diff --git a/ChangeLog.d/MD-X.509-hashing.txt b/ChangeLog.d/MD-X.509-hashing.txt
new file mode 100644
index 0000000..2ca989c
--- /dev/null
+++ b/ChangeLog.d/MD-X.509-hashing.txt
@@ -0,0 +1,2 @@
+Features
+   * The X.509 module now uses PSA hash acceleration if present.
diff --git a/library/x509_crt.c b/library/x509_crt.c
index c865444..d19502c 100644
--- a/library/x509_crt.c
+++ b/library/x509_crt.c
@@ -47,7 +47,7 @@
 #if defined(MBEDTLS_USE_PSA_CRYPTO)
 #include "psa/crypto.h"
 #include "mbedtls/psa_util.h"
-#endif
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
 
 #if defined(MBEDTLS_PLATFORM_C)
 #include "mbedtls/platform.h"
@@ -2336,8 +2336,14 @@
                                const mbedtls_x509_crt_profile *profile )
 {
     int flags = 0;
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+    unsigned char hash[PSA_HASH_MAX_SIZE];
+    psa_algorithm_t psa_algorithm;
+#else
     unsigned char hash[MBEDTLS_MD_MAX_SIZE];
     const mbedtls_md_info_t *md_info;
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+    size_t hash_length;
 
     if( ca == NULL )
         return( flags );
@@ -2370,19 +2376,38 @@
         if( x509_profile_check_pk_alg( profile, crl_list->sig_pk ) != 0 )
             flags |= MBEDTLS_X509_BADCRL_BAD_PK;
 
-        md_info = mbedtls_md_info_from_type( crl_list->sig_md );
-        if( mbedtls_md( md_info, crl_list->tbs.p, crl_list->tbs.len, hash ) != 0 )
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+        psa_algorithm = mbedtls_psa_translate_md( crl_list->sig_md );
+        if( psa_hash_compute( psa_algorithm,
+                              crl_list->tbs.p,
+                              crl_list->tbs.len,
+                              hash,
+                              sizeof( hash ),
+                              &hash_length ) != PSA_SUCCESS )
         {
             /* Note: this can't happen except after an internal error */
             flags |= MBEDTLS_X509_BADCRL_NOT_TRUSTED;
             break;
         }
+#else
+        md_info = mbedtls_md_info_from_type( crl_list->sig_md );
+        hash_length = mbedtls_md_get_size( md_info );
+        if( mbedtls_md( md_info,
+                        crl_list->tbs.p,
+                        crl_list->tbs.len,
+                        hash ) != 0 )
+        {
+            /* Note: this can't happen except after an internal error */
+            flags |= MBEDTLS_X509_BADCRL_NOT_TRUSTED;
+            break;
+        }
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
 
         if( x509_profile_check_key( profile, &ca->pk ) != 0 )
             flags |= MBEDTLS_X509_BADCERT_BAD_KEY;
 
         if( mbedtls_pk_verify_ext( crl_list->sig_pk, crl_list->sig_opts, &ca->pk,
-                           crl_list->sig_md, hash, mbedtls_md_get_size( md_info ),
+                           crl_list->sig_md, hash, hash_length,
                            crl_list->sig.p, crl_list->sig.len ) != 0 )
         {
             flags |= MBEDTLS_X509_BADCRL_NOT_TRUSTED;
@@ -2421,9 +2446,9 @@
                                      mbedtls_x509_crt *parent,
                                      mbedtls_x509_crt_restart_ctx *rs_ctx )
 {
-    unsigned char hash[MBEDTLS_MD_MAX_SIZE];
     size_t hash_len;
 #if !defined(MBEDTLS_USE_PSA_CRYPTO)
+    unsigned char hash[MBEDTLS_MD_MAX_SIZE];
     const mbedtls_md_info_t *md_info;
     md_info = mbedtls_md_info_from_type( child->sig_md );
     hash_len = mbedtls_md_get_size( md_info );
@@ -2432,23 +2457,21 @@
     if( mbedtls_md( md_info, child->tbs.p, child->tbs.len, hash ) != 0 )
         return( -1 );
 #else
-    psa_hash_operation_t hash_operation = PSA_HASH_OPERATION_INIT;
+    unsigned char hash[PSA_HASH_MAX_SIZE];
     psa_algorithm_t hash_alg = mbedtls_psa_translate_md( child->sig_md );
+    psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
 
