Curves Extension and the Supported Point Formats Extension.
When these extensions are sent:
The extensions SHOULD be sent along with any ClientHello message that
proposes ECC cipher suites.
Meaning of these extensions:
These extensions allow a client to enumerate the elliptic curves it
supports and/or the point formats it can parse.
Structure of these extensions:
The general structure of TLS extensions is described in [4], and this
specification adds two new types to ExtensionType.
enum { elliptic_curves(10), ec_point_formats(11) } ExtensionType;
elliptic_curves (Supported Elliptic Curves Extension): Indicates
the set of elliptic curves supported by the client. For this
extension, the opaque extension_data field contains
EllipticCurveList. See Section 5.1.1 for details.
ec_point_formats (Supported Point Formats Extension): Indicates the
set of point formats that the client can parse. For this
extension, the opaque extension_data field contains
ECPointFormatList. See Section 5.1.2 for details.
Actions of the sender:
A client that proposes ECC cipher suites in its ClientHello message
appends these extensions (along with any others), enumerating the
curves it supports and the point formats it can parse. Clients
SHOULD send both the Supported Elliptic Curves Extension and the
Supported Point Formats Extension. If the Supported Point Formats
Extension is indeed sent, it MUST contain the value 0 (uncompressed)
as one of the items in the list of point formats.
Actions of the receiver:
A server that receives a ClientHello containing one or both of these
extensions MUST use the client’s enumerated capabilities to guide its
selection of an appropriate cipher suite. One of the proposed ECC
cipher suites must be negotiated only if the server can successfully
complete the handshake while using the curves and point formats
supported by the client (cf. Sections 5.3 and 5.4).
NOTE: A server participating in an ECDHE-ECDSA key exchange may use
different curves for (i) the ECDSA key in its certificate, and (ii)
the ephemeral ECDH key in the ServerKeyExchange message. The server
must consider the extensions in both cases.
If a server does not understand the Supported Elliptic Curves
Extension, does not understand the Supported Point Formats Extension,
or is unable to complete the ECC handshake while restricting itself
to the enumerated curves and point formats, it MUST NOT negotiate the
use of an ECC cipher suite. Depending on what other cipher suites
are proposed by the client and supported by the server, this may
result in a fatal handshake failure alert due to the lack of common
cipher suites.
5.1.1. Supported Elliptic Curves Extension
enum {
sect163k1 (1), sect163r1 (2), sect163r2 (3),
sect193r1 (4), sect193r2 (5), sect233k1 (6),
sect233r1 (7), sect239k1 (8), sect283k1 (9),
sect283r1 (10), sect409k1 (11), sect409r1 (12),
sect571k1 (13), sect571r1 (14), secp160k1 (15),
secp160r1 (16), secp160r2 (17), secp192k1 (18),
secp192r1 (19), secp224k1 (20), secp224r1 (21),
secp256k1 (22), secp256r1 (23), secp384r1 (24),
secp521r1 (25),
reserved (0xFE00..0xFEFF),
arbitrary_explicit_prime_curves(0xFF01),
arbitrary_explicit_char2_curves(0xFF02),
(0xFFFF)
} NamedCurve;
sect163k1, etc: Indicates support of the corresponding named curve
or class of explicitly defined curves. The named curves defined
here are those specified in SEC 2 [13]. Note that many of these
curves are also recommended in ANSI X9.62 [7] and FIPS 186-2 [11].
Values 0xFE00 through 0xFEFF are reserved for private use. Values
0xFF01 and 0xFF02 indicate that the client supports arbitrary
prime and characteristic-2 curves, respectively (the curve
parameters must be encoded explicitly in ECParameters).
The NamedCurve name space is maintained by IANA. See Section 8 for
information on how new value assignments are added.
struct {
NamedCurve elliptic_curve_list<1..2^16-1>
} EllipticCurveList;
Items in elliptic_curve_list are ordered according to the client’s
preferences (favorite choice first).
