TLS Working Group V. Gupta
Internet-Draft Sun Labs
Expires: September 2, 2005 S. Blake-Wilson
BCI
B. Moeller
University of Calgary
C. Hawk
Corriente Networks
N. Bolyard
Mar. 2005
ECC Cipher Suites for TLS
<draft-ietf-tls-ecc-08.txt>
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Copyright (C) The Internet Society (2005).
Abstract
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This document describes new key exchange algorithms based on Elliptic
Curve Cryptography (ECC) for the TLS (Transport Layer Security)
protocol. In particular, it specifies the use of Elliptic Curve
Diffie-Hellman (ECDH) key agreement in a TLS handshake and the use of
Elliptic Curve Digital Signature Algorithm (ECDSA) as a new
authentication mechanism.
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [1].
Please send comments on this document to the TLS mailing list.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Key Exchange Algorithms . . . . . . . . . . . . . . . . . . 5
2.1 ECDH_ECDSA . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 ECDHE_ECDSA . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 ECDH_RSA . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 ECDHE_RSA . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 ECDH_anon . . . . . . . . . . . . . . . . . . . . . . . . 8
3. Client Authentication . . . . . . . . . . . . . . . . . . . 9
3.1 ECDSA_sign . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 ECDSA_fixed_ECDH . . . . . . . . . . . . . . . . . . . . . 10
3.3 RSA_fixed_ECDH . . . . . . . . . . . . . . . . . . . . . . 10
4. TLS Extensions for ECC . . . . . . . . . . . . . . . . . . . 11
5. Data Structures and Computations . . . . . . . . . . . . . . 12
5.1 Client Hello Extensions . . . . . . . . . . . . . . . . . 12
5.2 Server Hello Extensions . . . . . . . . . . . . . . . . . 15
5.3 Server Certificate . . . . . . . . . . . . . . . . . . . . 16
5.4 Server Key Exchange . . . . . . . . . . . . . . . . . . . 17
5.5 Certificate Request . . . . . . . . . . . . . . . . . . . 20
5.6 Client Certificate . . . . . . . . . . . . . . . . . . . . 21
5.7 Client Key Exchange . . . . . . . . . . . . . . . . . . . 22
5.8 Certificate Verify . . . . . . . . . . . . . . . . . . . . 23
5.9 Elliptic Curve Certificates . . . . . . . . . . . . . . . 25
5.10 ECDH, ECDSA and RSA Computations . . . . . . . . . . . . 25
6. Cipher Suites . . . . . . . . . . . . . . . . . . . . . . . 26
7. Security Considerations . . . . . . . . . . . . . . . . . . 28
8. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 29
9. References . . . . . . . . . . . . . . . . . . . . . . . . . 30
9.1 Normative References . . . . . . . . . . . . . . . . . . . 30
9.2 Informative References . . . . . . . . . . . . . . . . . . 30
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . 31
Intellectual Property and Copyright Statements . . . . . . . 33
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1. Introduction
Elliptic Curve Cryptography (ECC) is emerging as an attractive
public-key cryptosystem for mobile/wireless environments. Compared
to currently prevalent cryptosystems such as RSA, ECC offers
equivalent security with smaller key sizes. This is illustrated in
the following table, based on [12], which gives approximate
comparable key sizes for symmetric- and asymmetric-key cryptosystems
based on the best-known algorithms for attacking them.
Symmetric | ECC | DH/DSA/RSA
-------------+---------+------------
80 | 163 | 1024
112 | 233 | 2048
128 | 283 | 3072
192 | 409 | 7680
256 | 571 | 15360
Table 1: Comparable key sizes (in bits)
Figure 1
Smaller key sizes result in power, bandwidth and computational
savings that make ECC especially attractive for constrained
environments.
This document describes additions to TLS to support ECC. In
particular, it defines
o the use of the Elliptic Curve Diffie-Hellman (ECDH) key agreement
scheme with long-term or ephemeral keys to establish the TLS
premaster secret, and
o the use of fixed-ECDH certificates and ECDSA for authentication of
TLS peers.
The remainder of this document is organized as follows. Section 2
provides an overview of ECC-based key exchange algorithms for TLS.
Section 3 describes the use of ECC certificates for client
authentication. TLS extensions that allow a client to negotiate the
use of specific curves and point formats are presented in Section 4.