-    if( psa_hash_setup( &hash_operation, hash_alg ) != PSA_SUCCESS )
-        return( -1 );
-
-    if( psa_hash_update( &hash_operation, child->tbs.p, child->tbs.len )
-        != PSA_SUCCESS )
+    status = psa_hash_compute( hash_alg,
+                               child->tbs.p,
+                               child->tbs.len,
+                               hash,
+                               sizeof( hash ),
+                               &hash_len );
+    if( status != PSA_SUCCESS )
     {
-        return( -1 );
+        return( MBEDTLS_ERR_PLATFORM_HW_ACCEL_FAILED );
     }
 
-    if( psa_hash_finish( &hash_operation, hash, sizeof( hash ), &hash_len )
-        != PSA_SUCCESS )
-    {
-        return( -1 );
-    }
 #endif /* MBEDTLS_USE_PSA_CRYPTO */
     /* Skip expensive computation on obvious mismatch */
     if( ! mbedtls_pk_can_do( &parent->pk, child->sig_pk ) )
diff --git a/library/x509write_crt.c b/library/x509write_crt.c
index 17b3e79..6d1e7b3 100644
--- a/library/x509write_crt.c
+++ b/library/x509write_crt.c
@@ -40,6 +40,11 @@
 #include "mbedtls/pem.h"
 #endif /* MBEDTLS_PEM_WRITE_C */
 
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+#include "psa/crypto.h"
+#include "mbedtls/psa_util.h"
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+
 void mbedtls_x509write_crt_init( mbedtls_x509write_cert *ctx )
 {
     memset( ctx, 0, sizeof( mbedtls_x509write_cert ) );
@@ -167,66 +172,86 @@
 }
 
 #if defined(MBEDTLS_SHA1_C)
-int mbedtls_x509write_crt_set_subject_key_identifier( mbedtls_x509write_cert *ctx )
+static int mbedtls_x509write_crt_set_key_identifier( mbedtls_x509write_cert *ctx,
+                                              int is_ca,
+                                              unsigned char tag )
 {
     int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
     unsigned char buf[MBEDTLS_MPI_MAX_SIZE * 2 + 20]; /* tag, length + 2xMPI */
     unsigned char *c = buf + sizeof(buf);
     size_t len = 0;
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+    psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
+    size_t hash_length;
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
 
     memset( buf, 0, sizeof(buf) );
     MBEDTLS_ASN1_CHK_ADD( len,
-                mbedtls_pk_write_pubkey( &c, buf, ctx->subject_key ) );
+                          mbedtls_pk_write_pubkey( &c,
+                                                   buf,
+                                                   is_ca ?
+                                                   ctx->issuer_key :
+                                                   ctx->subject_key ) );
 
+
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+    status = psa_hash_compute( PSA_ALG_SHA_1,
+                               buf + sizeof(buf) - len,
+                               len,
+                               buf + sizeof(buf) - 20,
+                               20,
+                               &hash_length );
+    if( status != PSA_SUCCESS )
+    {
+        return( MBEDTLS_ERR_PLATFORM_HW_ACCEL_FAILED );
+    }
+#else
     ret = mbedtls_sha1( buf + sizeof( buf ) - len, len,
-                            buf + sizeof( buf ) - 20 );
+                        buf + sizeof( buf ) - 20 );
     if( ret != 0 )
         return( ret );
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+
     c = buf + sizeof( buf ) - 20;
     len = 20;
 
     MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_len( &c, buf, len ) );
-    MBEDTLS_ASN1_CHK_ADD( len,
-            mbedtls_asn1_write_tag( &c, buf, MBEDTLS_ASN1_OCTET_STRING ) );
+    MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_tag( &c, buf, tag ) );
 
-    return mbedtls_x509write_crt_set_extension( ctx,
-                 MBEDTLS_OID_SUBJECT_KEY_IDENTIFIER,
-                 MBEDTLS_OID_SIZE( MBEDTLS_OID_SUBJECT_KEY_IDENTIFIER ),
-                 0, buf + sizeof(buf) - len, len );
+    if( is_ca ) // writes AuthorityKeyIdentifier sequence
+    {
+        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_len( &c, buf, len ));
+        MBEDTLS_ASN1_CHK_ADD( len,
+                              mbedtls_asn1_write_tag( &c,
+                                                      buf,
+                                                      MBEDTLS_ASN1_CONSTRUCTED |
+                                                      MBEDTLS_ASN1_SEQUENCE ) );
+    }
+
+    if( is_ca )
+        return( mbedtls_x509write_crt_set_extension( ctx,
+                MBEDTLS_OID_AUTHORITY_KEY_IDENTIFIER,
+                MBEDTLS_OID_SIZE( MBEDTLS_OID_AUTHORITY_KEY_IDENTIFIER ),
+                0, buf + sizeof(buf) - len, len ) );
+    else
+        return( mbedtls_x509write_crt_set_extension( ctx,
+                MBEDTLS_OID_SUBJECT_KEY_IDENTIFIER,
+                MBEDTLS_OID_SIZE( MBEDTLS_OID_SUBJECT_KEY_IDENTIFIER ),
+                0, buf + sizeof(buf) - len, len ) );
+}
+
+int mbedtls_x509write_crt_set_subject_key_identifier( mbedtls_x509write_cert *ctx )
+{
+    return mbedtls_x509write_crt_set_key_identifier( ctx,
+                                                     0,
+                                                     MBEDTLS_ASN1_OCTET_STRING );
 }
 
 int mbedtls_x509write_crt_set_authority_key_identifier( mbedtls_x509write_cert *ctx )
 {
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    unsigned char buf[MBEDTLS_MPI_MAX_SIZE * 2 + 20]; /* tag, length + 2xMPI */
-    unsigned char *c = buf + sizeof( buf );
-    size_t len = 0;
-
-    memset( buf, 0, sizeof(buf) );
-    MBEDTLS_ASN1_CHK_ADD( len,
-                          mbedtls_pk_write_pubkey( &c, buf, ctx->issuer_key ) );
-
-    ret = mbedtls_sha1( buf + sizeof( buf ) - len, len,
-                            buf + sizeof( buf ) - 20 );
-    if( ret != 0 )
-        return( ret );
-    c = buf + sizeof( buf ) - 20;
-    len = 20;
-
-    MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_len( &c, buf, len ) );
-    MBEDTLS_ASN1_CHK_ADD( len,
-        mbedtls_asn1_write_tag( &c, buf, MBEDTLS_ASN1_CONTEXT_SPECIFIC | 0 ) );
-
-    MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_len( &c, buf, len ) );
-    MBEDTLS_ASN1_CHK_ADD( len,
-                          mbedtls_asn1_write_tag( &c, buf,
-                                                  MBEDTLS_ASN1_CONSTRUCTED |
-                                                  MBEDTLS_ASN1_SEQUENCE ) );
-
-    return mbedtls_x509write_crt_set_extension(
-        ctx, MBEDTLS_OID_AUTHORITY_KEY_IDENTIFIER,
-        MBEDTLS_OID_SIZE( MBEDTLS_OID_AUTHORITY_KEY_IDENTIFIER ),
-        0, buf + sizeof( buf ) - len, len );
+    return mbedtls_x509write_crt_set_key_identifier( ctx,
+                                                     1,
+                                                     (MBEDTLS_ASN1_CONTEXT_SPECIFIC | 0) );
 }
 #endif /* MBEDTLS_SHA1_C */
 