As an example, a client that only supports secp192r1 (aka NIST P-192;
value 19 = 0x0013) and secp224r1 (aka NIST P-224; value 21 = 0x0015)
and prefers to use secp192r1 would include a TLS extension consisting
of the following octets. Note that the first two octets indicate the
extension type (Supported Elliptic Curves Extension):
00 0A 00 06 00 04 00 13 00 15
A client that supports arbitrary explicit characteristic-2 curves
(value 0xFF02) would include an extension consisting of the following
octets:
00 0A 00 04 00 02 FF 02
5.1.2. Supported Point Formats Extension
enum { uncompressed (0), ansiX962_compressed_prime (1),
ansiX962_compressed_char2 (2), reserved (248..255)
} ECPointFormat;
struct {
ECPointFormat ec_point_format_list<1..2^8-1>
} ECPointFormatList;
Three point formats are included in the definition of ECPointFormat
above. The uncompressed point format is the default format in that
implementations of this document MUST support it for all of their
supported curves. Compressed point formats reduce bandwidth by
including only the x-coordinate and a single bit of the y-coordinate
of the point. Implementations of this document MAY support the
ansiX962_compressed_prime and ansiX962_compressed_char2 formats,
where the former applies only to prime curves and the latter applies
only to characteristic-2 curves. (These formats are specified in
[7].) Values 248 through 255 are reserved for private use.
The ECPointFormat name space is maintained by IANA. See Section 8
for information on how new value assignments are added.
Items in ec_point_format_list are ordered according to the client’s
preferences (favorite choice first).
A client that can parse only the uncompressed point format (value 0)
includes an extension consisting of the following octets; note that
the first two octets indicate the extension type (Supported Point
Formats Extension):
00 0B 00 02 01 00
A client that in the case of prime fields prefers the compressed
format (ansiX962_compressed_prime, value 1) over the uncompressed
format (value 0), but in the case of characteristic-2 fields prefers
the uncompressed format (value 0) over the compressed format
(ansiX962_compressed_char2, value 2), may indicate these preferences
by including an extension consisting of the following octets:
00 0B 00 04 03 01 00 02
5.2. Server Hello Extension
This section specifies a TLS extension that can be included with the
ServerHello message as described in [4], the Supported Point Formats
Extension.
When this extension is sent:
The Supported Point Formats Extension is included in a ServerHello
message in response to a ClientHello message containing the Supported
Point Formats Extension when negotiating an ECC cipher suite.
Meaning of this extension:
This extension allows a server to enumerate the point formats it can
parse (for the curve that will appear in its ServerKeyExchange
message when using the ECDHE_ECDSA, ECDHE_RSA, or ECDH_anon key
exchange algorithm, or for the curve that is used in the server’s
public key that will appear in its Certificate message when using the
ECDH_ECDSA or ECDH_RSA key exchange algorithm).
Structure of this extension:
The server’s Supported Point Formats Extension has the same structure
as the client’s Supported Point Formats Extension (see
Section 5.1.2). Items in elliptic_curve_list here are ordered
according to the server’s preference (favorite choice first). Note
that the server may include items that were not found in the client’s
list (e.g., the server may prefer to receive points in compressed
format even when a client cannot parse this format: the same client
may nevertheless be capable of outputting points in compressed
format).
Actions of the sender:
A server that selects an ECC cipher suite in response to a
ClientHello message including a Supported Point Formats Extension
appends this extension (along with others) to its ServerHello
message, enumerating the point formats it can parse. The Supported
Point Formats Extension, when used, MUST contain the value 0
(uncompressed) as one of the items in the list of point formats.
Actions of the receiver:
A client that receives a ServerHello message containing a Supported
Point Formats Extension MUST respect the server’s choice of point
formats during the handshake (cf. Sections 5.6 and 5.7). If no
Supported Point Formats Extension is received with the ServerHello,
this is equivalent to an extension allowing only the uncompressed
point format.
5.3. Server Certificate
When this message is sent:
This message is sent in all non-anonymous ECC-based key exchange
algorithms.
Meaning of this message:
This message is used to authentically convey the server’s static
public key to the client. The following table shows the server
certificate type appropriate for each key exchange algorithm. ECC
public keys MUST be encoded in certificates as described in
Section 5.9.
NOTE: The server’s Certificate message is capable of carrying a chain
of certificates. The restrictions mentioned in Table 3 apply only to
the server’s certificate (first in the chain).
Key Exchange Algorithm Server Certificate Type
---------------------- -----------------------
ECDH_ECDSA Certificate MUST contain an
ECDH-capable public key. It
MUST be signed with ECDSA.
ECDHE_ECDSA Certificate MUST contain an
ECDSA-capable public key. It
MUST be signed with ECDSA.
ECDH_RSA Certificate MUST contain an
ECDH-capable public key. It
MUST be signed with RSA.
ECDHE_RSA Certificate MUST contain an
RSA public key authorized for
use in digital signatures. It
MUST be signed with RSA.
Table 3: Server Certificate Types
Structure of this message:
Identical to the TLS Certificate format.