Section 5 specifies various data structures needed for an ECC-based
handshake, their encoding in TLS messages and the processing of those
messages. Section 6 defines new ECC-based cipher suites and
identifies a small subset of these as recommended for all
implementations of this specification. Section 7 and Section 8
mention security considerations and acknowledgments, respectively.
This is followed by a list of references cited in this document, the
authors' contact information, and statements on intellectual property
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rights and copyrights.
Implementation of this specification requires familiarity with TLS
[2], TLS extensions [3] and ECC [4][5][6][8] .
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2. Key Exchange Algorithms
This document introduces five new ECC-based key exchange algorithms
for TLS. All of them use ECDH to compute the TLS premaster secret
and differ only in the lifetime of ECDH keys (long-term or ephemeral)
and the mechanism (if any) used to authenticate them. The derivation
of the TLS master secret from the premaster secret and the subsequent
generation of bulk encryption/MAC keys and initialization vectors is
independent of the key exchange algorithm and not impacted by the
introduction of ECC.
The table below summarizes the new key exchange algorithms which
mimic DH_DSS, DH_RSA, DHE_DSS, DHE_RSA and DH_anon (see [2]),
respectively.
Key
Exchange
Algorithm Description
--------- -----------
ECDH_ECDSA Fixed ECDH with ECDSA-signed certificates.
ECDHE_ECDSA Ephemeral ECDH with ECDSA signatures.
ECDH_RSA Fixed ECDH with RSA-signed certificates.
ECDHE_RSA Ephemeral ECDH with RSA signatures.
ECDH_anon Anonymous ECDH, no signatures.
Table 2: ECC key exchange algorithms
Figure 2
The ECDHE_ECDSA and ECDHE_RSA key exchange mechanisms provide forward
secrecy. With ECDHE_RSA, a server can reuse its existing RSA
certificate and easily comply with a constrained client's elliptic
curve preferences (see Section 4). However, the computational cost
incurred by a server is higher for ECDHE_RSA than for the traditional
RSA key exchange which does not provide forward secrecy.
The ECDH_RSA mechanism requires a server to acquire an ECC
certificate but the certificate issuer can still use an existing RSA
key for signing. This eliminates the need to update the trusted key
store in TLS clients. The ECDH_ECDSA mechanism requires ECC keys for
the server as well as the certification authority and is best suited
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for constrained devices unable to support RSA.
The anonymous key exchange algorithm does not provide authentication
of the server or the client. Like other anonymous TLS key exchanges,
it is subject to man-in-the-middle attacks. Implementations of this
algorithm SHOULD provide authentication by other means.
Note that there is no structural difference between ECDH and ECDSA
keys. A certificate issuer may use X509.v3 keyUsage and
extendedKeyUsage extensions to restrict the use of an ECC public key
to certain computations. This document refers to an ECC key as
ECDH-capable if its use in ECDH is permitted. ECDSA-capable is
defined similarly.
Client Server
------ ------
ClientHello -------->
ServerHello
Certificate*
ServerKeyExchange*
CertificateRequest*+
<-------- ServerHelloDone
Certificate*+
ClientKeyExchange
CertificateVerify*+
[ChangeCipherSpec]
Finished -------->
[ChangeCipherSpec]
<-------- Finished
Application Data <-------> Application Data
Figure 1: Message flow in a full TLS handshake
* message is not sent under some conditions
+ message is not sent unless the client is
authenticated
Figure 3
Figure 1 shows all messages involved in the TLS key establishment
protocol (aka full handshake). The addition of ECC has direct impact
only on the ClientHello, the ServerHello, the server's Certificate
message, the ServerKeyExchange, the ClientKeyExchange, the
CertificateRequest, the client's Certificate message, and the
CertificateVerify. Next, we describe each ECC key exchange algorithm
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in greater detail in terms of the content and processing of these
messages. For ease of exposition, we defer discussion of client
authentication and associated messages (identified with a + in Figure
1) until Section 3 and of the optional ECC-specific extensions (which
impact the Hello messages) until Section 4.
2.1 ECDH_ECDSA
In ECDH_ECDSA, the server's certificate MUST contain an ECDH-capable
public key and be signed with ECDSA.
A ServerKeyExchange MUST NOT be sent (the server's certificate
contains all the necessary keying information required by the client
to arrive at the premaster secret).
