Secure Shell Working Group D. Stebila
Internet-Draft University of Waterloo
Intended status: Standards Track J. Green
Expires: April 4, 2009 October 1, 2008
Elliptic-Curve Algorithm Integration in the Secure Shell Transport Layer
draft-green-secsh-ecc-03
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Abstract
This document describes algorithms based on Elliptic Curve
Cryptography (ECC) for use within the Secure Shell (SSH) transport
protocol. In particular, it specifies: Elliptic Curve Diffie-Hellman
(ECDH) key agreement, Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key
agreement and Elliptic Curve Digital Signature Algorithm (ECDSA) for
use in the SSH Transport Layer protocol.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. ECC Public Key Algorithm . . . . . . . . . . . . . . . . . . . 5
3.1. Key Format . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1.1. Signature Algorithm . . . . . . . . . . . . . . . . . 5
3.1.2. Signature Encoding . . . . . . . . . . . . . . . . . . 5
4. ECDH Key Exchange . . . . . . . . . . . . . . . . . . . . . . 7
5. ECMQV Key Exchange . . . . . . . . . . . . . . . . . . . . . . 10
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 13
6.1. Elliptic Curve Domain Parameter Identifiers . . . . . . . 13
6.2. ECC Public Key Algorithm (ecdsa-sha2) . . . . . . . . . . 13
6.2.1. Elliptic Curve Digital Signature Algorithm . . . . . . 13
6.3. ECDH Key Exchange Method Names (ecdh-sha2-*) . . . . . . . 14
6.4. ECMQV Key Exchange and Verification Method Name
(ecmqv-sha2) . . . . . . . . . . . . . . . . . . . . . . . 14
7. Key Exchange Messages . . . . . . . . . . . . . . . . . . . . 16
7.1. ECDH Message Numbers . . . . . . . . . . . . . . . . . . . 16
7.2. ECMQV Message Numbers . . . . . . . . . . . . . . . . . . 16
8. Security Considerations . . . . . . . . . . . . . . . . . . . 17
9. Named Elliptic Curve Domain Parameters . . . . . . . . . . . . 18
9.1. Required and Recommended Curves . . . . . . . . . . . . . 18
9.2. SEC Equivalent NIST Curves and Encoded OIDs . . . . . . . 18
10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.1. Normative References . . . . . . . . . . . . . . . . . . . 21
10.2. Informative References . . . . . . . . . . . . . . . . . . 21
Appendix A. Acknowledgements . . . . . . . . . . . . . . . . . . 23
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 24
Intellectual Property and Copyright Statements . . . . . . . . . . 25
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1. Introduction
Due to its inclusion in NSA's Suite B and its small key sizes
elliptic curve cryptography (ECC) is becoming a widely utilized and
attractive public-key cryptosystem.
In the interest of adding Suite B algorithms to SSH this document
adds three ECC Suite B algorithms to the Secure Shell arsenal:
Elliptic Curve Menezes-Qu-Vanstone (ECMQV), Elliptic Curve Diffie-
Hellman (ECDH), and Elliptic Curve Digital Signature Algorithm
(ECDSA), as well as utilizing the SHA2 family of secure hash
algorithms.
Compared to cryptosystems such as RSA, DSA, and DH, ECC variations on
these schemes offer equivalent security with smaller key sizes. This
is illustrated in the following table, based on Section 5.6.1 of NIST
800-57 [NIST-800-57], which gives approximate comparable key sizes
for symmetric- and asymmetric-key cryptosystems based on the best
known algorithms for attacking them. L is field size and N is sub-
field size.