Actions of the sender:
The server constructs an appropriate certificate chain and conveys it
to the client in the Certificate message. If the client has used a
Supported Elliptic Curves Extension, the public key in the server’s
certificate MUST respect the client’s choice of elliptic curves; in
particular, the public key MUST employ a named curve (not the same
curve as an explicit curve) unless the client has indicated support
for explicit curves of the appropriate type. If the client has used
a Supported Point Formats Extension, both the server’s public key
point and (in the case of an explicit curve) the curve’s base point
MUST respect the client’s choice of point formats. (A server that
cannot satisfy these requirements MUST NOT choose an ECC cipher suite
in its ServerHello message.)
Actions of the receiver:
The client validates the certificate chain, extracts the server’s
public key, and checks that the key type is appropriate for the
negotiated key exchange algorithm. (A possible reason for a fatal
handshake failure is that the client’s capabilities for handling
elliptic curves and point formats are exceeded; cf. Section 5.1.)
5.4. Server Key Exchange
When this message is sent:
This message is sent when using the ECDHE_ECDSA, ECDHE_RSA, and
ECDH_anon key exchange algorithms.
Meaning of this message:
This message is used to convey the server’s ephemeral ECDH public key
(and the corresponding elliptic curve domain parameters) to the
client.
Structure of this message:
enum { explicit_prime (1), explicit_char2 (2),
named_curve (3), reserved(248..255) } ECCurveType;
explicit_prime: Indicates the elliptic curve domain parameters are
conveyed verbosely, and the underlying finite field is a prime
field.
explicit_char2: Indicates the elliptic curve domain parameters are
conveyed verbosely, and the underlying finite field is a
characteristic-2 field.
named_curve: Indicates that a named curve is used. This option
SHOULD be used when applicable.
Values 248 through 255 are reserved for private use.
The ECCurveType name space is maintained by IANA. See Section 8 for
information on how new value assignments are added.
struct {
opaque a <1..2^8-1>;
opaque b <1..2^8-1>;
} ECCurve;
a, b: These parameters specify the coefficients of the elliptic
curve. Each value contains the byte string representation of a
field element following the conversion routine in Section 4.3.3 of
ANSI X9.62 [7].
struct {
opaque point <1..2^8-1>;
} ECPoint;
point: This is the byte string representation of an elliptic curve
point following the conversion routine in Section 4.3.6 of ANSI
X9.62 [7]. This byte string may represent an elliptic curve point
in uncompressed or compressed format; it MUST conform to what the
client has requested through a Supported Point Formats Extension
if this extension was used.
enum { ec_basis_trinomial, ec_basis_pentanomial } ECBasisType;
ec_basis_trinomial: Indicates representation of a characteristic-2
field using a trinomial basis.
ec_basis_pentanomial: Indicates representation of a
characteristic-2 field using a pentanomial basis.
struct {
ECCurveType curve_type;
select (curve_type) {
case explicit_prime:
opaque prime_p <1..2^8-1>;
ECCurve curve;
ECPoint base;
opaque order <1..2^8-1>;
opaque cofactor <1..2^8-1>;
case explicit_char2:
uint16 m;
ECBasisType basis;
select (basis) {
case ec_trinomial:
opaque k <1..2^8-1>;
case ec_pentanomial:
opaque k1 <1..2^8-1>;
opaque k2 <1..2^8-1>;
opaque k3 <1..2^8-1>;
};
ECCurve curve;
ECPoint base;
opaque order <1..2^8-1>;
opaque cofactor <1..2^8-1>;
case named_curve:
NamedCurve namedcurve;
};
} ECParameters;
curve_type: This identifies the type of the elliptic curve domain
parameters.
prime_p: This is the odd prime defining the field Fp.
curve: Specifies the coefficients a and b of the elliptic curve E.
base: Specifies the base point G on the elliptic curve.
order: Specifies the order n of the base point.
cofactor: Specifies the cofactor h = #E(Fq)/n, where #E(Fq)
represents the number of points on the elliptic curve E defined
over the field Fq (either Fp or F2^m).
m: This is the degree of the characteristic-2 field F2^m.
k: The exponent k for the trinomial basis representation x^m + x^k
+1.
k1, k2, k3: The exponents for the pentanomial representation x^m +
x^k3 + x^k2 + x^k1 + 1 (such that k3 > k2 > k1).
namedcurve: Specifies a recommended set of elliptic curve domain
parameters. All those values of NamedCurve are allowed that refer
to a specific curve. Values of NamedCurve that indicate support
for a class of explicitly defined curves are not allowed here
(they are only permissible in the ClientHello extension); this
applies to arbitrary_explicit_prime_curves(0xFF01) and
arbitrary_explicit_char2_curves(0xFF02).
struct {
ECParameters curve_params;
ECPoint public;
} ServerECDHParams;
curve_params: Specifies the elliptic curve domain parameters
associated with the ECDH public key.
public: The ephemeral ECDH public key.
