diff --git a/src/libopensc/pkcs15-algo.c b/src/libopensc/pkcs15-algo.c
index 6e47c0b3..39539b36 100644
--- a/src/libopensc/pkcs15-algo.c
+++ b/src/libopensc/pkcs15-algo.c
@@ -450,11 +450,13 @@ static struct sc_asn1_pkcs15_algorithm_info algorithm_table[] = {
 #endif
 #ifdef SC_ALGORITHM_EDDSA
 	/* aka Ed25519 */
-	{ SC_ALGORITHM_EDDSA, {{1, 3, 6, 1, 4, 1, 11591, 15, 1, -1}}, NULL, NULL, NULL },
+	/* RFC 8410, needed to parse/create X509 certs/pubkeys */
+	{ SC_ALGORITHM_EDDSA, {{1, 3, 101, 112, -1}}, NULL, NULL, NULL },
 #endif
 #ifdef SC_ALGORITHM_XEDDSA
 	/* aka curve25519 */
-	{ SC_ALGORITHM_XEDDSA, {{1, 3, 6, 1, 4, 1, 3029, 1, 5, 1, -1}}, NULL, NULL, NULL },
+	/* RFC 8410, needed to parse/create X509 certs/pubkeys */
+	{ SC_ALGORITHM_XEDDSA, {{1, 3, 101, 110, -1}}, NULL, NULL, NULL },
 #endif
 	{ -1, {{ -1 }}, NULL, NULL, NULL }
 };
@@ -552,7 +554,11 @@ sc_asn1_encode_algorithm_id(struct sc_context *ctx, u8 **buf, size_t *len,
 	sc_format_asn1_entry(asn1_alg_id + 0, (void *) &id->oid, NULL, 1);
 
 	/* no parameters, write NULL tag */
-	if (!id->params || !alg_info->encode)
+	/* If it's EDDSA/XEDDSA, according to RFC8410, params
+	 * MUST be absent */
+	if (id->algorithm != SC_ALGORITHM_EDDSA &&
+	    id->algorithm != SC_ALGORITHM_XEDDSA &&
+	    (!id->params || !alg_info->encode))
 		asn1_alg_id[1].flags |= SC_ASN1_PRESENT;
 
 	r = _sc_asn1_encode(ctx, asn1_alg_id, buf, len, depth + 1);
diff --git a/src/libopensc/pkcs15-pubkey.c b/src/libopensc/pkcs15-pubkey.c
index e6a9e743..ac8fda7b 100644
--- a/src/libopensc/pkcs15-pubkey.c
+++ b/src/libopensc/pkcs15-pubkey.c
@@ -912,6 +912,14 @@ sc_pkcs15_encode_pubkey_as_spki(sc_context_t *ctx, struct sc_pkcs15_pubkey *pubk
 		r = sc_pkcs15_encode_pubkey(ctx, pubkey, &pkey.value, &pkey.len);
 		key_len = pkey.len * 8;
 		break;
+	case SC_ALGORITHM_EDDSA:
+	case SC_ALGORITHM_XEDDSA:
+		/* For a SPKI, the pubkey is placed directly in the BIT STRING */
+		pkey.value = malloc(pubkey->u.eddsa.pubkey.len);
+		memcpy(pkey.value, pubkey->u.eddsa.pubkey.value, pubkey->u.eddsa.pubkey.len);
+		// Should be pkey.len = 0 there?
+		key_len = pubkey->u.eddsa.pubkey.len * 8;
+		break;
 	default:
 		r = sc_pkcs15_encode_pubkey(ctx, pubkey, &pkey.value, &pkey.len);
 		key_len = pkey.len * 8;
@@ -1507,6 +1515,12 @@ sc_pkcs15_pubkey_from_spki_fields(struct sc_context *ctx, struct sc_pkcs15_pubke
 		}
 		memcpy(pubkey->u.ec.ecpointQ.value, pk.value, pk.len);
 		pubkey->u.ec.ecpointQ.len = pk.len;
+	} else if (pk_alg.algorithm == SC_ALGORITHM_EDDSA ||
+		   pk_alg.algorithm == SC_ALGORITHM_XEDDSA) {
+		/* EDDSA/XEDDSA public key is not encapsulated into BIT STRING -- it's a BIT STRING */
+		pubkey->u.eddsa.pubkey.value = malloc(pk.len);
+		memcpy(pubkey->u.eddsa.pubkey.value, pk.value, pk.len);
+		pubkey->u.eddsa.pubkey.len = pk.len;
 	} else {
 		/* Public key is expected to be encapsulated into BIT STRING */
 		r = sc_pkcs15_decode_pubkey(ctx, pubkey, pk.value, pk.len);