diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index b1caf6e99..fec97cb5e 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -1591,6 +1591,130 @@ component_test_no_use_psa_crypto_full_cmake_asan() {
     env OPENSSL_CMD="$OPENSSL_NEXT" tests/compat.sh -e '^$' -f 'ARIA\|CHACHA'
 }
 
+component_test_psa_crypto_config_accel_ecdsa () {
+    msg "test: MBEDTLS_PSA_CRYPTO_CONFIG with accelerated ECDSA"
+
+    # Disable ALG_STREAM_CIPHER and ALG_ECB_NO_PADDING to avoid having
+    # partial support for cipher operations in the driver test library.
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_STREAM_CIPHER
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_ECB_NO_PADDING
+
+    # SHA384 needed for some ECDSA signature tests.
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h set MBEDTLS_SHA512_C
+
+    loc_accel_list="ALG_ECDSA ALG_DETERMINISTIC_ECDSA KEY_TYPE_ECC_KEY_PAIR KEY_TYPE_ECC_PUBLIC_KEY"
+    loc_accel_flags=$( echo "$loc_accel_list" | sed 's/[^ ]* */-DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_&/g' )
+    make -C tests libtestdriver1.a CFLAGS="$ASAN_CFLAGS $loc_accel_flags" LDFLAGS="$ASAN_CFLAGS"
+
+    # Restore test driver base configuration
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h unset MBEDTLS_SHA512_C
+
+    scripts/config.py set MBEDTLS_PSA_CRYPTO_DRIVERS
+    scripts/config.py set MBEDTLS_PSA_CRYPTO_CONFIG
+    scripts/config.py unset MBEDTLS_USE_PSA_CRYPTO
+    scripts/config.py unset MBEDTLS_ECDSA_C
+    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
+    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_ECDH_ECDSA_ENABLED
+
+    loc_accel_flags="$loc_accel_flags $( echo "$loc_accel_list" | sed 's/[^ ]* */-DMBEDTLS_PSA_ACCEL_&/g' )"
+    make CFLAGS="$ASAN_CFLAGS -O -Werror -I../tests/include -I../tests -DPSA_CRYPTO_DRIVER_TEST -DMBEDTLS_TEST_LIBTESTDRIVER1 $loc_accel_flags" LDFLAGS="-ltestdriver1 $ASAN_CFLAGS"
+
+    unset loc_accel_flags
+    unset loc_accel_list
+
+    if_build_succeeded not grep mbedtls_ecdsa_ library/ecdsa.o
+
+    msg "test: MBEDTLS_PSA_CRYPTO_CONFIG with accelerated ECDSA"
+    make test
+}
+
+component_test_psa_crypto_config_accel_rsa_signature () {
+    msg "test: MBEDTLS_PSA_CRYPTO_CONFIG with accelerated RSA signature"
+
+    # Disable ALG_STREAM_CIPHER and ALG_ECB_NO_PADDING to avoid having
+    # partial support for cipher operations in the driver test library.
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_STREAM_CIPHER
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_ECB_NO_PADDING
+
+    # It seems it is not possible to remove only the support for RSA signature
+    # in the library. Thus we have to remove all RSA support (signature and
+    # encryption/decryption). AS there is no driver support for asymmetric
+    # encryption/decryption so far remove RSA encryption/decryption from the
+    # application algorithm list.
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_RSA_OAEP
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
+
+    # Make sure both the library and the test library support the SHA hash
+    # algorithms and only those ones (SHA256 is included by default). That way:
+    # - the test library can compute the RSA signatures even in the case of a
+    #   composite RSA signature algorithm based on a SHA hash (no other hash
+    #   used in the unit tests).
+    # - the dependency of RSA signature tests on PSA_WANT_ALG_SHA_xyz is
+    #   fulfilled as the hash SHA algorithm is supported by the library, and
+    #   thus the tests are run, not skipped.
