Hello all,

I want to use mbedtls-functions for "Shared Secret" according ECDH with C448. First I want to check the test vectors mentioned in RFC7748 (chapter 6.2).

But it fails in function mbedtls_ecdh_compute_shared(...) with return value -0x4C80 MBEDTLS_ERR_ECP_INVALID_KEY (please see code below)

But up to now I can't find the root cause. Is there a similar example available?

Regards, Tom

// Alice's private key static const unsigned char alice_private_key[] = { 0x77, 0x07, 0x6d, 0x0a, 0x73, 0x18, 0xa5, 0x7d, 0x3c, 0x16, 0xc1, 0x72, 0x51, 0xb2, 0x66, 0x45, 0xdf, 0x4c, 0x2f, 0x87, 0xeb, 0xc0, 0x99, 0x2a, 0xb1, 0x77, 0xfb, 0xa5, 0x1d, 0xb9, 0x2c, 0x2a };

// Bob's private key static const unsigned char bob_private_key[] = { 0x5d, 0xab, 0x08, 0x7e, 0x62, 0x4a, 0x8a, 0x4b, 0x79, 0xe1, 0x7f, 0x8b, 0x83, 0x80, 0x0e, 0xe6, 0x6f, 0x3b, 0xb1, 0x29, 0x26, 0x18, 0xb6, 0xfd, 0x1c, 0x2f, 0x8b, 0x27, 0xff, 0x88, 0xe0, 0xeb };

int main() { mbedtls_ecdh_context ecdh; unsigned char shared_secret[32]; size_t olen; int ret;

mbedtls_ecdh_init(&ecdh);

// Load Bob's private key ret = mbedtls_ecp_group_load(&ecdh.grp, MBEDTLS_ECP_DP_CURVE25519); if (ret != 0) { printf("Failed to load group\n"); return 1; }

ret = mbedtls_mpi_read_binary(&ecdh.d, bob_private_key, sizeof(bob_private_key)); if (ret != 0) { printf("Failed to read private key\n"); return 1; }

// Compute the shared secret ret = mbedtls_ecdh_compute_shared(&ecdh.grp, &ecdh.z, &ecdh.Qp, &ecdh.d, mbedtls_ctr_drbg_random, NULL); if (ret != 0) { printf("Failed to compute shared secret\n"); return 1; } ...

Test vector:

Alice's private key, a: 9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28d d9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b Alice's public key, X448(a, 5): 9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c 22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0 Bob's private key, b: 1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d 6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d Bob's public key, X448(b, 5): 3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b430 27d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609 Their shared secret, K: 07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282b b60c0b56fd2464c335543936521c24403085d59a449a5037514a879d