare
+ *        pubkey2:  second public key to compare
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_cmp(
+    const secp256k1_context* ctx,
+    const secp256k1_pubkey* pubkey1,
+    const secp256k1_pubkey* pubkey2
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
 /** Parse an ECDSA signature in compact (64 bytes) format.
  *
  *  Returns: 1 when the signature could be parsed, 0 otherwise.

src/secp256k1/include/secp256k1_extrakeys.h

@@ -15,9 +15,9 @@ extern "C" {
  *  The exact representation of data inside is implementation defined and not
  *  guaranteed to be portable between different platforms or versions. It is
  *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
- *  If you need to convert to a format suitable for storage, transmission, or
- *  comparison, use secp256k1_xonly_pubkey_serialize and
- *  secp256k1_xonly_pubkey_parse.
+ *  If you need to convert to a format suitable for storage, transmission, use
+ *  use secp256k1_xonly_pubkey_serialize and secp256k1_xonly_pubkey_parse. To
+ *  compare keys, use secp256k1_xonly_pubkey_cmp.
  */
 typedef struct {
     unsigned char data[64];
@@ -67,6 +67,21 @@ SECP256K1_API int secp256k1_xonly_pubkey_serialize(
     const secp256k1_xonly_pubkey* pubkey
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
+/** Compare two x-only public keys using lexicographic order
+ *
+ *  Returns: <0 if the first public key is less than the second
+ *           >0 if the first public key is greater than the second
+ *           0 if the two public keys are equal
+ *  Args: ctx:      a secp256k1 context object.
+ *  In:   pubkey1:  first public key to compare
+ *        pubkey2:  second public key to compare
+ */
+SECP256K1_API int secp256k1_xonly_pubkey_cmp(
+    const secp256k1_context* ctx,
+    const secp256k1_xonly_pubkey* pk1,
+    const secp256k1_xonly_pubkey* pk2
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
 /** Converts a secp256k1_pubkey into a secp256k1_xonly_pubkey.
  *
  *  Returns: 1 if the public key was successfully converted

src/secp256k1/src/modules/extrakeys/main_impl.h

@@ -55,6 +55,32 @@ int secp256k1_xonly_pubkey_serialize(const secp256k1_context* ctx, unsigned char
     return 1;
 }
 
+int secp256k1_xonly_pubkey_cmp(const secp256k1_context* ctx, const secp256k1_xonly_pubkey* pk0, const secp256k1_xonly_pubkey* pk1) {
+    unsigned char out[2][32];
+    const secp256k1_xonly_pubkey* pk[2];
+    int i;
+
+    VERIFY_CHECK(ctx != NULL);
+    pk[0] = pk0; pk[1] = pk1;
+    for (i = 0; i < 2; i++) {
+        /* If the public key is NULL or invalid, xonly_pubkey_serialize will
+         * call the illegal_callback and return 0. In that case we will
+         * serialize the key as all zeros which is less than any valid public
+         * key. This results in consistent comparisons even if NULL or invalid
+         * pubkeys are involved and prevents edge cases such as sorting
+         * algorithms that use this function and do not terminate as a
+         * result. */
+        if (!secp256k1_xonly_pubkey_serialize(ctx, out[i], pk[i])) {
+            /* Note that xonly_pubkey_serialize should already set the output to
+             * zero in that case, but it's not guaranteed by the API, we can't
+             * test it and writing a VERIFY_CHECK is more complex than
+             * explicitly memsetting (again). */
+            memset(out[i], 0, sizeof(out[i]));
+        }
+    }
+    return secp256k1_memcmp_var(out[0], out[1], sizeof(out[1]));
+}
+
 /** Keeps a group element as is if it has an even Y and otherwise negates it.
  *  y_parity is set to 0 in the former case and to 1 in the latter case.
  *  Requires that the coordinates of r are normalized. */

src/secp256k1/src/modules/extrakeys/tests_impl.h

@@ -137,6 +137,43 @@ void test_xonly_pubkey(void) {
     secp256k1_context_destroy(verify);
 }
 
+void test_xonly_pubkey_comparison(void) {
+    unsigned char pk1_ser[32] = {
+        0x58, 0x84, 0xb3, 0xa2, 0x4b, 0x97, 0x37, 0x88, 0x92, 0x38, 0xa6, 0x26, 0x62, 0x52, 0x35, 0x11,
+        0xd0, 0x9a, 0xa1, 0x1b, 0x80, 0x0b, 0x5e, 0x93, 0x80, 0x26, 0x11, 0xef, 0x67, 0x4b, 0xd9, 0x23
+    };
+    const unsigned char pk2_ser[32] = {
+        0xde, 0x36, 0x0e, 0x87, 0x59, 0x8f, 0x3c, 0x01, 0x36, 0x2a, 0x2a, 0xb8, 0xc6, 0xf4, 0x5e, 0x4d,
+        0xb2, 0xc2, 0xd5, 0x03, 0xa7, 0xf9, 0xf1, 0x4f, 0xa8, 0xfa, 0x95, 0xa8, 0xe9, 0x69, 0x76, 0x1c
+    };
+    secp256k1_xonly_pubkey pk1;
+    secp256k1_xonly_pubkey pk2;
+    int ecount = 0;
+    secp256k1_context *none = api_test_context(SECP256K1_CONTEXT_NONE, &ecount);
+
+    CHECK(secp256k1_xonly_pubkey_parse(none, &pk1, pk1_ser) == 1);
+    CHECK(secp256k1_xonly_pubkey_parse(none, &pk2, pk2_ser) == 1);
+
+    CHECK(secp256k1_xonly_pubkey_cmp(none, NULL, &pk2) < 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, NULL) > 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, &pk2) < 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk2, &pk1) > 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, &pk1) == 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk2, &pk2) == 0);
+    CHECK(ecount == 2);
+    memset(&pk1, 0, sizeof(pk1)); /* illegal pubkey */
+    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, &pk2) < 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, &pk1) == 0);
+    CHECK(ecount == 5);
+    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk2, &pk1) > 0);
+    CHECK(ecount == 6);
+
+    secp256k1_context_destroy(none);
+}
+
 void test_xonly_pubkey_tweak(void) {
     unsigned char zeros64[64] = { 0 };
     unsigned char overflows[32];
@@ -540,6 +577,7 @@ void run_extrakeys_tests(void) {
     test_xonly_pubkey_tweak();
     test_xonly_pubkey_tweak_check();
     test_xonly_pubkey_tweak_recursive();
+    test_xonly_pubkey_comparison();
 