+    # - when testing a signature key with an algorithm wildcard built from
+    #   PSA_ALG_ANY_HASH as algorithm to test with the key, the chosen hash
+    #   algorithm based on the hashes supported by the library is also
+    #   supported by the test library.
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_MD2
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_MD4
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_MD5
+    scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_RIPEMD160_C
+
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h set MBEDTLS_SHA1_C
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h set MBEDTLS_SHA512_C
+    # We need PEM parsing in the test library as well to support the import
+    # of PEM encoded RSA keys.
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h set MBEDTLS_PEM_PARSE_C
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h set MBEDTLS_BASE64_C
+
+    loc_accel_list="ALG_RSA_PKCS1V15_SIGN ALG_RSA_PSS KEY_TYPE_RSA_KEY_PAIR KEY_TYPE_RSA_PUBLIC_KEY"
+    loc_accel_flags=$( echo "$loc_accel_list" | sed 's/[^ ]* */-DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_&/g' )
+    make -C tests libtestdriver1.a CFLAGS="$ASAN_CFLAGS $loc_accel_flags" LDFLAGS="$ASAN_CFLAGS"
+
+    # Restore test driver base configuration
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h unset MBEDTLS_SHA1_C
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h unset MBEDTLS_SHA512_C
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h unset MBEDTLS_PEM_PARSE_C
+    scripts/config.py -f tests/include/test/drivers/config_test_driver.h unset MBEDTLS_BASE64_C
+
+
+    # Mbed TLS library build
+    scripts/config.py set MBEDTLS_PSA_CRYPTO_DRIVERS
+    scripts/config.py set MBEDTLS_PSA_CRYPTO_CONFIG
+
+    # Remove RSA support and its dependencies
+    scripts/config.py unset MBEDTLS_PKCS1_V15
+    scripts/config.py unset MBEDTLS_PKCS1_V21
+    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_DHE_RSA_ENABLED
+    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_ECDH_RSA_ENABLED
+    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_ECDHE_RSA_ENABLED
+    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_RSA_PSK_ENABLED
+    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_RSA_ENABLED
+    scripts/config.py unset MBEDTLS_RSA_C
+    scripts/config.py unset MBEDTLS_X509_RSASSA_PSS_SUPPORT
+
+    scripts/config.py unset MBEDTLS_MD2_C
+    scripts/config.py unset MBEDTLS_MD4_C
+    scripts/config.py unset MBEDTLS_MD5_C
+    scripts/config.py unset MBEDTLS_RIPEMD160_C
+    scripts/config.py unset MBEDTLS_SSL_PROTO_TLS1
+    scripts/config.py unset MBEDTLS_SSL_PROTO_TLS1_1
+    scripts/config.py unset MBEDTLS_SSL_CBC_RECORD_SPLITTING
+
+    loc_accel_flags="$loc_accel_flags $( echo "$loc_accel_list" | sed 's/[^ ]* */-DMBEDTLS_PSA_ACCEL_&/g' )"
+    make CFLAGS="$ASAN_CFLAGS -Werror -I../tests/include -I../tests -DPSA_CRYPTO_DRIVER_TEST -DMBEDTLS_TEST_LIBTESTDRIVER1 $loc_accel_flags" LDFLAGS="-ltestdriver1 $ASAN_CFLAGS"
+
+    unset loc_accel_flags
+    unset loc_accel_list
+
+    if_build_succeeded not grep mbedtls_rsa_rsassa_pkcs1_v15_sign library/rsa.o
+    if_build_succeeded not grep mbedtls_rsa_rsassa_pss_sign_ext library/rsa.o
+
+    msg "test: MBEDTLS_PSA_CRYPTO_CONFIG with accelerated RSA signature"
+    make test
+}
+
 component_test_psa_crypto_config_no_driver() {
     # full plus MBEDTLS_PSA_CRYPTO_CONFIG
     msg "build: full + MBEDTLS_PSA_CRYPTO_CONFIG minus MBEDTLS_PSA_CRYPTO_DRIVERS"