The client MUST generate an ECDH key pair on the same curve as the
server's long-term public key and send its public key in the
ClientKeyExchange message (except when using client authentication
algorithm ECDSA_fixed_ECDH or RSA_fixed_ECDH, in which case the
modifications from section Section 3.2 or Section 3.3 apply).
Both client and server MUST perform an ECDH operation and use the
resultant shared secret as the premaster secret. All ECDH
calculations are performed as specified in Section 5.10
2.2 ECDHE_ECDSA
In ECDHE_ECDSA, the server's certificate MUST contain an
ECDSA-capable public key and be signed with ECDSA.
The server MUST send its ephemeral ECDH public key and a
specification of the corresponding curve in the ServerKeyExchange
message. These parameters MUST be signed with ECDSA using the
private key corresponding to the public key in the server's
Certificate.
The client MUST generate an ECDH key pair on the same curve as the
server's ephemeral ECDH key and send its public key in the
ClientKeyExchange message.
Both client and server MUST perform an ECDH operation (Section 5.10)
and use the resultant shared secret as the premaster secret.
2.3 ECDH_RSA
This key exchange algorithm is the same as ECDH_ECDSA except the
server's certificate MUST be signed with RSA rather than ECDSA.
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2.4 ECDHE_RSA
This key exchange algorithm is the same as ECDHE_ECDSA except the
server's certificate MUST contain an RSA public key authorized for
signing and the signature in the ServerKeyExchange message MUST be
computed with the corresponding RSA private key. The server
certificate MUST be signed with RSA.
2.5 ECDH_anon
In ECDH_anon, the server's Certificate, the CertificateRequest, the
client's Certificate, and the CertificateVerify messages MUST NOT be
sent.
The server MUST send an ephemeral ECDH public key and a specification
of the corresponding curve in the ServerKeyExchange message. These
parameters MUST NOT be signed.
The client MUST generate an ECDH key pair on the same curve as the
server's ephemeral ECDH key and send its public key in the
ClientKeyExchange message.
Both client and server MUST perform an ECDH operation and use the
resultant shared secret as the premaster secret. All ECDH
calculations are performed as specified in Section 5.10
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3. Client Authentication
This document defines three new client authentication mechanisms
named after the type of client certificate involved: ECDSA_sign,
ECDSA_fixed_ECDH and RSA_fixed_ECDH. The ECDSA_sign mechanism is
usable with any of the non-anonymous ECC key exchange algorithms
described in Section 2 as well as other non-anonymous (non-ECC) key
exchange algorithms defined in TLS [2]. The ECDSA_fixed_ECDH and
RSA_fixed_ECDH mechanisms are usable with ECDH_ECDSA and ECDH_RSA.
Their use with ECDHE_ECDSA and ECDHE_RSA is prohibited because the
use of a long-term ECDH client key would jeopardize the forward
secrecy property of these algorithms.
The server can request ECC-based client authentication by including
one or more of these certificate types in its CertificateRequest
message. The server MUST NOT include any certificate types that are
prohibited for the negotiated key exchange algorithm. The client
must check if it possesses a certificate appropriate for any of the
methods suggested by the server and is willing to use it for
authentication.
If these conditions are not met, the client should send a client
Certificate message containing no certificates. In this case, the
ClientKeyExchange should be sent as described in Section 2 and the
CertificateVerify should not be sent. If the server requires client
authentication, it may respond with a fatal handshake failure alert.
If the client has an appropriate certificate and is willing to use it
for authentication, it MUST send that certificate in the client's
Certificate message (as per Section 5.6) and prove possession of the
private key corresponding to the certified key. The process of
determining an appropriate certificate and proving possession is
different for each authentication mechanism and described below.
NOTE: It is permissible for a server to request (and the client to
send) a client certificate of a different type than the server
certificate.
3.1 ECDSA_sign
To use this authentication mechanism, the client MUST possess a
certificate containing an ECDSA-capable public key and signed with
ECDSA.
The client MUST prove possession of the private key corresponding to
the certified key by including a signature in the CertificateVerify
message as described in Section 5.8.
