diff --git a/ChangeLog.d/fix-ecp-mul-memory-leak.txt b/ChangeLog.d/fix-ecp-mul-memory-leak.txt
new file mode 100644
index 0000000..e82cadc
--- /dev/null
+++ b/ChangeLog.d/fix-ecp-mul-memory-leak.txt
@@ -0,0 +1,3 @@
+Bugfix
+   * Fix potential memory leaks in ecp_randomize_jac() and ecp_randomize_mxz()
+     when PRNG function fails. Contributed by Jonas Lejeune in #3318.
diff --git a/library/ecp.c b/library/ecp.c
index 108695b..d48e3e8 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -1134,7 +1134,10 @@
             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
 
         if( count++ > 10 )
-            return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
+        {
+            ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
+            goto cleanup;
+        }
     }
     while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
 
@@ -1552,7 +1555,10 @@
             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
 
         if( count++ > 10 )
-            return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
+        {
+            ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
+            goto cleanup;
+        }
     }
     while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
 
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index d5fa23a..c99c2a6 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -795,7 +795,23 @@
     msg "test: no CTR_DRBG"
     make test
 
-    # no SSL tests as they all depend on CTR_DRBG so far
+    # no ssl-opt.sh/compat.sh as they all depend on CTR_DRBG so far
+}
+
+component_test_no_hmac_drbg () {
+    msg "build: Full minus HMAC_DRBG"
+    scripts/config.pl full
+    scripts/config.pl unset MBEDTLS_HMAC_DRBG_C
+    scripts/config.pl unset MBEDTLS_ECDSA_DETERMINISTIC # requires HMAC_DRBG
+
+    CC=gcc cmake -D CMAKE_BUILD_TYPE:String=Asan .
+    make
+
+    msg "test: no HMAC_DRBG"
+    make test
+
+    # No ssl-opt.sh/compat.sh as they never use HMAC_DRBG so far,
+    # so there's little value in running those lengthy tests here.
 }
 
 component_test_full_cmake_clang () {
diff --git a/tests/suites/test_suite_ecp.data b/tests/suites/test_suite_ecp.data
index a43e7d7..8cc57b7 100644
--- a/tests/suites/test_suite_ecp.data
+++ b/tests/suites/test_suite_ecp.data
@@ -330,6 +330,14 @@
 depends_on:MBEDTLS_ECP_DP_CURVE25519_ENABLED
 ecp_test_vec_x:MBEDTLS_ECP_DP_CURVE25519:"5AC99F33632E5A768DE7E81BF854C27C46E3FBF2ABBACD29EC4AFF517369C660":"057E23EA9F1CBE8A27168F6E696A791DE61DD3AF7ACD4EEACC6E7BA514FDA863":"47DC3D214174820E1154B49BC6CDB2ABD45EE95817055D255AA35831B70D3260":"6EB89DA91989AE37C7EAC7618D9E5C4951DBA1D73C285AE1CD26A855020EEF04":"61450CD98E36016B58776A897A9F0AEF738B99F09468B8D6B8511184D53494AB"
 
+ECP point multiplication rng fail secp256r1
+depends_on:MBEDTLS_ECP_DP_SECP256R1_ENABLED
+ecp_test_mul_rng:MBEDTLS_ECP_DP_SECP256R1:"814264145F2F56F2E96A8E337A1284993FAF432A5ABCE59E867B7291D507A3AF"
+
+ECP point multiplication rng fail Curve25519
+depends_on:MBEDTLS_ECP_DP_CURVE25519_ENABLED
+ecp_test_mul_rng:MBEDTLS_ECP_DP_CURVE25519:"5AC99F33632E5A768DE7E81BF854C27C46E3FBF2ABBACD29EC4AFF517369C660"
+
 ECP test vectors secp192k1
 depends_on:MBEDTLS_ECP_DP_SECP192K1_ENABLED
 ecp_test_vect:MBEDTLS_ECP_DP_SECP192K1:"D1E13A359F6E0F0698791938E6D60246030AE4B0D8D4E9DE":"281BCA982F187ED30AD5E088461EBE0A5FADBB682546DF79":"3F68A8E9441FB93A4DD48CB70B504FCC9AA01902EF5BE0F3":"BE97C5D2A1A94D081E3FACE53E65A27108B7467BDF58DE43":"5EB35E922CD693F7947124F5920022C4891C04F6A8B8DCB2":"60ECF73D0FC43E0C42E8E155FFE39F9F0B531F87B34B6C3C":"372F5C5D0E18313C82AEF940EC3AFEE26087A46F1EBAE923":"D5A9F9182EC09CEAEA5F57EA10225EC77FA44174511985FD"
diff --git a/tests/suites/test_suite_ecp.function b/tests/suites/test_suite_ecp.function
index 99780c0..1c4fb52 100644
--- a/tests/suites/test_suite_ecp.function
+++ b/tests/suites/test_suite_ecp.function
@@ -158,6 +158,31 @@
 /* END_CASE */
 
 /* BEGIN_CASE */
+void ecp_test_mul_rng( int id, char *d_hex )
+{
+    mbedtls_ecp_group grp;
+    mbedtls_mpi d;
+    mbedtls_ecp_point Q;
+
+    mbedtls_ecp_group_init( &grp ); mbedtls_mpi_init( &d );
+    mbedtls_ecp_point_init( &Q );
+
+    TEST_ASSERT( mbedtls_ecp_group_load( &grp, id ) == 0 );
+
+    TEST_ASSERT( mbedtls_ecp_check_pubkey( &grp, &grp.G ) == 0 );
+
+    TEST_ASSERT( mbedtls_mpi_read_string( &d, 16, d_hex ) == 0 );
+
+    TEST_ASSERT( mbedtls_ecp_mul( &grp, &Q, &d, &grp.G, &rnd_zero_rand, NULL )
+                 == MBEDTLS_ERR_ECP_RANDOM_FAILED );
+
+exit:
+    mbedtls_ecp_group_free( &grp ); mbedtls_mpi_free( &d );
+    mbedtls_ecp_point_free( &Q );
+}
+/* END_CASE */
+
+/* BEGIN_CASE */
 void ecp_fast_mod( int id, char *N_str )
 {
     mbedtls_ecp_group grp;