diff --git a/library/pkparse.c b/library/pkparse.c
index ec9b55f8c5a0..3bad0ce6dd75 100644
--- a/library/pkparse.c
+++ b/library/pkparse.c
@@ -754,14 +754,40 @@ static int pk_parse_key_pkcs1_der( mbedtls_rsa_context *rsa,
         goto cleanup;
     p += len;
 
-    /* Complete the RSA private key */
-    if( ( ret = mbedtls_rsa_complete( rsa ) ) != 0 )
-        goto cleanup;
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    /*
+    * 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_mpi( &p, end, &rsa->DP ) ) != 0)
+       goto cleanup;
+
+    /* Import DQ */
+    if( ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->DQ ) ) != 0)
+       goto cleanup;
+
+    /* Import QP */
+    if( ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->QP ) ) != 0)
+       goto cleanup;
 
-    /* Check optional parameters */
+#else
+    /* Verify existance of the CRT params */
     if( ( ret = mbedtls_asn1_get_mpi( &p, end, &T ) ) != 0 ||
         ( ret = mbedtls_asn1_get_mpi( &p, end, &T ) ) != 0 ||
         ( ret = mbedtls_asn1_get_mpi( &p, end, &T ) ) != 0 )
+       goto cleanup;
+#endif
+
+    /* Complete the RSA private key */
+    if( ( ret = mbedtls_rsa_complete( rsa ) ) != 0 )
         goto cleanup;
 
     if( p != end )
diff --git a/library/rsa.c b/library/rsa.c
index 4b3cc0213d3a..98c529f00509 100644
--- a/library/rsa.c
+++ b/library/rsa.c
@@ -251,6 +251,12 @@ int mbedtls_rsa_complete( mbedtls_rsa_context *ctx )
     const int have_D = ( mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 );
     const int have_E = ( mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0 );
 
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    const int have_DP = ( mbedtls_mpi_cmp_int( &ctx->DP, 0 ) != 0 );
+    const int have_DQ = ( mbedtls_mpi_cmp_int( &ctx->DQ, 0 ) != 0 );
+    const int have_QP = ( mbedtls_mpi_cmp_int( &ctx->QP, 0 ) != 0 );
+#endif
+
     /*
      * Check whether provided parameters are enough
      * to deduce all others. The following incomplete
@@ -316,7 +322,7 @@ int mbedtls_rsa_complete( mbedtls_rsa_context *ctx )
      */
 
 #if !defined(MBEDTLS_RSA_NO_CRT)
-    if( is_priv )
+    if( is_priv && ! ( have_DP && have_DQ && have_QP ) )
     {
         ret = mbedtls_rsa_deduce_crt( &ctx->P,  &ctx->Q,  &ctx->D,
                                       &ctx->DP, &ctx->DQ, &ctx->QP );