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3.2 ECDSA_fixed_ECDH
To use this authentication mechanism, the client MUST possess a
certificate containing an ECDH-capable public key and that
certificate MUST be signed with ECDSA. Furthermore, the client's
ECDH key MUST be on the same elliptic curve as the server's long-term
(certified) ECDH key. This might limit use of this mechanism to
closed environments. In situations where the client has an ECC key
on a different curve, it would have to authenticate either using
ECDSA_sign or a non-ECC mechanism (e.g. RSA). Using fixed ECDH for
both servers and clients is computationally more efficient than
mechanisms providing forward secrecy.
When using this authentication mechanism, the client MUST send an
empty ClientKeyExchange as described in Section 5.7 and MUST NOT send
the CertificateVerify message. The ClientKeyExchange is empty since
the client's ECDH public key required by the server to compute the
premaster secret is available inside the client's certificate. The
client's ability to arrive at the same premaster secret as the server
(demonstrated by a successful exchange of Finished messages) proves
possession of the private key corresponding to the certified public
key and the CertificateVerify message is unnecessary.
3.3 RSA_fixed_ECDH
This authentication mechanism is identical to ECDSA_fixed_ECDH except
the client's certificate MUST be signed with RSA.
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4. TLS Extensions for ECC
Two new TLS extensions --- (i) the Supported Elliptic Curves
Extension, and (ii) the Supported Point Formats Extension --- allow a
client to negotiate the use of specific curves and point formats
(e.g. compressed v/s uncompressed), respectively. These extensions
are especially relevant for constrained clients that may only support
a limited number of curves or point formats. They follow the general
approach outlined in [3]. The client enumerates the curves and point
formats it supports by including the appropriate extensions in its
ClientHello message. By echoing that extension in its ServerHello,
the server agrees to restrict its key selection or encoding to the
choices specified by the client.
A TLS client that proposes ECC cipher suites in its ClientHello
message SHOULD include these extensions. Servers implementing ECC
cipher suites MUST support these extensions and negotiate the use of
an ECC cipher suite only if they can complete the handshake while
limiting themselves to the curves and compression techniques
enumerated by the client. This eliminates the possibility that a
negotiated ECC handshake will be subsequently aborted due to a
client's inability to deal with the server's EC key.
These extensions MUST NOT be included if the client does not propose
any ECC cipher suites. A client that proposes ECC cipher suites may
choose not to include these extension. In this case, the server is
free to choose any one of the elliptic curves or point formats listed
in Section 5. That section also describes the structure and
processing of these extensions in greater detail.
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5. Data Structures and Computations
This section specifies the data structures and computations used by
ECC-based key mechanisms specified in Section 2, Section 3 and
Section 4. The presentation language used here is the same as that
used in TLS [2]. Since this specification extends TLS, these
descriptions should be merged with those in the TLS specification and
any others that extend TLS. This means that enum types may not
specify all possible values and structures with multiple formats
chosen with a select() clause may not indicate all possible cases.
5.1 Client Hello Extensions
When this message is sent:
The ECC extensions SHOULD be sent along with any ClientHello message
that proposes ECC cipher suites.
Meaning of this message:
These extensions allow a constrained client to enumerate the elliptic
curves and/or point formats it supports.
Structure of this message:
The general structure of TLS extensions is described in [3] and this
specification adds two new types to ExtensionType.
enum { elliptic_curves(??), ec_point_formats(??) } ExtensionType;
elliptic_curves: Indicates the set of elliptic curves supported by
the client. For this extension, the opaque extension_data field
contains EllipticCurveList.
ec_point_formats: Indicates the set of point formats supported by
the client. For this extension, the opaque extension_data field
contains ECPointFormatList.
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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 (240..247),
arbitrary_explicit_prime_curves(253),
arbitrary_explicit_char2_curves(254),
(255)
} NamedCurve;
sect163k1, etc: Indicates support of the corresponding named curve
specified in SEC 2 [10]. Note that many of these curves are also
recommended in ANSI X9.62 [6], and FIPS 186-2 [8]. Values 240
through 247 are reserved for private use. Values 253 and 254
indicate that the client supports arbitrary prime and
characteristic-2 curves, respectively (the curve parameters must
be encoded explicitly in ECParameters).
