diff --git a/src/tests.c b/src/tests.c
index 26063a81569bc..7dbe4644a84c9 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -451,14 +451,18 @@ void run_ctz_tests(void) {
 
 /***** HASH TESTS *****/
 
-void run_sha256_tests(void) {
-    static const char *inputs[8] = {
+void run_sha256_known_output_tests(void) {
+    static const char *inputs[] = {
         "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe",
         "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",
         "For this sample, this 63-byte string will be used as input data",
-        "This is exactly 64 bytes long, not counting the terminating byte"
+        "This is exactly 64 bytes long, not counting the terminating byte",
+        "aaaaa",
     };
-    static const unsigned char outputs[8][32] = {
+    static const unsigned int repeat[] = {
+        1, 1, 1, 1, 1, 1, 1, 1, 1000000/5
+    };
+    static const unsigned char outputs[][32] = {
         {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55},
         {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad},
         {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50},
@@ -466,21 +470,38 @@ void run_sha256_tests(void) {
         {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30},
         {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1},
         {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42},
-        {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8}
+        {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8},
+        {0xcd, 0xc7, 0x6e, 0x5c, 0x99, 0x14, 0xfb, 0x92, 0x81, 0xa1, 0xc7, 0xe2, 0x84, 0xd7, 0x3e, 0x67, 0xf1, 0x80, 0x9a, 0x48, 0xa4, 0x97, 0x20, 0x0e, 0x04, 0x6d, 0x39, 0xcc, 0xc7, 0x11, 0x2c, 0xd0},
     };
-    int i;
-    for (i = 0; i < 8; i++) {
+    unsigned int i, ninputs;
+
+    /* Skip last input vector for low iteration counts */
+    ninputs = sizeof(inputs)/sizeof(inputs[0]) - 1;
+    CONDITIONAL_TEST(16, "run_sha256_known_output_tests 1000000") ninputs++;
+
+    for (i = 0; i < ninputs; i++) {
         unsigned char out[32];
         secp256k1_sha256 hasher;
+        unsigned int j;
+        /* 1. Run: simply write the input bytestrings */
+        j = repeat[i];
         secp256k1_sha256_initialize(&hasher);
-        secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+        while (j > 0) {
+            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+            j--;
+        }
         secp256k1_sha256_finalize(&hasher, out);
         CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
+        /* 2. Run: split the input bytestrings randomly before writing */
         if (strlen(inputs[i]) > 0) {
             int split = secp256k1_testrand_int(strlen(inputs[i]));
             secp256k1_sha256_initialize(&hasher);
-            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
-            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+            j = repeat[i];
+            while (j > 0) {
+                secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
+                secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+                j--;
+            }
             secp256k1_sha256_finalize(&hasher, out);
             CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         }
@@ -6964,7 +6985,7 @@ int main(int argc, char **argv) {
     run_modinv_tests();
     run_inverse_tests();
 
-    run_sha256_tests();
+    run_sha256_known_output_tests();
     run_hmac_sha256_tests();
     run_rfc6979_hmac_sha256_tests();
     run_tagged_sha256_tests();