diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index a5fb4c712b..5d7e97b90f 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -7294,6 +7294,83 @@ PSA (raw) key agreement: X25519 (RFC 7748: Bob)
 depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
 key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a":"4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742":PSA_SUCCESS
 
+# RFC 7748 says we need clip the input to 255 bits, see decodeUCoordinate().
+# Check we indeed do that: same inputs as above except the MSB is set in the
+# peer's public key (little endian, so that's the MSB of the last byte).
+PSA (raw) key agreement: X25519 (RFC 7748: Alice with MSB set)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a":"de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882bcf":"4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742":PSA_SUCCESS
+
+PSA (raw) key agreement: X25519 (RFC 7748: Bob with MSB set)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4eea":"4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742":PSA_SUCCESS
+
+# BEGIN list from https://cr.yp.to/ecdh.html#validate
+PSA (raw) key agreement: X25519 (peer key is 0)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"0000000000000000000000000000000000000000000000000000000000000000":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X25519 (peer key is 1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"0100000000000000000000000000000000000000000000000000000000000000":"":PSA_ERROR_INVALID_ARGUMENT
+
+# this is x25519_bad_point_1 in ecp.c
+PSA (raw) key agreement: X25519 (peer key is bad_point_1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"e0eb7a7c3b41b8ae1656e3faf19fc46ada098deb9c32b1fd866205165f49b800":"":PSA_ERROR_INVALID_ARGUMENT
+
+# this is x25519_bad_point_2 in ecp.c
+PSA (raw) key agreement: X25519 (peer key is bad_point_2)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"5f9c95bca3508c24b1d0b1559c83ef5b04445cc4581c8e86d8224eddd09f1157":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X25519 (peer key is p-1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X25519 (peer key is p)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X25519 (peer key is p+1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"eeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f":"":PSA_ERROR_INVALID_ARGUMENT
+# END list from https://cr.yp.to/ecdh.html#validate
+# Further values in that list are larger that 2^255, and per RFC 7748
+# we clip the input to 255 bits, that is, set bit 255 to zero.
+# So, what's actually useful to test is 2^255 + x (aka x | (1 << 255))
+# where x is any of the values above. (Reminder: little-endian.)
+
+PSA (raw) key agreement: X25519 (peer key is 2^255 + 0)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"0000000000000000000000000000000000000000000000000000000000000080":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X25519 (peer key is 2^255 + 1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"0100000000000000000000000000000000000000000000000000000000000080":"":PSA_ERROR_INVALID_ARGUMENT
+
+# this is x25519_bad_point_1 in ecp.c
+PSA (raw) key agreement: X25519 (peer key is 2^255 + bad_point_1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"e0eb7a7c3b41b8ae1656e3faf19fc46ada098deb9c32b1fd866205165f49b880":"":PSA_ERROR_INVALID_ARGUMENT
+
+# this is x25519_bad_point_2 in ecp.c
+PSA (raw) key agreement: X25519 (peer key is 2^255 + bad_point_2)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"5f9c95bca3508c24b1d0b1559c83ef5b04445cc4581c8e86d8224eddd09f11d7":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X25519 (peer key is 2^255 + p-1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X25519 (peer key is 2^255 + p)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X25519 (peer key is 2^255 + p+1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb":"eeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff":"":PSA_ERROR_INVALID_ARGUMENT
+
 # see generating script in commit message
 PSA (raw) key agreement: X25519 (shared secret with MSB 0)
 depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_255
@@ -7307,6 +7384,29 @@ PSA (raw) key agreement: X448 (RFC 7748: Bob)
 depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_448
 key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d":"9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0":"07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d":PSA_SUCCESS
 
+# curve448 only has 4 low-order points, whose X coordinates are 0, 1, -1.
+# https://elligator.org/formulas -> search "Curve 448 has 4 low order points"
+# Since the input is 448-bit, test 0, 1, p-1, p (= 0 mod p), p+1 (= 1 mod p).
+PSA (raw) key agreement: X448 (RFC 7748: peer key is 0)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_448
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d":"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X448 (RFC 7748: peer key is 1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_448
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d":"0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X448 (RFC 7748: peer key is p-1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_448
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d":"fefffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X448 (RFC 7748: peer key is p)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_448
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d":"fffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff":"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA (raw) key agreement: X448 (RFC 7748: peer key is p+1)
+depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_448
+key_agreement:PSA_ALG_ECDH:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_MONTGOMERY):"1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d":"00000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff":"":PSA_ERROR_INVALID_ARGUMENT
+
 # see generating script in commit message
 PSA (raw) key agreement: X448 (shared secret with MSB 0)
 depends_on:PSA_WANT_ALG_ECDH:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_MONTGOMERY_448