struct {
NamedCurve elliptic_curve_list<1..2^8-1>
} 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)
and secp224r1 (aka NIST P-224) and prefers to use secp192r1, would
include an elliptic_curves extension with the following octets:
00 ?? 00 03 02 13 15
A client that supports arbitrary explicit binary polynomial curves
would include an extension with the following octets:
00 ?? 00 02 01 fe
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enum { uncompressed (0), ansiX963_compressed (1),
ansiX963_hybrid (2), (255)
} ECPointFormat;
struct {
ECPointFormat ec_point_format_list<1..2^8-1>
} ECPointFormatList;
Three point formats are included in the defintion of ECPointFormat
above. The uncompressed point format is the default format that
implementations of this document MUST support. The
ansix963_compressed format reduces bandwidth by including only the
x-coordinate and a single bit of the y-coordinate of the point. The
ansix963_hybrid format includes both the full y-coordinate and the
compressed y-coordinate to allow flexibility and improve efficiency
in some cases. Implementations of this document MAY support the
ansix963_compressed and ansix963_hybrid point formats.
Items in ec_point_format_list are ordered according to the client's
preferences (favorite choice first).
A client that only supports the uncompressed point format includes an
extension with the following octets:
00 ?? 00 02 01 00
A client that prefers the use of the ansiX963_compressed format over
uncompressed may indicate that preference by including an extension
with the following octets:
00 ?? 00 03 02 01 00
Actions of the sender:
A client that proposes ECC cipher suites in its ClientHello appends
these extensions (along with any others) enumerating the curves and
point formats it supports.
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.
NOTE: A server participating in an ECDHE-ECDSA key exchange may use
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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 "elliptic_curves" extension in selecting both of
these curves.
If a server does not understand the "elliptic_curves" extension or is
unable to complete the ECC handshake while restricting itself to the
enumerated curves, 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.
5.2 Server Hello Extensions
When this message is sent:
The ServerHello ECC extensions are sent in response to a Client Hello
message containing ECC extensions when negotiating an ECC cipher
suite.
Meaning of this message:
These extensions indicate the server's agreement to use only the
elliptic curves and point formats supported by the client during the
ECC-based key exchange.
Structure of this message:
The ECC extensions echoed by the server are the same as those in the
ClientHello except the "extension_data" field is empty.
For example, a server indicates its acceptance of the client's
elliptic_curves extension by sending an extension with the following
octets:
00 ?? 00 00
Actions of the sender:
A server makes sure that it can complete a proposed ECC key exchange
mechanism by restricting itself to the curves/point formats supported
by the client before sending these extensions.
Actions of the receiver:
A client that receives a ServerHello with ECC extensions proceeds
with an ECC key exchange assured that it will be able to handle the
server's EC key(s).
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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:
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The server constructs an appropriate certificate chain and conveys it
to the client in the Certificate 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.
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), (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.
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 [6].
struct {
opaque point <1..2^8-1>;
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} 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 [6]. Note that this byte string may represent an elliptic
curve point in compressed or uncompressed form.
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.
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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.
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 enum values of NamedCurve are allowed except for
arbitrary_explicit_prime_curves(253) and
arbitrary_explicit_char2_curves(254). These two values are only
allowed in the ClientHello extension.
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;
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select (SignatureAlgorithm) {
case ecdsa:
digitally-signed struct {
opaque sha_hash[sha_size];
};
} Signature;
NOTE: SignatureAlgorithm is 'rsa' for the ECDHE_RSA key exchange
algorithm and 'anonymous' for ECDH_anon. These cases are defined in
TLS [2]. SignatureAlgorithm is 'ecdsa' for ECDHE_ECDSA. ECDSA
signatures are generated and verified as described in Section 5.10.
As per ANSI X9.62, an ECDSA signature consists of a pair of integers
r and s. These integers are both converted into byte strings of the
same length as the curve order n using the conversion routine
specified in Section 4.3.1 of [6]. The two byte strings are
concatenated, and the result is placed in the signature field.
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 [5]. It conveys this information to
the client in the ServerKeyExchange message using the format defined
above.
Actions of the recipient:
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.
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(?), rsa_fixed_ecdh(?),
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ecdsa_fixed_ecdh(?), (255)
} ClientCertificateType;
ecdsa_sign, etc Indicates that the server would like to use the
corresponding client authentication method specified in Section 3.
EDITOR: The values used for ecdsa_sign, rsa_fixed_ecdh, and
ecdsa_fixed_ecdh have been left as ?. These values will be
assigned when this draft progresses to RFC. Earlier versions of
this draft used the values 5, 6, and 7 - however these values have
been removed since they are used differently by SSL 3.0 [13] and
their use by TLS is being deprecated.