     /* keypair tests */
     test_keypair();

src/secp256k1/src/secp256k1.c

@@ -316,6 +316,32 @@ int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *o
     return ret;
 }
 
+int secp256k1_ec_pubkey_cmp(const secp256k1_context* ctx, const secp256k1_pubkey* pubkey0, const secp256k1_pubkey* pubkey1) {
+    unsigned char out[2][33];
+    const secp256k1_pubkey* pk[2];
+    int i;
+
+    VERIFY_CHECK(ctx != NULL);
+    pk[0] = pubkey0; pk[1] = pubkey1;
+    for (i = 0; i < 2; i++) {
+        size_t out_size = sizeof(out[i]);
+        /* If the public key is NULL or invalid, ec_pubkey_serialize will call
+         * the illegal_callback and return 0. In that case we will serialize the
+         * key as all zeros which is less than any valid public key. This
+         * results in consistent comparisons even if NULL or invalid pubkeys are
+         * involved and prevents edge cases such as sorting algorithms that use
+         * this function and do not terminate as a result. */
+        if (!secp256k1_ec_pubkey_serialize(ctx, out[i], &out_size, pk[i], SECP256K1_EC_COMPRESSED)) {
+            /* Note that ec_pubkey_serialize should already set the output to
+             * zero in that case, but it's not guaranteed by the API, we can't
+             * test it and writing a VERIFY_CHECK is more complex than
+             * explicitly memsetting (again). */
+            memset(out[i], 0, sizeof(out[i]));
+        }
+    }
+    return secp256k1_memcmp_var(out[0], out[1], sizeof(out[0]));
+}
+
 static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) {
     (void)ctx;
     if (sizeof(secp256k1_scalar) == 32) {

src/secp256k1/src/tests.c

@@ -4829,6 +4829,55 @@ void test_random_pubkeys(void) {
     }
 }
 
+void run_pubkey_comparison(void) {
+    unsigned char pk1_ser[33] = {
+        0x02,
+        0x58, 0x84, 0xb3, 0xa2, 0x4b, 0x97, 0x37, 0x88, 0x92, 0x38, 0xa6, 0x26, 0x62, 0x52, 0x35, 0x11,
+        0xd0, 0x9a, 0xa1, 0x1b, 0x80, 0x0b, 0x5e, 0x93, 0x80, 0x26, 0x11, 0xef, 0x67, 0x4b, 0xd9, 0x23
+    };
+    const unsigned char pk2_ser[33] = {
+        0x02,
+        0xde, 0x36, 0x0e, 0x87, 0x59, 0x8f, 0x3c, 0x01, 0x36, 0x2a, 0x2a, 0xb8, 0xc6, 0xf4, 0x5e, 0x4d,
+        0xb2, 0xc2, 0xd5, 0x03, 0xa7, 0xf9, 0xf1, 0x4f, 0xa8, 0xfa, 0x95, 0xa8, 0xe9, 0x69, 0x76, 0x1c
+    };
+    secp256k1_pubkey pk1;
+    secp256k1_pubkey pk2;
+    int32_t ecount = 0;
+
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pk1, pk1_ser, sizeof(pk1_ser)) == 1);
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pk2, pk2_ser, sizeof(pk2_ser)) == 1);
+
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    CHECK(secp256k1_ec_pubkey_cmp(ctx, NULL, &pk2) < 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk1, NULL) > 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk1, &pk2) < 0);
+    CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk2, &pk1) > 0);
+    CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk1, &pk1) == 0);
+    CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk2, &pk2) == 0);
+    CHECK(ecount == 2);
+    {
+        secp256k1_pubkey pk_tmp;
+        memset(&pk_tmp, 0, sizeof(pk_tmp)); /* illegal pubkey */
+        CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk_tmp, &pk2) < 0);
+        CHECK(ecount == 3);
+        CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk_tmp, &pk_tmp) == 0);
+        CHECK(ecount == 5);
+        CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk2, &pk_tmp) > 0);
+        CHECK(ecount == 6);
+    }
+
+    secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+
+    /* Make pk2 the same as pk1 but with 3 rather than 2. Note that in
+     * an uncompressed encoding, these would have the opposite ordering */
+    pk1_ser[0] = 3;
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pk2, pk1_ser, sizeof(pk1_ser)) == 1);
+    CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk1, &pk2) < 0);
+    CHECK(secp256k1_ec_pubkey_cmp(ctx, &pk2, &pk1) > 0);
+}
+
 void run_random_pubkeys(void) {
     int i;
     for (i = 0; i < 10*count; i++) {
@@ -5778,6 +5827,7 @@ int main(int argc, char **argv) {
 #endif
 
     /* ecdsa tests */
+    run_pubkey_comparison();
     run_random_pubkeys();
     run_ecdsa_der_parse();
     run_ecdsa_sign_verify();