Improve examples: remove key generation loops

improving examples bitcoin-core#2: fixing my mistakes; changing comments

improving examples bitcoin-core#3: changing comments

fixing syntax - adjustment to schnorr examples

fixing comments

fix schnorr signature tests

examples/ecdh.c

@@ -42,18 +42,16 @@ int main(void) {
     assert(return_val);
 
     /*** Key Generation ***/
-
-    /* If the secret key is zero or out of range (bigger than secp256k1's
-     * order), we try to sample a new key. Note that the probability of this
-     * happening is negligible. */
-    while (1) {
-        if (!fill_random(seckey1, sizeof(seckey1)) || !fill_random(seckey2, sizeof(seckey2))) {
-            printf("Failed to generate randomness\n");
-            return 1;
-        }
-        if (secp256k1_ec_seckey_verify(ctx, seckey1) && secp256k1_ec_seckey_verify(ctx, seckey2)) {
-            break;
-        }
+    /* If the secret key is zero or out of range (greater than secp256k1's
+    * order), we return 1. Note that the probability of this occurring
+    * is negligible with a properly functioning random number generator. */
+    if (!fill_random(seckey1, sizeof(seckey1)) || !fill_random(seckey2, sizeof(seckey2))) {
+        printf("Failed to generate randomness\n");
+        return 1;
+    }
+    if (!secp256k1_ec_seckey_verify(ctx, seckey1) || !secp256k1_ec_seckey_verify(ctx, seckey2)) {
+        printf("Generated secret key is invalid. This indicates an issue with the random number generator.\n");
+        return 1;
     }
 
     /* Public key creation using a valid context with a verified secret key should never fail */

examples/ecdsa.c

@@ -49,18 +49,16 @@ int main(void) {
     assert(return_val);
 
     /*** Key Generation ***/
-
-    /* If the secret key is zero or out of range (bigger than secp256k1's
-     * order), we try to sample a new key. Note that the probability of this
-     * happening is negligible. */
-    while (1) {
-        if (!fill_random(seckey, sizeof(seckey))) {
-            printf("Failed to generate randomness\n");
-            return 1;
-        }
-        if (secp256k1_ec_seckey_verify(ctx, seckey)) {
-            break;
-        }
+    /* If the secret key is zero or out of range (greater than secp256k1's
+    * order), we return 1. Note that the probability of this occurring
+    * is negligible with a properly functioning random number generator. */
+    if (!fill_random(seckey, sizeof(seckey))) {
+        printf("Failed to generate randomness\n");
+        return 1;
+    }
+    if (!secp256k1_ec_seckey_verify(ctx, seckey)) {
+        printf("Generated secret key is invalid. This indicates an issue with the random number generator.\n");
+        return 1;
     }
 
     /* Public key creation using a valid context with a verified secret key should never fail */

examples/ellswift.c

@@ -48,17 +48,16 @@ int main(void) {
 
     /*** Generate secret keys ***/
 
-    /* If the secret key is zero or out of range (bigger than secp256k1's
-     * order), we try to sample a new key. Note that the probability of this
-     * happening is negligible. */
-    while (1) {
-        if (!fill_random(seckey1, sizeof(seckey1)) || !fill_random(seckey2, sizeof(seckey2))) {
-            printf("Failed to generate randomness\n");
-            return 1;
-        }
-        if (secp256k1_ec_seckey_verify(ctx, seckey1) && secp256k1_ec_seckey_verify(ctx, seckey2)) {
-            break;
-        }
+/* If the secret key is zero or out of range (greater than secp256k1's
+* order), we return 1. Note that the probability of this occurring
+* is negligible with a properly functioning random number generator. */
+    if (!fill_random(seckey1, sizeof(seckey1)) || !fill_random(seckey2, sizeof(seckey2))) {
+        printf("Failed to generate randomness\n");
+        return 1;
+    }
+    if (!secp256k1_ec_seckey_verify(ctx, seckey1) || !secp256k1_ec_seckey_verify(ctx, seckey2)) {
+        printf("Generated secret key is invalid. This indicates an issue with the random number generator.\n");
+        return 1;
     }
 
     /* Generate ElligatorSwift public keys. This should never fail with valid context and

examples/schnorr.c

@@ -43,20 +43,18 @@ int main(void) {
     assert(return_val);
 
     /*** Key Generation ***/
-
-    /* If the secret key is zero or out of range (bigger than secp256k1's
-     * order), we try to sample a new key. Note that the probability of this
-     * happening is negligible. */
-    while (1) {
-        if (!fill_random(seckey, sizeof(seckey))) {
-            printf("Failed to generate randomness\n");
-            return 1;
-        }
-        /* Try to create a keypair with a valid context, it should only fail if
-         * the secret key is zero or out of range. */
-        if (secp256k1_keypair_create(ctx, &keypair, seckey)) {
-            break;
-        }
+/* If the secret key is zero or out of range (greater than secp256k1's
+ * order), we return 1. Note that the probability of this occurring
+ * is negligible with a properly functioning random number generator. */
+    if (!fill_random(seckey, sizeof(seckey))) {
+        printf("Failed to generate randomness\n");
+        return 1;
+    }
+    /* Try to create a keypair with a valid context, it should only fail if
+     * the secret key is zero or out of range. */
+    if (!secp256k1_keypair_create(ctx, &keypair, seckey)) {
+        printf("Generated secret key is invalid. This indicates an issue with the random number generator.\n");
+	return 1;
     }
 
     /* Extract the X-only public key from the keypair. We pass NULL for