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 an appropriate certificate for
use with any of the requested methods, and decides whether or not 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.
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).
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Client
Authentication Method Client Certificate Type
--------------------- -----------------------
ECDSA_sign Certificate must contain an
ECDSA-capable public key and
be signed with ECDSA.
ECDSA_fixed_ECDH Certificate must contain an
ECDH-capable public key on the
same elliptic curve as the server's
long-term ECDH key. This certificate
must be signed with ECDSA.
RSA_fixed_ECDH Certificate must contain an
ECDH-capable public key on the
same elliptic curve as the server's
long-term ECDH key. This certificate
must be signed with RSA.
Table 4: Client certificate types
Structure of this message:
Identical to the TLS client Certificate format.
Actions of the sender:
The client constructs an appropriate certificate chain, and conveys
it to the server in the Certificate message.
Actions of the receiver:
The TLS server validates the certificate chain, extracts the client's
public key, and checks that the key type is appropriate for the
client authentication method.
5.7 Client Key Exchange
When this message is sent:
This message is sent in all key exchange algorithms. If client
authentication with ECDSA_fixed_ECDH or RSA_fixed_ECDH is used, this
message is empty. Otherwise, it contains the client's ephemeral ECDH
public key.
Meaning of the message:
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This message is used to convey ephemeral data relating to the key
exchange belonging to the client (such as its ephemeral ECDH public
key).
Structure of this message:
The TLS ClientKeyExchange message is extended as follows.
enum { yes, no } EphemeralPublicKey;
yes, no: Indicates whether or not the client is providing an
ephemeral ECDH public key. (In ECC ciphersuites, this is "yes"
except when the client uses the ECDSA_fixed_ECDH or RSA_fixed_ECDH
client authentication mechanism.)
struct {
select (EphemeralPublicKey) {
case yes: ECPoint ecdh_Yc;
case no: struct { };
} ecdh_public;
} ClientECDiffieHellmanPublic;
ecdh_Yc: Contains the client's ephemeral ECDH public key.
struct {
select (KeyExchangeAlgorithm) {
case ec_diffie_hellman: ClientECDiffieHellmanPublic;
} exchange_keys;
} ClientKeyExchange;
Actions of the sender:
The client selects an ephemeral ECDH public key corresponding to the
parameters it received from the server according to the ECKAS-DH1
scheme from IEEE 1363 [5]. It conveys this information to the client
in the ClientKeyExchange message using the format defined above.
Actions of the recipient:
The server retrieves the client's ephemeral ECDH public key from the
ClientKeyExchange message and checks that it is on the same elliptic
curve as the server's ECDH key.
5.8 Certificate Verify
When this message is sent:
This message is sent when the client sends a client certificate
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containing a public key usable for digital signatures, e.g. when the
client is authenticated using the ECDSA_sign mechanism.
Meaning of the message:
This message contains a signature that proves possession of the
private key corresponding to the public key in the client's
Certificate message.
Structure of this message:
The TLS CertificateVerify message is extended as follows.
enum { ecdsa } SignatureAlgorithm;
select (SignatureAlgorithm) {
case ecdsa:
digitally-signed struct {
opaque sha_hash[sha_size];
};
} Signature;
For the ecdsa case, the signature field in the CertificateVerify
message contains an ECDSA signature computed over handshake messages
exchanged so far. ECDSA signatures are computed as described in
Section 5.10. As per ANSI X9.62, an ECDSA signature consists of a
pair of integers r and s. These integers are both converted into
byte strings of the same length as the curve order n using the
conversion routine specified in Section 4.3.1 of [6]. The two byte
strings are concatenated, and the result is placed in the signature
field.
Actions of the sender:
The client computes its signature over all handshake messages sent or
received starting at client hello up to but not including this
message. It uses the private key corresponding to its certified
public key to compute the signature which is conveyed in the format
defined above.
Actions of the receiver:
The server extracts the client's signature from the CertificateVerify
message, and verifies the signature using the public key it received
in the client's Certificate message.
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5.9 Elliptic Curve Certificates
X509 certificates containing ECC public keys or signed using ECDSA
MUST comply with [11] or another RFC that replaces or extends it.