+-----------+-----------------------------+-------+---------+
| Symmetric | Discrete Log (eg. DSA, DH) | RSA | ECC |
+-----------+-----------------------------+-------+---------+
| 80 | L = 1024 N = 160 | 1024 | 160-223 |
| | | | |
| 112 | L = 2048 N = 256 | 2048 | 224-255 |
| | | | |
| 128 | L = 3072 N = 256 | 3072 | 256-383 |
| | | | |
| 192 | L = 7680 N = 384 | 7680 | 384-511 |
| | | | |
| 256 | L = 15360 N = 512 | 15360 | 512+ |
+-----------+-----------------------------+-------+---------+
Implementation of this specification requires familiarity with both
SSH [RFC4251] [RFC4253] [RFC4250] and ECC [SEC1] [IEEE1363]
[ANSI-X9.63].
This document is concerned with SSH implementation details;
specification of the underlying cryptographic algorithms is left to
other standards documents.
Comments on this draft are solicited and should be addressed to
Douglas Stebila .
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2. Notation
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 [RFC2119].
The data types boolean, uint32, uint64, string, and mpint are to be
interpreted in this document as described in [RFC4251].
The size of a set of elliptic curve domain parameters on a prime
curve is defined as the number of bits in the binary representation
of the field order, commonly denoted p. Size on a characteristic-2
curve is defined as the number of bits in the binary representation
of the field, commonly denoted m. A set of elliptic curve domain
parameters defines a group of order n generated by a base point P.
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3. ECC Public Key Algorithm
The ECC public key algorithm is defined by its key format,
corresponding signature algorithm ECDSA, signature encoding and
algorithm identifiers.
This section defines the "ecdsa-sha2" public key format and
corresponding signature format.
3.1. Key Format
The "ecdsa-sha2" key format has the following encoding:
string "ecdsa-sha2"
byte[n] ecc_key_blob
The ecc_key_blob value has the following specific encoding:
string [identifier]
string Q
The string [identifier] is the identifier of the elliptic curve
domain parameters. The format of this string is specified in
Section 6.1. Information on the required and recommended sets of
elliptic curve domain parameters for use with this algorithm can be
found in Section 9.
Q is the public key encoded from an elliptic curve point into an
octet string as defined in Section 2.3.3 of [SEC1].
The algorithm for ECC key generation can be found in Section 3.2 of
[SEC1]. Given some elliptic curve domain parameters, an ECC key pair
can be generated containing a private key, an integer d, and a public
key, an elliptic curve point Q.
3.1.1. Signature Algorithm
Signing and verifying is done using the Elliptic Curve Digital
Signature Algorithm (ECDSA). ECDSA is specified in [SEC1] and in
[ANSI-X9.62]. The message hashing algorithm must be from the SHA2
family of hash functions [RFC4634] and is chosen according to the
curve size as specified in Section 6.2.1.
3.1.2. Signature Encoding
Signatures are encoded as follows:
string "ecdsa-sha2"
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string ecdsa_signature_blob
The ecdsa_signature_blob value has the following specific encoding:
mpint r
mpint s
The integers r and s are the output of the ECDSA algorithm.
The width of the integer fields is determined by the curve being
used. Note that the integers r and s are integers modulo the order
of the curve, which is may be larger than the size of the finite
field. Thus, the integers r and s are encoding as octet strings each
of length ciel(log[2](n)/8) using Section 2.3.7 of [SEC1], where n is
the order of the elliptic curve group.
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4. ECDH Key Exchange
The Elliptic Curve Diffie-Hellman (ECDH) key exchange method
generates a shared secret from an ephemeral elliptic curve local
private key and remote public key. This key exchange method provides
explicit server authentication as defined in [RFC4253] using a
signature on the exchange hash.
The primitive used for shared key generation is ECDH with cofactor
multiplication, the full specification of which can be found in
Section 3.3.2 of [SEC1]. The algorithm for key pair generation can
be found in Section 3.2 of [SEC1].
The family of key exchange method names defined for use with this key
exchange can be found in Section 6.3. Algorithm negotiation chooses
the public key algorithm to be used for signing and the method name
of the key exchange. The method name of the key exchange chosen
determines the elliptic curve domain parameters and hash function to
be used in the remainder of this section.
Information on the required and recommended elliptic curve domain
parameters for use with this method can be found in Section 9.
