diff --git a/include/secp256k1.h b/include/secp256k1.h
index fc27626dd8..b67897bdae 100644
--- a/include/secp256k1.h
+++ b/include/secp256k1.h
@@ -549,7 +549,10 @@ SECP256K1_API int secp256k1_ecdsa_sign(
     const void *ndata
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
 
-/** Verify an ECDSA secret key.
+/** Verify an ECDSA secret key. It is valid if it is not 0 and less than the
+ *  secp256k1 curve order when interpreted as an integer (most significant byte
+ *  first). The probability of choosing a 32-byte string at random which is an
+ *  invalid secret key is negligible.
  *
  *  Returns: 1: secret key is valid
  *           0: secret key is invalid
@@ -577,9 +580,11 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
 
 /** Negates a private key in place.
  *
- *  Returns: 1 always
+ *  Returns: 1 if seckey was successfully negated and 0 otherwise
  *  Args:   ctx:        pointer to a context object
- *  In/Out: seckey:     pointer to the 32-byte private key to be negated (cannot be NULL)
+ *  In/Out: seckey:     pointer to the 32-byte private key to be negated. The private
+ *                      key should be valid according to secp256k1_ec_seckey_verify
+ *                      (cannot be NULL)
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_negate(
     const secp256k1_context* ctx,
diff --git a/src/secp256k1.c b/src/secp256k1.c
index a3f446e507..c49308f4e2 100644
--- a/src/secp256k1.c
+++ b/src/secp256k1.c
@@ -530,10 +530,14 @@ int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *p
 
 int secp256k1_ec_privkey_negate(const secp256k1_context* ctx, unsigned char *seckey) {
     secp256k1_scalar sec;
+    int overflow;
     VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(seckey != NULL);
 
-    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&sec)) {
+        return 0;
+    }
     secp256k1_scalar_negate(&sec, &sec);
     secp256k1_scalar_get_b32(seckey, &sec);
 
diff --git a/src/tests.c b/src/tests.c
index d408a5c30a..46761f0ba1 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -1097,16 +1097,43 @@ void run_scalar_tests(void) {
 
 #ifndef USE_NUM_NONE
     {
-        /* A scalar with value of the curve order should be 0. */
+        /* Test secp256k1_scalar_set_b32 boundary conditions */
         secp256k1_num order;
-        secp256k1_scalar zero;
+        secp256k1_scalar scalar;
         unsigned char bin[32];
+        unsigned char bin_tmp[32];
         int overflow = 0;
+        /* 2^256-1 - order */
+        static const secp256k1_scalar all_ones_minus_order = SECP256K1_SCALAR_CONST(
+            0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000001UL,
+            0x45512319UL, 0x50B75FC4UL, 0x402DA173UL, 0x2FC9BEBEUL
+        );
+
+        /* A scalar set to 0s should be 0. */
+        memset(bin, 0, 32);
+        secp256k1_scalar_set_b32(&scalar, bin, &overflow);
+        CHECK(overflow == 0);
+        CHECK(secp256k1_scalar_is_zero(&scalar));
+
+        /* A scalar with value of the curve order should be 0. */
         secp256k1_scalar_order_get_num(&order);
         secp256k1_num_get_bin(bin, 32, &order);
-        secp256k1_scalar_set_b32(&zero, bin, &overflow);
+        secp256k1_scalar_set_b32(&scalar, bin, &overflow);
+        CHECK(overflow == 1);
+        CHECK(secp256k1_scalar_is_zero(&scalar));
+
+        /* A scalar with value of the curve order minus one should not overflow. */
+        bin[31] -= 1;
+        secp256k1_scalar_set_b32(&scalar, bin, &overflow);
+        CHECK(overflow == 0);
+        secp256k1_scalar_get_b32(bin_tmp, &scalar);
+        CHECK(memcmp(bin, bin_tmp, 32) == 0);
+
+        /* A scalar set to all 1s should overflow. */
+        memset(bin, 0xFF, 32);
+        secp256k1_scalar_set_b32(&scalar, bin, &overflow);
         CHECK(overflow == 1);
-        CHECK(secp256k1_scalar_is_zero(&zero));
+        CHECK(secp256k1_scalar_eq(&scalar, &all_ones_minus_order));
     }
 #endif
 
@@ -4104,6 +4131,37 @@ void run_eckey_edge_case_test(void) {
     secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
 }
 
+void run_eckey_arithmetic_test(void) {
+    unsigned char seckey[32];
+    unsigned char seckey_tmp[32];
+
+    secp256k1_rand256_test(seckey);
+    memcpy(seckey_tmp, seckey, 32);
+
+    /* Verify negation changes the key and changes it back */
+    CHECK(secp256k1_ec_privkey_negate(ctx, seckey) == 1);
+    CHECK(memcmp(seckey, seckey_tmp, 32) != 0);
+    CHECK(secp256k1_ec_privkey_negate(ctx, seckey) == 1);
+    CHECK(memcmp(seckey, seckey_tmp, 32) == 0);
+
+    /* Negating all 0s fails */
+    memset(seckey, 0, 32);
+    memset(seckey_tmp, 0, 32);
+    CHECK(secp256k1_ec_privkey_negate(ctx, seckey) == 0);
+    /* Check that seckey is not modified */
+    CHECK(memcmp(seckey, seckey_tmp, 32) == 0);
+
+    /* Negating an overflowing seckey fails and the seckey is not modified. In
+     * this test, the seckey has 16 random bytes to ensure that
+     * ec_privkey_negate doesn't just set seckey to a constant value in case of
+     * failure.*/
+    secp256k1_rand256_test(seckey);
+    memset(seckey, 0xFF, 16);
+    memcpy(seckey_tmp, seckey, 32);
+    CHECK(secp256k1_ec_privkey_negate(ctx, seckey) == 0);
+    CHECK(memcmp(seckey, seckey_tmp, 32) == 0);
+}
+
 void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
     secp256k1_scalar nonce;
     do {
@@ -5270,6 +5328,9 @@ int main(int argc, char **argv) {
     /* EC key edge cases */
     run_eckey_edge_case_test();
 
+    /* EC key arithmetic test */
+    run_eckey_arithmetic_test();
+
 #ifdef ENABLE_MODULE_ECDH
     /* ecdh tests */
     run_ecdh_tests();