Clients SHOULD use the elliptic curve domain parameters recommended
in ANSI X9.62 [6], FIPS 186-2 [8], and SEC 2 [10].
5.10 ECDH, ECDSA and RSA Computations
All ECDH calculations (including parameter and key generation as well
as the shared secret calculation) MUST be performed according to [5]
using the ECKAS-DH1 scheme with the identity map as key derivation
function, so that the premaster secret is the x-coordinate of the
ECDH shared secret elliptic curve point, i.e. the octet string Z in
IEEE 1363 terminology.
Note that a new extension may be introduced in the future to allow
the use of a different KDF during computation of the premaster
secret. In this event, the new KDF would be used in place of the
process detailed above. This may be desirable, for example, to
support compatibility with the planned NIST key agreement standard.
All ECDSA computations MUST be performed according to ANSI X9.62 [6]
or its successors. Data to be signed/verified is hashed and the
result run directly through the ECDSA algorithm with no additional
hashing. The default hash function is SHA-1 [7] and sha_size (see
Section 5.4 and Section 5.8) is 20. However, an alternative hash
function, such as one of the new SHA hash functions specified in FIPS
180-2 [7], may be used instead if the certificate containing the EC
public key explicitly requires use of another hash function. (The
mechanism for specifying the required hash function has not been
standardized but this provision anticipates such standardization and
obviates the need to update this document in response. Future PKIX
RFCs may choose, for example, to specify the hash function to be used
with a public key in the parameters field of subjectPublicKeyInfo.)
All RSA signatures must be generated and verified according to PKCS#1
[9].
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6. Cipher Suites
The table below defines new ECC cipher suites that use the key
exchange algorithms specified in Section 2.
CipherSuite TLS_ECDH_ECDSA_WITH_NULL_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_ECDSA_WITH_RC4_128_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_ECDSA_WITH_DES_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_ECDSA_WITH_3DES_EDE_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_ECDSA_WITH_AES_128_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_ECDSA_WITH_AES_256_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_ECDSA_WITH_NULL_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_ECDSA_WITH_RC4_128_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_ECDSA_WITH_3DES_EDE_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_RSA_WITH_NULL_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_RSA_WITH_RC4_128_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_RSA_WITH_AES_128_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_RSA_WITH_AES_256_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_RSA_WITH_NULL_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_RSA_WITH_RC4_128_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_anon_NULL_WITH_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_anon_WITH_RC4_128_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_anon_WITH_3DES_EDE_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_anon_WITH_AES_128_CBC_SHA = { 0x00, 0x?? }
CipherSuite TLS_ECDH_anon_WITH_AES_256_CBC_SHA = { 0x00, 0x?? }
Table 5: TLS ECC cipher suites
Figure 30
The key exchange method, cipher, and hash algorithm for each of these
cipher suites are easily determined by examining the name. Ciphers
other than AES ciphers, and hash algorithms are defined in [2]. AES
ciphers are defined in [14].
Server implementations SHOULD support all of the following cipher
suites, and client implementations SHOULD support at least one of
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them: TLS_ECDH_ECDSA_WITH_3DES_EDE_CBC_SHA,
TLS_ECDH_ECDSA_WITH_AES_128_CBC_SHA,
TLS_ECDHE_RSA_WITH_3DES_EDE_CBC_SHA, and
TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA.
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7. Security Considerations
This document is based on [2], [5], [6] and [14]. The appropriate
security considerations of those documents apply.
One important issue that implementors and users must consider is
elliptic curve selection. Guidance on selecting an appropriate
elliptic curve size is given in Figure 1.
Beyond elliptic curve size, the main issue is elliptic curve
structure. As a general principle, it is more conservative to use
elliptic curves with as little algebraic structure as possible - thus
random curves are more conservative than special curves such as
Koblitz curves, and curves over F_p with p random are more
conservative than curves over F_p with p of a special form (and
curves over F_p with p random might be considered more conservative
than curves over F_2^m as there is no choice between multiple fields
of similar size for characteristic 2). Note, however, that algebraic
structure can also lead to implementation efficiencies and
implementors and users may, therefore, need to balance conservatism
against a need for efficiency. Concrete attacks are known against
only very few special classes of curves, such as supersingular
curves, and these classes are excluded from the ECC standards that
this document references [5], [6].
