diff --git a/src/tests.c b/src/tests.c
index 305a240e6c..3af19e906e 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -400,6 +400,30 @@ void scalar_test(void) {
         CHECK(secp256k1_scalar_eq(&r1, &r2));
     }
 
+    {
+        /* Test multiplicative identity. */
+        secp256k1_scalar_t r1, v1;
+        secp256k1_scalar_set_int(&v1,1);
+        secp256k1_scalar_mul(&r1, &s1, &v1);
+        CHECK(secp256k1_scalar_eq(&r1, &s1));
+    }
+
+    {
+        /* Test additive identity. */
+        secp256k1_scalar_t r1, v0;
+        secp256k1_scalar_set_int(&v0,0);
+        secp256k1_scalar_add(&r1, &s1, &v0);
+        CHECK(secp256k1_scalar_eq(&r1, &s1));
+    }
+
+    {
+        /* Test zero product property. */
+        secp256k1_scalar_t r1, v0;
+        secp256k1_scalar_set_int(&v0,0);
+        secp256k1_scalar_mul(&r1, &s1, &v0);
+        CHECK(secp256k1_scalar_eq(&r1, &v0));
+    }
+
 }
 
 void run_scalar_tests(void) {
@@ -411,9 +435,12 @@ void run_scalar_tests(void) {
         /* (-1)+1 should be zero. */
         secp256k1_scalar_t s, o;
         secp256k1_scalar_set_int(&s, 1);
+        CHECK(secp256k1_scalar_is_one(&s));
         secp256k1_scalar_negate(&o, &s);
         secp256k1_scalar_add(&o, &o, &s);
         CHECK(secp256k1_scalar_is_zero(&o));
+        secp256k1_scalar_negate(&o, &o);
+        CHECK(secp256k1_scalar_is_zero(&o));
     }
 
 #ifndef USE_NUM_NONE
@@ -466,7 +493,7 @@ void random_fe_non_square(secp256k1_fe_t *ns) {
 
 int check_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
     secp256k1_fe_t an = *a; secp256k1_fe_normalize(&an);
-    secp256k1_fe_t bn = *b; secp256k1_fe_normalize(&bn);
+    secp256k1_fe_t bn = *b; secp256k1_fe_normalize_var(&bn);
     return secp256k1_fe_equal(&an, &bn);
 }
 
@@ -476,6 +503,55 @@ int check_fe_inverse(const secp256k1_fe_t *a, const secp256k1_fe_t *ai) {
     return check_fe_equal(&x, &one);
 }
 
+void run_field_misc(void) {
+    const unsigned char f32_5[32] = {
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x05,
+    };
+    secp256k1_fe_t x;
+    secp256k1_fe_t y;
+    secp256k1_fe_t z;
+    secp256k1_fe_t q;
+    secp256k1_fe_t fe5;
+    CHECK(secp256k1_fe_set_b32(&fe5, f32_5));
+    for (int i=0; i<5*count; i++) {
+        random_fe(&x);
+        random_fe_non_zero(&y);
+        /* Test the fe equality and comparison operations. */
+        CHECK(secp256k1_fe_cmp_var(&x, &x) == 0);
+        CHECK(secp256k1_fe_equal(&x, &x));
+        z = x;
+        secp256k1_fe_add(&z,&y);
+        secp256k1_fe_normalize(&z);
+        /* Test the conditional move. */
+        secp256k1_fe_cmov(&z, &x, 0);
+        CHECK(secp256k1_fe_equal(&x, &z) == 0);
+        CHECK(secp256k1_fe_cmp_var(&x, &z) != 0);
+        secp256k1_fe_cmov(&y, &x, 1);
+        CHECK(secp256k1_fe_equal(&x, &y));
+        /* Test that mul_int, mul, and add agree. */
+        secp256k1_fe_add(&y, &x);
+        secp256k1_fe_add(&y, &x);
+        z = x;
+        secp256k1_fe_mul_int(&z, 3);
+        CHECK(check_fe_equal(&y, &z));
+        secp256k1_fe_add(&y, &x);
+        secp256k1_fe_add(&z, &x);
+        CHECK(check_fe_equal(&z, &y));
+        z = x;
+        secp256k1_fe_mul_int(&z, 5);
+        secp256k1_fe_mul(&q, &x, &fe5);
+        CHECK(check_fe_equal(&z, &q));
+        secp256k1_fe_negate(&x, &x, 1);
+        secp256k1_fe_add(&z, &x);
+        secp256k1_fe_add(&q, &x);
+        CHECK(check_fe_equal(&y, &z));
+        CHECK(check_fe_equal(&q, &y));
+    }
+}
+
 void run_field_inv(void) {
     secp256k1_fe_t x, xi, xii;
     for (int i=0; i<10*count; i++) {
@@ -752,6 +828,7 @@ void run_ecmult_chain(void) {
 }
 
