diff --git a/crypto/ec_extra/ec_asn1.c b/crypto/ec_extra/ec_asn1.c
index 31988f3..9769d01 100644
--- a/crypto/ec_extra/ec_asn1.c
+++ b/crypto/ec_extra/ec_asn1.c
@@ -264,7 +264,8 @@
                                       CBS *out_base_y, CBS *out_order) {
   // See RFC 3279, section 2.3.5. Note that RFC 3279 calls this structure an
   // ECParameters while RFC 5480 calls it a SpecifiedECDomain.
-  CBS params, field_id, field_type, curve, base;
+  CBS params, field_id, field_type, curve, base, cofactor;
+  int has_cofactor;
   uint64_t version;
   if (!CBS_get_asn1(in, &params, CBS_ASN1_SEQUENCE) ||
       !CBS_get_asn1_uint64(&params, &version) ||
@@ -272,7 +273,8 @@
       !CBS_get_asn1(&params, &field_id, CBS_ASN1_SEQUENCE) ||
       !CBS_get_asn1(&field_id, &field_type, CBS_ASN1_OBJECT) ||
       CBS_len(&field_type) != sizeof(kPrimeField) ||
-      OPENSSL_memcmp(CBS_data(&field_type), kPrimeField, sizeof(kPrimeField)) != 0 ||
+      OPENSSL_memcmp(CBS_data(&field_type), kPrimeField, sizeof(kPrimeField)) !=
+          0 ||
       !CBS_get_asn1(&field_id, out_prime, CBS_ASN1_INTEGER) ||
       !is_unsigned_integer(out_prime) ||
       CBS_len(&field_id) != 0 ||
@@ -280,16 +282,26 @@
       !CBS_get_asn1(&curve, out_a, CBS_ASN1_OCTETSTRING) ||
       !CBS_get_asn1(&curve, out_b, CBS_ASN1_OCTETSTRING) ||
       // |curve| has an optional BIT STRING seed which we ignore.
+      !CBS_get_optional_asn1(&curve, NULL, NULL, CBS_ASN1_BITSTRING) ||
+      CBS_len(&curve) != 0 ||
       !CBS_get_asn1(&params, &base, CBS_ASN1_OCTETSTRING) ||
       !CBS_get_asn1(&params, out_order, CBS_ASN1_INTEGER) ||
-      !is_unsigned_integer(out_order)) {
+      !is_unsigned_integer(out_order) ||
+      !CBS_get_optional_asn1(&params, &cofactor, &has_cofactor,
+                             CBS_ASN1_INTEGER) ||
+      CBS_len(&params) != 0) {
     OPENSSL_PUT_ERROR(EC, EC_R_DECODE_ERROR);
     return 0;
   }
 
-  // |params| has an optional cofactor which we ignore. With the optional seed
-  // in |curve|, a group already has arbitrarily many encodings. Parse enough to
-  // uniquely determine the curve.
+  if (has_cofactor) {
+    // We only support prime-order curves so the cofactor must be one.
+    if (CBS_len(&cofactor) != 1 ||
+        CBS_data(&cofactor)[0] != 1) {
+      OPENSSL_PUT_ERROR(EC, EC_R_UNKNOWN_GROUP);
+      return 0;
+    }
+  }
 
   // Require that the base point use uncompressed form.
   uint8_t form;
diff --git a/crypto/evp/evp_tests.txt b/crypto/evp/evp_tests.txt
index 2ac51d3..0c890fd 100644
--- a/crypto/evp/evp_tests.txt
+++ b/crypto/evp/evp_tests.txt
@@ -73,6 +73,32 @@
 Input = 308190020100301306072a8648ce3d020106082a8648ce3d0301070476307402010104208a872fb62893c4d1ffc5b9f0f91758069f8352e08fa05a49f8db926cb5728725a00706052b81040022a144034200042c150f429ce70f216c252cf5e062ce1f639cd5d165c7f89424072c27197d78b33b920e95cdb664e990dcf0cfea0d94e2a8e6af9d0e58056e653104925b9fe6c9
 Error = GROUP_MISMATCH
 
+# The same key, but with the curve spelled explicitly.
+PrivateKey = P-256-ExplicitParameters
+Type = EC
+Input = 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
+Output = 308187020100301306072a8648ce3d020106082a8648ce3d030107046d306b02010104208a872fb62893c4d1ffc5b9f0f91758069f8352e08fa05a49f8db926cb5728725a144034200042c150f429ce70f216c252cf5e062ce1f639cd5d165c7f89424072c27197d78b33b920e95cdb664e990dcf0cfea0d94e2a8e6af9d0e58056e653104925b9fe6c9
+ExpectNoRawPrivate
+ExpectNoRawPublic
+
+# The same as above, but with the optional cofactor omitted.
+PrivateKey = P-256-ExplicitParameters-NoCofactor
+Type = EC
+Input = 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
+Output = 308187020100301306072a8648ce3d020106082a8648ce3d030107046d306b02010104208a872fb62893c4d1ffc5b9f0f91758069f8352e08fa05a49f8db926cb5728725a144034200042c150f429ce70f216c252cf5e062ce1f639cd5d165c7f89424072c27197d78b33b920e95cdb664e990dcf0cfea0d94e2a8e6af9d0e58056e653104925b9fe6c9
+ExpectNoRawPrivate
+ExpectNoRawPublic
+
+# The same as above, but the cofactor is zero instead of one.
+PrivateKey = P-256-ExplicitParameters-CofactorZero
+Input = 308201610201003081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d0101022100ffffffff00000001000000000000000000000000ffffffffffffffffffffffff30440420ffffffff00000001000000000000000000000000fffffffffffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551020100046d306b02010104208a872fb62893c4d1ffc5b9f0f91758069f8352e08fa05a49f8db926cb5728725a144034200042c150f429ce70f216c252cf5e062ce1f639cd5d165c7f89424072c27197d78b33b920e95cdb664e990dcf0cfea0d94e2a8e6af9d0e58056e653104925b9fe6c9
+Error = UNKNOWN_GROUP
+
+# The same as above, but the cofactor is two instead of one.
+PrivateKey = P-256-ExplicitParameters-CofactorTwo
+Input = 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
+Error = UNKNOWN_GROUP
+
 # The public half of the same key encoded as a PublicKey.
 PublicKey = P-256-SPKI
 Type = EC