diff --git a/ChangeLog.d/issue1792.txt b/ChangeLog.d/issue1792.txt
index 39dbe5b..bd3d248 100644
--- a/ChangeLog.d/issue1792.txt
+++ b/ChangeLog.d/issue1792.txt
@@ -1,4 +1,4 @@
 Bugfix
-   * Fix a bug in ECDSA that would cause it to fail when the payload is all-bits
+   * Fix a bug in ECDSA that would cause it to fail when the hash is all-bits
      zero.
      Fixes #1792
diff --git a/tests/suites/test_suite_ecdsa.function b/tests/suites/test_suite_ecdsa.function
index e6da884..08bbe63 100644
--- a/tests/suites/test_suite_ecdsa.function
+++ b/tests/suites/test_suite_ecdsa.function
@@ -212,6 +212,7 @@
     mbedtls_mpi d, r, s;
     mbedtls_test_rnd_pseudo_info rnd_info;
     unsigned char buf[MBEDTLS_MD_MAX_SIZE];
+    int test_runs = 2;
 
     mbedtls_ecp_group_init( &grp );
     mbedtls_ecp_point_init( &Q );
@@ -219,18 +220,31 @@
     memset( &rnd_info, 0x00, sizeof( mbedtls_test_rnd_pseudo_info ) );
     memset( buf, 0, sizeof( buf ) );
 
-    /* prepare material for signature */
-    TEST_ASSERT( mbedtls_test_rnd_pseudo_rand( &rnd_info,
-                                               buf, sizeof( buf ) ) == 0 );
-    TEST_ASSERT( mbedtls_ecp_group_load( &grp, id ) == 0 );
-    TEST_ASSERT( mbedtls_ecp_gen_keypair( &grp, &d, &Q,
-                                          &mbedtls_test_rnd_pseudo_rand,
-                                          &rnd_info ) == 0 );
+    while ( test_runs-- )
+    {
+        /* prepare material for signature */
+        if ( test_runs == 1 )
+        {
+            TEST_ASSERT( mbedtls_test_rnd_pseudo_rand( &rnd_info,
+                                                       buf, sizeof( buf ) ) 
+                                                     == 0 );
+        } else {
+            TEST_ASSERT( mbedtls_test_rnd_zero_rand( NULL,
+                                                     buf, sizeof( buf ) ) 
+                                                   == 0 );
+        }
 
-    TEST_ASSERT( mbedtls_ecdsa_sign( &grp, &r, &s, &d, buf, sizeof( buf ),
-                                     &mbedtls_test_rnd_pseudo_rand,
-                                     &rnd_info ) == 0 );
-    TEST_ASSERT( mbedtls_ecdsa_verify( &grp, buf, sizeof( buf ), &Q, &r, &s ) == 0 );
+        TEST_ASSERT( mbedtls_ecp_group_load( &grp, id ) == 0 );
+        TEST_ASSERT( mbedtls_ecp_gen_keypair( &grp, &d, &Q,
+                                              &mbedtls_test_rnd_pseudo_rand,
+                                              &rnd_info ) == 0 );
+
+        TEST_ASSERT( mbedtls_ecdsa_sign( &grp, &r, &s, &d, buf, sizeof( buf ),
+                                         &mbedtls_test_rnd_pseudo_rand,
+                                         &rnd_info ) == 0 );
+        TEST_ASSERT( mbedtls_ecdsa_verify( &grp, buf, sizeof( buf ), &Q, &r, &s ) 
+                                         == 0 );
+    }
 
 exit:
     mbedtls_ecp_group_free( &grp );
@@ -354,56 +368,70 @@
     unsigned char hash[32];
     unsigned char sig[200];
     size_t sig_len, i;
+    int test_runs = 2;
 
     mbedtls_ecdsa_init( &ctx );
     memset( &rnd_info, 0x00, sizeof( mbedtls_test_rnd_pseudo_info ) );
     memset( hash, 0, sizeof( hash ) );
-    memset( sig, 0x2a, sizeof( sig ) );
 