 void test_point_times_order(const secp256k1_gej_t *point) {
+    unsigned char pub[65];
     /* X * (point + G) + (order-X) * (pointer + G) = 0 */
     secp256k1_scalar_t x;
     random_scalar_order_test(&x);
@@ -767,6 +844,10 @@ void test_point_times_order(const secp256k1_gej_t *point) {
     secp256k1_ge_set_gej(&res3, &res1);
     CHECK(secp256k1_ge_is_infinity(&res3));
     CHECK(secp256k1_ge_is_valid_var(&res3) == 0);
+    int psize = 65;
+    CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0);
+    psize = 65;
+    CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
 }
 
 void run_point_times_order(void) {
@@ -877,7 +958,10 @@ void test_ecdsa_end_to_end(void) {
     /* Construct and verify corresponding public key. */
     CHECK(secp256k1_ec_seckey_verify(privkey) == 1);
     unsigned char pubkey[65]; int pubkeylen = 65;
-    CHECK(secp256k1_ec_pubkey_create(pubkey, &pubkeylen, privkey, secp256k1_rand32() % 2) == 1);
+    CHECK(secp256k1_ec_pubkey_create(pubkey, &pubkeylen, privkey, (secp256k1_rand32() & 3) != 0) == 1);
+    if (secp256k1_rand32() & 1) {
+        CHECK(secp256k1_ec_pubkey_decompress(pubkey, &pubkeylen));
+    }
     CHECK(secp256k1_ec_pubkey_verify(pubkey, pubkeylen));
 
     /* Verify private key import and export. */
@@ -999,6 +1083,36 @@ void test_ecdsa_edge_cases(void) {
     for (int recid = 0; recid < 4; recid++) {
         /* (4,4) encoded in DER. */
         unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04};
+        unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01};
+        unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00};
+        unsigned char sigbderalt1[39] = {
+            0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+        };
+        unsigned char sigbderalt2[39] = {
+            0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        };
+        unsigned char sigbderalt3[40] = {
+            0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+        };
+        unsigned char sigbderalt4[40] = {
+            0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        };
         /* (order + r,4) encoded in DER. */
         unsigned char sigbderlong[40] = {
             0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF,
@@ -1016,9 +1130,36 @@ void test_ecdsa_edge_cases(void) {
             /* Verifying with (order + r,4) should always fail. */
             CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbderlong, sizeof(sigbderlong), pubkey2b, pubkey2blen) != 1);
         }
+        /* DER parsing tests. */
+        /* Zero length r/s. */
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigcder_zr, sizeof(sigcder_zr), pubkeyb, pubkeyblen) == -2);
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigcder_zs, sizeof(sigcder_zs), pubkeyb, pubkeyblen) == -2);
+        /* Leading zeros. */
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbderalt1, sizeof(sigbderalt1), pubkeyb, pubkeyblen) == 1);
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbderalt2, sizeof(sigbderalt2), pubkeyb, pubkeyblen) == 1);
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbderalt3, sizeof(sigbderalt3), pubkeyb, pubkeyblen) == 1);
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbderalt4, sizeof(sigbderalt4), pubkeyb, pubkeyblen) == 1);
+        sigbderalt3[4] = 1;
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbderalt3, sizeof(sigbderalt3), pubkeyb, pubkeyblen) == -2);
+        sigbderalt4[7] = 1;
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbderalt4, sizeof(sigbderalt4), pubkeyb, pubkeyblen) == -2);
         /* Damage signature. */
         sigbder[7]++;
         CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) == 0);
+        sigbder[7]--;
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbder, 6, pubkeyb, pubkeyblen) == -2);
+        CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbder, sizeof(sigbder)-1, pubkeyb, pubkeyblen) == -2);
+        for(int i = 0; i<8; i++) {
+            unsigned char orig = sigbder[i];
+            /*Try every single-byte change.*/
+            for (int c=0; c<256; c++) {
+                if (c == orig ) continue;
+                sigbder[i] = c;
+                CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) ==
+                  (i==4 || i==7) ? 0 : -2 );
+            }
+            sigbder[i] = orig;
+        }
     }
 
     /* Test the case where ECDSA recomputes a point that is infinity. */
@@ -1065,6 +1206,34 @@ void test_ecdsa_edge_cases(void) {
         CHECK(secp256k1_ecdsa_recover_compact(msg32, 32, sigc64, pubkeyb, &pubkeyblen, 1, 0) == 0);
         CHECK(secp256k1_ecdsa_verify(msg32, 32, sigcder, sizeof(sigcder), pubkeyc, pubkeyclen) == 0);
     }
+
+    /*Signature where s would be zero.*/
+    {
+        const unsigned char nonce[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        };
+        const unsigned char key[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        };
+        unsigned char msg[32] = {
+            0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53,
+            0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7,
+            0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62,
+            0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9,
+        };
+        unsigned char sig[72];
+        int siglen = 72;
+        CHECK(secp256k1_ecdsa_sign(msg, 32, sig, &siglen, key, nonce) == 0);
+        msg[31] = 0xaa;
+        siglen = 72;
+        CHECK(secp256k1_ecdsa_sign(msg, 32, sig, &siglen, key, nonce) == 1);
+    }
 }
 
 void run_ecdsa_edge_cases(void) {
@@ -1169,6 +1338,7 @@ int main(int argc, char **argv) {
     run_field_inv();
     run_field_inv_var();
     run_field_inv_all_var();
+    run_field_misc();
     run_sqr();
     run_sqrt();