The ServerKeyExchange message is extended as follows.
enum { ec_diffie_hellman } KeyExchangeAlgorithm;
ec_diffie_hellman: Indicates the ServerKeyExchange message contains
an ECDH public key.
select (KeyExchangeAlgorithm) {
case ec_diffie_hellman:
ServerECDHParams params;
Signature signed_params;
} ServerKeyExchange;
params: Specifies the ECDH public key and associated domain
parameters.
signed_params: A hash of the params, with the signature appropriate
to that hash applied. The private key corresponding to the
certified public key in the server’s Certificate message is used
for signing.
enum { ecdsa } SignatureAlgorithm;
select (SignatureAlgorithm) {
case ecdsa:
digitally-signed struct {
opaque sha_hash[sha_size];
};
} Signature;
ServerKeyExchange.signed_params.sha_hash
SHA(ClientHello.random + ServerHello.random +
ServerKeyExchange.params);
NOTE: SignatureAlgorithm is "rsa" for the ECDHE_RSA key exchange
algorithm and "anonymous" for ECDH_anon. These cases are defined in
TLS [2][3]. SignatureAlgorithm is "ecdsa" for ECDHE_ECDSA. ECDSA
signatures are generated and verified as described in Section 5.10,
and SHA in the above template for sha_hash accordingly may denote a
hash algorithm other than SHA-1. As per ANSI X9.62, an ECDSA
signature consists of a pair of integers, r and s. The digitally-
signed element is encoded as an opaque vector <0..2^16-1>, the
contents of which are the DER encoding [9] corresponding to the
following ASN.1 notation [8].
Ecdsa-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER
}
Actions of the sender:
The server selects elliptic curve domain parameters and an ephemeral
ECDH public key corresponding to these parameters according to the
ECKAS-DH1 scheme from IEEE 1363 [6]. It conveys this information to
the client in the ServerKeyExchange message using the format defined
above.
Actions of the receiver:
The client verifies the signature (when present) and retrieves the
server’s elliptic curve domain parameters and ephemeral ECDH public
key from the ServerKeyExchange message. (A possible reason for a
fatal handshake failure is that the client’s capabilities for
handling elliptic curves and point formats are exceeded;
cf. Section 5.1.)
5.5. Certificate Request
When this message is sent:
This message is sent when requesting client authentication.
Meaning of this message:
The server uses this message to suggest acceptable client
authentication methods.
Structure of this message:
The TLS CertificateRequest message is extended as follows.
enum {
ecdsa_sign(64), rsa_fixed_ecdh(65),
ecdsa_fixed_ecdh(66), (255)
} ClientCertificateType;
ecdsa_sign, etc. Indicates that the server would like to use the
corresponding client authentication method specified in Section 3.
Actions of the sender:
The server decides which client authentication methods it would like
to use, and conveys this information to the client using the format
defined above.
Actions of the receiver:
The client determines whether it has a suitable certificate for use
with any of the requested methods and whether to proceed with client
authentication.
5.6. Client Certificate
When this message is sent:
This message is sent in response to a CertificateRequest when a
client has a suitable certificate and has decided to proceed with
client authentication. (Note that if the server has used a Supported
Point Formats Extension, a certificate can only be considered
suitable for use with the ECDSA_sign, RSA_fixed_ECDH, and
ECDSA_fixed_ECDH authentication methods if the public key point
specified in it respects the server’s choice of point formats. If no
Supported Point Formats Extension has been used, a certificate can
only be considered suitable for use with these authentication methods
if the point is represented in uncompressed point format.)
Meaning of this message:
This message is used to authentically convey the client’s static
public key to the server. The following table summarizes what client
certificate types are appropriate for the ECC-based client
authentication mechanisms described in Section 3. ECC public keys
must be encoded in certificates as described in Section 5.9.
NOTE: The client’s Certificate message is capable of carrying a chain
of certificates. The restrictions mentioned in Table 4 apply only to
the client’s certificate (first in the chain).
Client
Authentication Method Client Certificate Type
--------------------- -----------------------
ECDSA_sign Certificate MUST contain an