-    /* prepare material for signature */
-    TEST_ASSERT( mbedtls_test_rnd_pseudo_rand( &rnd_info,
-                                               hash, sizeof( hash ) ) == 0 );
+    while ( test_runs-- )
+    {
+        memset( sig, 0x2a, sizeof( sig ) );
 
-    /* generate signing key */
-    TEST_ASSERT( mbedtls_ecdsa_genkey( &ctx, id,
-                                       &mbedtls_test_rnd_pseudo_rand,
-                                       &rnd_info ) == 0 );
+        /* prepare material for signature */
+        if ( test_runs == 1 )
+        {
+            TEST_ASSERT( mbedtls_test_rnd_pseudo_rand( &rnd_info,
+                                                       hash, sizeof( hash ) ) 
+                                                     == 0 );
+        } else {
+            TEST_ASSERT( mbedtls_test_rnd_zero_rand( NULL,
+                                                       hash, sizeof( hash ) ) 
+                                                    == 0 );
+        }
 
-    /* generate and write signature, then read and verify it */
-    TEST_ASSERT( mbedtls_ecdsa_write_signature( &ctx, MBEDTLS_MD_SHA256,
-                 hash, sizeof( hash ),
-                 sig, &sig_len, &mbedtls_test_rnd_pseudo_rand,
-                 &rnd_info ) == 0 );
-    TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
-                 sig, sig_len ) == 0 );
+        /* generate signing key */
+        TEST_ASSERT( mbedtls_ecdsa_genkey( &ctx, id,
+                                           &mbedtls_test_rnd_pseudo_rand,
+                                           &rnd_info ) == 0 );
 
-    /* check we didn't write past the announced length */
-    for( i = sig_len; i < sizeof( sig ); i++ )
-        TEST_ASSERT( sig[i] == 0x2a );
+        /* generate and write signature, then read and verify it */
+        TEST_ASSERT( mbedtls_ecdsa_write_signature( &ctx, MBEDTLS_MD_SHA256,
+                     hash, sizeof( hash ),
+                     sig, &sig_len, &mbedtls_test_rnd_pseudo_rand,
+                     &rnd_info ) == 0 );
 
-    /* try verification with invalid length */
-    TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
-                 sig, sig_len - 1 ) != 0 );
-    TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
-                 sig, sig_len + 1 ) != 0 );
+        TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
+                     sig, sig_len ) == 0 );
 
-    /* try invalid sequence tag */
-    sig[0]++;
-    TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
-                 sig, sig_len ) != 0 );
-    sig[0]--;
+        /* check we didn't write past the announced length */
+        for( i = sig_len; i < sizeof( sig ); i++ )
+            TEST_ASSERT( sig[i] == 0x2a );
 
-    /* try modifying r */
-    sig[10]++;
-    TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
-                 sig, sig_len ) == MBEDTLS_ERR_ECP_VERIFY_FAILED );
-    sig[10]--;
+        /* try verification with invalid length */
+        TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
+                     sig, sig_len - 1 ) != 0 );
+        TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
+                     sig, sig_len + 1 ) != 0 );
 
-    /* try modifying s */
-    sig[sig_len - 1]++;
-    TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
-                 sig, sig_len ) == MBEDTLS_ERR_ECP_VERIFY_FAILED );
-    sig[sig_len - 1]--;
+        /* try invalid sequence tag */
+        sig[0]++;
+        TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
+                     sig, sig_len ) != 0 );
+        sig[0]--;
+
+        /* try modifying r */
+        sig[10]++;
+        TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
+                     sig, sig_len ) == MBEDTLS_ERR_ECP_VERIFY_FAILED );
+        sig[10]--;
+
+        /* try modifying s */
+        sig[sig_len - 1]++;
+        TEST_ASSERT( mbedtls_ecdsa_read_signature( &ctx, hash, sizeof( hash ),
+                     sig, sig_len ) == MBEDTLS_ERR_ECP_VERIFY_FAILED );
+        sig[sig_len - 1]--;
+    }
 
 exit:
     mbedtls_ecdsa_free( &ctx );