All elliptic curve public keys MUST be validated after they are
received. An example of a validation algorithm can be found in
A.16.10 of [IEEE1363]. If a key fails validation the key exchange
MUST fail.
The elliptic curve public keys (points) that must be transmitted are
encoded into octet strings before they are transmitted. The
transformation between elliptic curve points and octet strings is
specified in Section 2.3 of [SEC1]. The output of shared key
generation is a field element xp. The ssh framework requires that
the shared key be an integer. The conversion between a field element
and an integer is specified in Section 2.3.9 of [SEC1].
Specification of the message numbers SSH_MSG_KEX_ECDH_INIT and
SSH_MSG_KEX_ECDH_REPLY are found in Section 7.
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The following is an overview of the key exchange process:
Client Server
------ ------
Generate ephemeral key pair.
SSH_MSG_KEX_ECDH_INIT -------------->
Verify received key is valid.
Generate ephemeral key pair.
Compute shared secret.
Generate and sign exchange hash.
<------------- SSH_MSG_KEX_ECDH_REPLY
Verify received key is valid.
*Verify host key belongs to server.
Compute shared secret.
Generate exchange hash.
Verify server's signature.
*It is recommended that the client verify that the host key sent is
the server's host key (Using certificates or a local database). The
client is allowed to accept the host key without verification, but
doing so will render the protocol insecure against active attacks.
This is implemented using the following messages.
The client sends:
byte SSH_MSG_KEX_ECDH_INIT
string client's ephemeral public key octet string
The server responds with:
byte SSH_MSG_KEX_ECDH_REPLY
string server's public host key and/or certificates
string server's ephemeral public key octet string
string the signature on the exchange hash
The exchange hash H is computed as the hash of the concatenation of
the following.
string client's version string (CR and NL excluded)
string server's version string (CR and NL excluded)
string payload of the client's SSH_MSG_KEXINIT
string payload of the server's SSH_MSG_KEXINIT
string server's public host key
string client's ephemeral public key octet string
string server's ephemeral public key octet string
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mpint shared secret
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5. ECMQV Key Exchange
The Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key exchange algorithm
generates a shared secret from two local elliptic curve key pairs and
two remote public keys. This key exchange method provides implicit
server authentication as defined in [RFC4253].
The key exchange method name defined for use with this key exchange
is "ecmqv-sha2". This method name gives a hashing algorithm that is
to be used for the HMAC below. Future RFCs may define new method
names specifying new hash algorithms for use with ECMQV. More
information about the method name and HMAC can be found in
Section 6.4.
In general the ECMQV key exchange is performed using the ephemeral
and long term key pair of both the client and server, a total of 4
keys. Within the framework of SSH the client does not have a long
term key pair that needs to be authenticated. Therefore we generate
an ephemeral key and use that as both the clients keys. This is more
efficient than using two different ephemeral keys and does not
adversely affect security (it is analogous to the one-pass protocol
in Section 6.1 of [LMQSV98]).
A full description of the ECMQV primitive can be found in Section 3.4
of [SEC1]. The algorithm for key pair generation can be found in
Section 3.2 of [SEC1].
During algorithm negotiation with the SSH_MSG_KEXINIT messages the
ECMQV key exchange method can only be chosen if a Public Key
Algorithm supporting ECC host keys can also be chosen. This is due
to the use of implicit server authentication in this key exchange
method. This case is handled the same way that key exchange methods
requiring encryption/signature capable public key algorithms are
handled in Section 7.1 of [RFC4253]. If ECMQV key exchange is chosen
then the Public Key Algorithm supporting ECC host keys MUST also be
chosen.
ECMQV requires that all the keys used to generate a shared secret are
generated over the same elliptic curve domain parameters. Since the
host key is used in the generation of the shared secret, allowing for
implicit server authentication, the domain parameters associated with
the host key are used throughout this section.
All elliptic curve public keys MUST be validated after they are
received. An example of a validation algorithm can be found in
A.16.10 of [IEEE1363]. If a key fails validation the key exchange
MUST fail.
