diff --git a/library/pkparse.c b/library/pkparse.c
index 2311986f7f..724197d79a 100644
--- a/library/pkparse.c
+++ b/library/pkparse.c
@@ -769,6 +769,17 @@ static int pk_parse_key_pkcs1_der( mbedtls_rsa_context *rsa,
         goto cleanup;
     p += len;
 
+    /*
+    * The RSA CRT parameters DP, DQ and QP are nominally redundant, in
+    * that they can be easily recomputed from D, P and Q. However by
+    * parsing them from the PKCS1 structure it is possible to avoid
+    * recalculating them which both reduces the overhead of loading
+    * RSA private keys into memory and also avoids side channels which
+    * can arise when computing those values, since all of D, P, and Q
+    * are secret. See https://eprint.iacr.org/2020/055 for a
+    * description of one such attack.
+    */
+
     /* Import DP */
     if( ( ret = mbedtls_asn1_get_tag( &p, end, &len,
                                       MBEDTLS_ASN1_INTEGER ) ) != 0 ||
diff --git a/library/rsa.c b/library/rsa.c
index 7ea72cd846..dc34e38b4e 100644
--- a/library/rsa.c
+++ b/library/rsa.c
@@ -249,7 +249,10 @@ static int rsa_check_context( mbedtls_rsa_context const *ctx, int is_priv,
 int mbedtls_rsa_complete( mbedtls_rsa_context *ctx )
 {
     int ret = 0;
-    int have_N, have_P, have_Q, have_D, have_E, have_DP, have_DQ, have_QP;
+    int have_N, have_P, have_Q, have_D, have_E;
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    int have_DP, have_DQ, have_QP;
+#endif
     int n_missing, pq_missing, d_missing, is_pub, is_priv;
 
     RSA_VALIDATE_RET( ctx != NULL );
@@ -259,10 +262,12 @@ int mbedtls_rsa_complete( mbedtls_rsa_context *ctx )
     have_Q = ( mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 );
     have_D = ( mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 );
     have_E = ( mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0 );
+
+#if !defined(MBEDTLS_RSA_NO_CRT)
     have_DP = ( mbedtls_mpi_cmp_int( &ctx->DP, 0 ) != 0 );
     have_DQ = ( mbedtls_mpi_cmp_int( &ctx->DQ, 0 ) != 0 );
     have_QP = ( mbedtls_mpi_cmp_int( &ctx->QP, 0 ) != 0 );
-
+#endif
 
     /*
      * Check whether provided parameters are enough