diff --git a/include/mbedtls/ecp.h b/include/mbedtls/ecp.h
index 49e85d9..f203a7b 100644
--- a/include/mbedtls/ecp.h
+++ b/include/mbedtls/ecp.h
@@ -911,15 +911,8 @@
  * \note            To prevent timing attacks, this function
  *                  executes the exact same sequence of base-field
  *                  operations for any valid \p m. It avoids any if-branch or
- *                  array index depending on the value of \p m.
- *
- * \note            If \p f_rng is not NULL, it is used to randomize
- *                  intermediate results to prevent potential timing attacks
- *                  targeting these results. We recommend always providing
- *                  a non-NULL \p f_rng. The overhead is negligible.
- *                  Note: unless #MBEDTLS_ECP_NO_INTERNAL_RNG is defined, when
- *                  \p f_rng is NULL, an internal RNG (seeded from the value
- *                  of \p m) will be used instead.
+ *                  array index depending on the value of \p m. If also uses
+ *                  \p f_rng to randomize some intermediate results.
  *
  * \param grp       The ECP group to use.
  *                  This must be initialized and have group parameters
@@ -928,9 +921,9 @@
  *                  This must be initialized.
  * \param m         The integer by which to multiply. This must be initialized.
  * \param P         The point to multiply. This must be initialized.
- * \param f_rng     The RNG function. This may be \c NULL if randomization
- *                  of intermediate results isn't desired (discouraged).
- * \param p_rng     The RNG context to be passed to \p p_rng.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
+ *                  NULL if \p f_rng doesn't need a context.
  *
  * \return          \c 0 on success.
  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
@@ -959,9 +952,9 @@
  *                  This must be initialized.
  * \param m         The integer by which to multiply. This must be initialized.
  * \param P         The point to multiply. This must be initialized.
- * \param f_rng     The RNG function. This may be \c NULL if randomization
- *                  of intermediate results isn't desired (discouraged).
- * \param p_rng     The RNG context to be passed to \p p_rng.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
+ *                  NULL if \p f_rng doesn't need a context.
  * \param rs_ctx    The restart context (NULL disables restart).
  *
  * \return          \c 0 on success.
diff --git a/library/ecjpake.c b/library/ecjpake.c
index de43ddb..d229311 100644
--- a/library/ecjpake.c
+++ b/library/ecjpake.c
@@ -962,6 +962,28 @@
     0xb4, 0x38, 0xf7, 0x19, 0xd3, 0xc4, 0xf3, 0x51
 };
 
+/*
+ * PRNG for test - !!!INSECURE NEVER USE IN PRODUCTION!!!
+ *
+ * This is the linear congruential generator from numerical recipes,
+ * except we only use the low byte as the output. See
+ * https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use
+ */
+static int self_test_rng( void *ctx, unsigned char *out, size_t len )
+{
+    static uint32_t state = 42;
+
+    (void) ctx;
+
+    for( size_t i = 0; i < len; i++ )
+    {
+        state = state * 1664525u + 1013904223u;
+        out[i] = (unsigned char) state;
+    }
+
+    return( 0 );
+}
+
 /* Load my private keys and generate the corresponding public keys */
 static int ecjpake_test_load( mbedtls_ecjpake_context *ctx,
                               const unsigned char *xm1, size_t len1,
@@ -972,9 +994,9 @@
     MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->xm1, xm1, len1 ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->xm2, xm2, len2 ) );
     MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &ctx->grp, &ctx->Xm1, &ctx->xm1,
-                                      &ctx->grp.G, NULL, NULL ) );
+                                      &ctx->grp.G, self_test_rng, NULL ) );
     MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &ctx->grp, &ctx->Xm2, &ctx->xm2,
-                                      &ctx->grp.G, NULL, NULL ) );
+                                      &ctx->grp.G, self_test_rng, NULL ) );
 
 cleanup:
     return( ret );
diff --git a/library/ecp.c b/library/ecp.c
index 044bbe1..873b4c8 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -2684,6 +2684,9 @@
     ECP_VALIDATE_RET( m   != NULL );
     ECP_VALIDATE_RET( P   != NULL );
 
+    if( f_rng == NULL )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
 #if defined(MBEDTLS_ECP_RESTARTABLE)
     /* reset ops count for this call if top-level */
     if( rs_ctx != NULL && rs_ctx->depth++ == 0 )
@@ -3315,6 +3318,28 @@
 
 #if defined(MBEDTLS_SELF_TEST)
 
+/*
+ * PRNG for test - !!!INSECURE NEVER USE IN PRODUCTION!!!
+ *
+ * This is the linear congruential generator from numerical recipes,
+ * except we only use the low byte as the output. See
+ * https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use
+ */
+static int self_test_rng( void *ctx, unsigned char *out, size_t len )
+{
+    static uint32_t state = 42;
+
+    (void) ctx;
+
+    for( size_t i = 0; i < len; i++ )
+    {
+        state = state * 1664525u + 1013904223u;
+        out[i] = (unsigned char) state;
+    }
+
+    return( 0 );
+}
+
 /* Adjust the exponent to be a valid private point for the specified curve.
  * This is sometimes necessary because we use a single set of exponents
  * for all curves but the validity of values depends on the curve. */
@@ -3370,7 +3395,7 @@
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[0] ) );
     MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
-    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, self_test_rng, NULL ) );
 
     for( i = 1; i < n_exponents; i++ )
     {
@@ -3383,7 +3408,7 @@
 
         MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[i] ) );
         MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
-        MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
+        MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, self_test_rng, NULL ) );
 
