diff --git a/library/ecp.c b/library/ecp.c
index 983a67f..1447a5a 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -3076,15 +3076,17 @@
 
 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
 MBEDTLS_STATIC_TESTABLE
-int mbedtls_ecp_gen_privkey_sw( const mbedtls_mpi *N, size_t n_bits,
-                                mbedtls_mpi *d,
-                                int (*f_rng)(void *, unsigned char *, size_t),
-                                void *p_rng )
+int mbedtls_mpi_random( mbedtls_mpi *X,
+                        mbedtls_mpi_sint min,
+                        const mbedtls_mpi *N,
+                        int (*f_rng)(void *, unsigned char *, size_t),
+                        void *p_rng )
 {
-    /* SEC1 3.2.1: Generate d such that 1 <= n < N */
-    int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
+    /* SEC1 3.2.1: Generate X such that 1 <= n < N */
+    int ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
     int count = 0;
     unsigned cmp = 0;
+    size_t n_bits = mbedtls_mpi_bitlen( N );
     size_t n_bytes = ( n_bits + 7 ) / 8;
 
     /*
@@ -3097,8 +3099,8 @@
      */
     do
     {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_bytes, f_rng, p_rng ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_bytes - n_bits ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n_bytes, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, 8 * n_bytes - n_bits ) );
 
         /*
          * Each try has at worst a probability 1/2 of failing (the msb has
@@ -3111,17 +3113,17 @@
          */
         if( ++count > 30 )
         {
-            ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
+            ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
             goto cleanup;
         }
 
-        ret = mbedtls_mpi_lt_mpi_ct( d, N, &cmp );
+        ret = mbedtls_mpi_lt_mpi_ct( X, N, &cmp );
         if( ret != 0 )
         {
             goto cleanup;
         }
     }
-    while( mbedtls_mpi_cmp_int( d, 1 ) < 0 || cmp != 1 );
+    while( mbedtls_mpi_cmp_int( X, min ) < 0 || cmp != 1 );
 
 cleanup:
     return( ret );
@@ -3147,8 +3149,7 @@
 
 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
     if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
-        return( mbedtls_ecp_gen_privkey_sw( &grp->N, grp->nbits, d,
-                                            f_rng, p_rng ) );
+        return( mbedtls_mpi_random( d, 1, &grp->N, f_rng, p_rng ) );
 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
 
     return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
diff --git a/library/ecp_invasive.h b/library/ecp_invasive.h
index eeb4305..1ca65fd 100644
--- a/library/ecp_invasive.h
+++ b/library/ecp_invasive.h
@@ -77,25 +77,36 @@
 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
 
 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
-/** Generate a private key on a short Weierstrass curve.
+/** Generate a random number uniformly in a range.
+ *
+ * This function generates a random number between \p min inclusive and
+ * \p N exclusive.
  *
  * The procedure complies with RFC 6979 §3.3 (deterministic ECDSA)
- * when the RNG is a suitably parametrized instance of HMAC_DRBG.
+ * when the RNG is a suitably parametrized instance of HMAC_DRBG
+ * and \p min is \c 1.
  *
- * \p N             The upper bound of the range.
- * \p n_bits        The size of \p N in bits. This value must be correct,
- *                  otherwise the result is unpredictable.
- * \param d         A random number, uniformly generated in the range [1, N-1].
- * \param f_rng     The RNG function.
- * \param p_rng     The RNG context to be passed to \p f_rng.
+ * \note           There are `N - min` possible outputs. The lower bound
+ *                 \p min can be reached, but the upper bound \p N cannot.
  *
- * \return          \c 0 on success.
- * \return          \c MBEDTLS_ERR_ECP_xxx or MBEDTLS_ERR_MPI_xxx on failure.
+ * \param X        The destination MPI. This must point to an initialized MPI.
+ * \param min      The minimum value to return.
+ *                 It must be nonnegative.
+ * \param N        The upper bound of the range, exclusive.
+ *                 In other words, this is one plus the maximum value to return.
+ *                 \p N must be strictly larger than \p min.
+ * \param f_rng    The RNG function to use. This must not be \c NULL.
+ * \param p_rng    The RNG parameter to be passed to \p f_rng.
+ *
+ * \return         \c 0 if successful.
+ * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
+ * \return         Another negative error code on failure.
  */
-int mbedtls_ecp_gen_privkey_sw( const mbedtls_mpi *N, size_t n_bits,
-                                mbedtls_mpi *d,
-                                int (*f_rng)(void *, unsigned char *, size_t),
-                                void *p_rng );
+int mbedtls_mpi_random( mbedtls_mpi *X,
+                        mbedtls_mpi_sint min,
+                        const mbedtls_mpi *N,
+                        int (*f_rng)(void *, unsigned char *, size_t),
+                        void *p_rng );
 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
 
 #endif /* MBEDTLS_TEST_HOOKS && MBEDTLS_ECP_C */