@@ -330,8 +355,16 @@
     const char *sig_oid;
     size_t sig_oid_len = 0;
     unsigned char *c, *c2;
-    unsigned char hash[64];
     unsigned char sig[MBEDTLS_PK_SIGNATURE_MAX_SIZE];
+    size_t hash_length = 0;
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+    psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
+    psa_algorithm_t psa_algorithm;
+    unsigned char hash[PSA_HASH_MAX_SIZE];
+#else
+    unsigned char hash[64];
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+
     size_t sub_len = 0, pub_len = 0, sig_and_oid_len = 0, sig_len;
     size_t len = 0;
     mbedtls_pk_type_t pk_alg;
@@ -466,14 +499,30 @@
      */
 
     /* Compute hash of CRT. */
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+    psa_algorithm = mbedtls_psa_translate_md( ctx->md_alg );
+
+    status = psa_hash_compute( psa_algorithm,
+                               c,
+                               len,
+                               hash,
+                               sizeof( hash ),
+                               &hash_length );
+    if( status != PSA_SUCCESS )
+    {
+        return( MBEDTLS_ERR_PLATFORM_HW_ACCEL_FAILED );
+    }
+#else
     if( ( ret = mbedtls_md( mbedtls_md_info_from_type( ctx->md_alg ), c,
                             len, hash ) ) != 0 )
     {
         return( ret );
     }
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+
 
     if( ( ret = mbedtls_pk_sign( ctx->issuer_key, ctx->md_alg,
-                                 hash, 0, sig, sizeof( sig ), &sig_len,
+                                 hash, hash_length, sig, sizeof( sig ), &sig_len,
                                  f_rng, p_rng ) ) != 0 )
     {
         return( ret );
diff --git a/library/x509write_csr.c b/library/x509write_csr.c
index 555f296..1cee318 100644
--- a/library/x509write_csr.c
+++ b/library/x509write_csr.c
@@ -35,7 +35,7 @@
 #if defined(MBEDTLS_USE_PSA_CRYPTO)
 #include "psa/crypto.h"
 #include "mbedtls/psa_util.h"
-#endif
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
 
 #include <string.h>
 #include <stdlib.h>
@@ -149,7 +149,6 @@
     size_t len = 0;
     mbedtls_pk_type_t pk_alg;
 #if defined(MBEDTLS_USE_PSA_CRYPTO)
-    psa_hash_operation_t hash_operation = PSA_HASH_OPERATION_INIT;
     size_t hash_len;
     psa_algorithm_t hash_alg = mbedtls_psa_translate_md( ctx->md_alg );
 #endif /* MBEDTLS_USE_PSA_CRYPTO */
@@ -219,16 +218,14 @@
      * Note: hash errors can happen only after an internal error
      */
 #if defined(MBEDTLS_USE_PSA_CRYPTO)
-    if( psa_hash_setup( &hash_operation, hash_alg ) != PSA_SUCCESS )
-        return( MBEDTLS_ERR_X509_FATAL_ERROR );
-
-    if( psa_hash_update( &hash_operation, c, len ) != PSA_SUCCESS )
-        return( MBEDTLS_ERR_X509_FATAL_ERROR );
-
-    if( psa_hash_finish( &hash_operation, hash, sizeof( hash ), &hash_len )
-        != PSA_SUCCESS )
+    if( psa_hash_compute( hash_alg,
+                          c,
+                          len,
+                          hash,
+                          sizeof( hash ),
+                          &hash_len ) != PSA_SUCCESS )
     {
-        return( MBEDTLS_ERR_X509_FATAL_ERROR );
+        return( MBEDTLS_ERR_PLATFORM_HW_ACCEL_FAILED );
     }
 #else /* MBEDTLS_USE_PSA_CRYPTO */
     ret = mbedtls_md( mbedtls_md_info_from_type( ctx->md_alg ), c, len, hash );