         if( add_count != add_c_prev ||
             dbl_count != dbl_c_prev ||
@@ -3461,7 +3486,7 @@
         mbedtls_printf( "  ECP SW test #1 (constant op_count, base point G): " );
     /* Do a dummy multiplication first to trigger precomputation */
     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
-    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, self_test_rng, NULL ) );
     ret = self_test_point( verbose,
                            &grp, &R, &m, &grp.G,
                            sw_exponents,
diff --git a/tests/suites/test_suite_ecp.function b/tests/suites/test_suite_ecp.function
index f2b6376..e820067 100644
--- a/tests/suites/test_suite_ecp.function
+++ b/tests/suites/test_suite_ecp.function
@@ -124,12 +124,14 @@
     mbedtls_mpi dA, xA, yA, dB, xZ, yZ;
     int cnt_restarts;
     int ret;
+    mbedtls_test_rnd_pseudo_info rnd_info;
 
     mbedtls_ecp_restart_init( &ctx );
     mbedtls_ecp_group_init( &grp );
     mbedtls_ecp_point_init( &R ); mbedtls_ecp_point_init( &P );
     mbedtls_mpi_init( &dA ); mbedtls_mpi_init( &xA ); mbedtls_mpi_init( &yA );
     mbedtls_mpi_init( &dB ); mbedtls_mpi_init( &xZ ); mbedtls_mpi_init( &yZ );
+    memset( &rnd_info, 0x00, sizeof( mbedtls_test_rnd_pseudo_info ) );
 
     TEST_ASSERT( mbedtls_ecp_group_load( &grp, id ) == 0 );
 
@@ -147,7 +149,8 @@
     cnt_restarts = 0;
     do {
         ECP_PT_RESET( &R );
-        ret = mbedtls_ecp_mul_restartable( &grp, &R, &dA, &grp.G, NULL, NULL, &ctx );
+        ret = mbedtls_ecp_mul_restartable( &grp, &R, &dA, &grp.G,
+                &mbedtls_test_rnd_pseudo_rand, &rnd_info, &ctx );
     } while( ret == MBEDTLS_ERR_ECP_IN_PROGRESS && ++cnt_restarts );
 
     TEST_ASSERT( ret == 0 );
@@ -162,7 +165,8 @@
     cnt_restarts = 0;
     do {
         ECP_PT_RESET( &R );
-        ret = mbedtls_ecp_mul_restartable( &grp, &R, &dB, &P, NULL, NULL, &ctx );
+        ret = mbedtls_ecp_mul_restartable( &grp, &R, &dB, &P,
+                &mbedtls_test_rnd_pseudo_rand, &rnd_info, &ctx );
     } while( ret == MBEDTLS_ERR_ECP_IN_PROGRESS && ++cnt_restarts );
 
     TEST_ASSERT( ret == 0 );
@@ -176,7 +180,8 @@
      * This test only makes sense when we actually restart */
     if( min_restarts > 0 )
     {
-        ret = mbedtls_ecp_mul_restartable( &grp, &R, &dB, &P, NULL, NULL, &ctx );
+        ret = mbedtls_ecp_mul_restartable( &grp, &R, &dB, &P,
+                &mbedtls_test_rnd_pseudo_rand, &rnd_info, &ctx );
         TEST_ASSERT( ret == MBEDTLS_ERR_ECP_IN_PROGRESS );
     }
 
@@ -294,12 +299,14 @@
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.X, &xA ) == 0 );
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.Y, &yA ) == 0 );
     TEST_ASSERT( mbedtls_ecp_check_pubkey( &grp, &R ) == 0 );
-    TEST_ASSERT( mbedtls_ecp_mul( &grp, &R, &dB, &R, NULL, NULL ) == 0 );
+    TEST_ASSERT( mbedtls_ecp_mul( &grp, &R, &dB, &R,
+                          &mbedtls_test_rnd_pseudo_rand, &rnd_info ) == 0 );
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.X, &xZ ) == 0 );
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.Y, &yZ ) == 0 );
     TEST_ASSERT( mbedtls_ecp_check_pubkey( &grp, &R ) == 0 );
 
-    TEST_ASSERT( mbedtls_ecp_mul( &grp, &R, &dB, &grp.G, NULL, NULL ) == 0 );
+    TEST_ASSERT( mbedtls_ecp_mul( &grp, &R, &dB, &grp.G,
+                          &mbedtls_test_rnd_pseudo_rand, &rnd_info ) == 0 );
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.X, &xB ) == 0 );
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.Y, &yB ) == 0 );
     TEST_ASSERT( mbedtls_ecp_check_pubkey( &grp, &R ) == 0 );
@@ -351,11 +358,13 @@
     TEST_ASSERT( mbedtls_ecp_check_pubkey( &grp, &R ) == 0 );
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.X, &xS ) == 0 );
 
-    TEST_ASSERT( mbedtls_ecp_mul( &grp, &R, &dB, &grp.G, NULL, NULL ) == 0 );
+    TEST_ASSERT( mbedtls_ecp_mul( &grp, &R, &dB, &grp.G,
+                          &mbedtls_test_rnd_pseudo_rand, &rnd_info ) == 0 );
     TEST_ASSERT( mbedtls_ecp_check_pubkey( &grp, &R ) == 0 );
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.X, &xB ) == 0 );
 
-    TEST_ASSERT( mbedtls_ecp_mul( &grp, &R, &dA, &R, NULL, NULL ) == 0 );
+    TEST_ASSERT( mbedtls_ecp_mul( &grp, &R, &dA, &R,
+                          &mbedtls_test_rnd_pseudo_rand, &rnd_info ) == 0 );
     TEST_ASSERT( mbedtls_ecp_check_pubkey( &grp, &R ) == 0 );
     TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R.X, &xS ) == 0 );