Another issue is the potential for catastrophic failures when a
single elliptic curve is widely used. In this case, an attack on the
elliptic curve might result in the compromise of a large number of
keys. Again, this concern may need to be balanced against efficiency
and interoperability improvements associated with widely-used curves.
Substantial additional information on elliptic curve choice can be
found in [4], [5], [6], [8].
Implementors and users must also consider whether they need forward
secrecy. Forward secrecy refers to the property that session keys
are not compromised if the static, certified keys belonging to the
server and client are compromised. The ECDHE_ECDSA and ECDHE_RSA key
exchange algorithms provide forward secrecy protection in the event
of server key compromise, while ECDH_ECDSA and ECDH_RSA do not.
Similarly if the client is providing a static, certified key,
ECDSA_sign client authentication provides forward secrecy protection
in the event of client key compromise, while ECDSA_fixed_ECDH and
RSA_fixed_ECDH do not. Thus to obtain complete forward secrecy
protection, ECDHE_ECDSA or ECDHE_RSA must be used for key exchange,
with ECDSA_sign used for client authentication if necessary. Here
again the security benefits of forward secrecy may need to be
balanced against the improved efficiency offered by other options.
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8. Acknowledgments
The authors wish to thank Bill Anderson and Tim Dierks.
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9. References
9.1 Normative References
[1] Bradner, S., "Key Words for Use in RFCs to Indicate Requirement
Levels", RFC 2119, March 1997.
[2] Dierks, T. and C. Allen, "The TLS Protocol Version 1.0",
RFC 2246, January 1999.
[3] Blake-Wilson, S., Nystrom, M., Hopwood, D., Mikkelsen, J. and
T. Wright, "Transport Layer Security (TLS) Extensions",
Internet-draft draft-ietf-tls-rfc3546bis-00.txt, Nov. 2004.
[4] SECG, "Elliptic Curve Cryptography", SEC 1, 2000,
<http://www.secg.org/>.
[5] IEEE, "Standard Specifications for Public Key Cryptography",
IEEE 1363, 2000.
[6] ANSI, "Public Key Cryptography For The Financial Services
Industry: The Elliptic Curve Digital Signature Algorithm
(ECDSA)", ANSI X9.62, 1998.
[7] NIST, "Secure Hash Standard", FIPS 180-2, 2002.
[8] NIST, "Digital Signature Standard", FIPS 186-2, 2000.
[9] RSA Laboratories, "PKCS#1: RSA Encryption Standard version
1.5", PKCS 1, November 1993.
[10] SECG, "Recommended Elliptic Curve Domain Parameters", SEC 2,
2000, <http://www.secg.org/>.
[11] Polk, T., Housley, R. and L. Bassham, "Algorithms and
Identifiers for the Internet X.509 Public Key Infrastructure
Certificate and Certificate Revocation List (CRL) Profile",
RFC 3279, April 2002.
9.2 Informative References
[12] Lenstra, A. and E. Verheul, "Selecting Cryptographic Key
Sizes", Journal of Cryptology 14 (2001) 255-293,
<http://www.cryptosavvy.com/>.
[13] Freier, A., Karlton, P. and P. Kocher, "The SSL Protocol
Version 3.0", November 1996,
<http://wp.netscape.com/eng/ssl3/draft302.txt>.
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[14] Chown, P., "Advanced Encryption Standard (AES) Ciphersuites for
Transport Layer Security (TLS)", RFC 3268, June 2002.
[15] Hovey, R. and S. Bradner, "The Organizations Involved in the
IETF Standards Process", RFC 2028, BCP 11, October 1996.
Authors' Addresses
Vipul Gupta
Sun Microsystems Laboratories
16 Network Circle
MS UMPK16-160
Menlo Park, CA 94025
USA
Phone: +1 650 786 7551
Email: vipul.gupta@sun.com
Simon Blake-Wilson
Basic Commerce & Industries, Inc.
96 Spandia Ave
Unit 606
Toronto, ON M6G 2T6
Canada
Phone: +1 416 214 5961
Email: sblakewilson@bcisse.com
Bodo Moeller
University of Calgary
Dept of Math & Stats
2500 University Dr NW
Calgary, AB T2N 1N4
CA
Email: bodo@openssl.org
Chris Hawk
Corriente Networks
Email: chris@corriente.net
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Nelson Bolyard
Email: nelson@bolyard.com
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