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 104e1f1..9522edf 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -1544,7 +1544,10 @@
             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 );
 
@@ -2278,7 +2281,10 @@
             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 );
 
@@ -2856,7 +2862,10 @@
              * such as secp224k1 are actually very close to the worst case.
              */
             if( ++count > 30 )
-                return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
+            {
+                ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
+                goto cleanup;
+            }
 
             ret = mbedtls_mpi_lt_mpi_ct( d, &grp->N, &cmp );
             if( ret != 0 )
diff --git a/tests/suites/test_suite_ecp.data b/tests/suites/test_suite_ecp.data
index 9219179..b84868c 100644
--- a/tests/suites/test_suite_ecp.data
+++ b/tests/suites/test_suite_ecp.data
@@ -446,6 +446,14 @@
 depends_on:MBEDTLS_ECP_DP_CURVE25519_ENABLED
 ecp_test_mul:MBEDTLS_ECP_DP_CURVE25519:"5AC99F33632E5A768DE7E81BF854C27C46E3FBF2ABBACD29EC4AFF517369C660":"B8495F16056286FDB1329CEB8D09DA6AC49FF1FAE35616AEB8413B7C7AEBE0":"00":"01":"00":"01":"00":MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
 
+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 Curve448 (RFC 7748 6.2, after decodeUCoordinate)
 depends_on:MBEDTLS_ECP_DP_CURVE448_ENABLED
 ecp_test_vec_x:MBEDTLS_ECP_DP_CURVE448:"eb7298a5c0d8c29a1dab27f1a6826300917389449741a974f5bac9d98dc298d46555bce8bae89eeed400584bb046cf75579f51d125498f98":"a01fc432e5807f17530d1288da125b0cd453d941726436c8bbd9c5222c3da7fa639ce03db8d23b274a0721a1aed5227de6e3b731ccf7089b":"ad997351b6106f36b0d1091b929c4c37213e0d2b97e85ebb20c127691d0dad8f1d8175b0723745e639a3cb7044290b99e0e2a0c27a6a301c":"0936f37bc6c1bd07ae3dec7ab5dc06a73ca13242fb343efc72b9d82730b445f3d4b0bd077162a46dcfec6f9b590bfcbcf520cdb029a8b73e":"9d874a5137509a449ad5853040241c5236395435c36424fd560b0cb62b281d285275a740ce32a22dd1740f4aa9161cec95ccc61a18f4ff07"
diff --git a/tests/suites/test_suite_ecp.function b/tests/suites/test_suite_ecp.function
index 03c3e53..6385e77 100644
--- a/tests/suites/test_suite_ecp.function
+++ b/tests/suites/test_suite_ecp.function
@@ -725,6 +725,31 @@
 /* END_CASE */
 
 /* BEGIN_CASE */
+void ecp_test_mul_rng( int id, data_t * 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_binary( &d, d_hex->x, d_hex->len ) == 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;