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The elliptic curve public keys (points) that must be transmitted are
encoded into octet strings before they are transmitted. The
transformation between elliptic curve points and octet strings is
specified in Section 2.3 of [SEC1]. The output of shared key
generation is a field element xp. The ssh framework requires that
the shared key be an integer. The conversion between a field element
and an integer is specified in Section 2.3.9 of [SEC1].
The following is an overview of the key exchange process:
Client Server
------ ------
Generate ephemeral key pair.
SSH_MSG_KEX_ECMQV_INIT ------------->
Verify received key is valid.
Generate ephemeral key pair.
Compute shared secret.
Generate exchange hash and compute
HMAC over it using the shared secret.
<------------- SSH_MSG_KEX_ECDH_REPLY
Verify received keys are valid.
*Verify host key belongs to server.
Compute shared secret.
Verify HMAC.
*It is recommended that the client verify that the host key sent is
the server's host key (Using certificates or a local database). The
client is allowed to accept the host key without verification, but
doing so will render the protocol insecure against active attacks.
The specification of the message numbers SSH_MSG_ECMQV_INIT and
SSH_MSG_ECMQV_REPLY can be found in Section 7.
This key exchange algorithm is implemented with the following
messages.
The client sends:
byte SSH_MSG_ECMQV_INIT
string client's ephemeral public key octet string
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The server sends:
byte SSH_MSG_ECMQV_REPLY
string server's public host key octet string
string server's ephemeral public key octet string
string HMAC tag computed on H using the shared secret
The hash H is formed by applying the algorithm HASH on a
concatenation of the following:
string client's version string (CR and NL excluded)
string server's version string (CR and NL excluded)
string payload of the client's SSH_MSG_KEXINIT
string payload of the server's SSH_MSG_KEXINIT
string client's ephemeral public key octet
string server's public host key octet
string server's ephemeral public key octet
mpint shared secret
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6. IANA Considerations
This document defines a new family of key exchange method names, a
new key exchange method name, and a new public key algorithm name in
the SSH name registry. These additions to the SSH name space will
have to be approved the IANA.
6.1. Elliptic Curve Domain Parameter Identifiers
This section specifies identifiers encoding named elliptic curve
domain parameters. These identifiers are used in this document to
identify the curve used in the ECC public key format, the ECDSA
signature blob, and the ECDH method name.
An elliptic curve domain parameter identifier is the Base64 encoding
of the MD5 hash [RFC1321] of the ASN.1 Distinguished Encoding Rules
(DER) encoding [ASN1] of the ASN.1 Object Identifier (OID) of the
named curve domain parameters that are associated with the server's
ECC host keys. Every identifier is precisely 24 characters in
length. Base64 encoding is described in Section 6.8 of [RFC2045]. A
list of the required and recommended curves, their OIDs, and the
encoding of their identifiers can be found in Section 9.
For example: the identifier for the sect163k1 elliptic curve domain
parameters would be "4MHB+NBt3AlaSRQ7MnB4cg==".
6.2. ECC Public Key Algorithm (ecdsa-sha2)
The ECC Public Key Algorithm is specified by the public key format
identifier "ecdsa-sha2".
6.2.1. Elliptic Curve Digital Signature Algorithm
The Elliptic Curve Digital Signature Algorithm (ECDSA) is specified
for use with the ECC Public Key Algorithm.
The hashing algorithm defined by this family of method names is the
SHA2 family of hashing algorithms [RFC4634]. The algorithm from the
SHA2 family that will be used is chosen based on the size of the
named curve specified in the public key:
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+----------------+----------------+
| Curve Size | Hash Algorithm |
+----------------+----------------+
| b <= 256 | SHA-256 |
| | |
| 256 < b <= 384 | SHA-384 |
| | |
| 384 < b | SHA-512 |
+----------------+----------------+
6.3. ECDH Key Exchange Method Names (ecdh-sha2-*)
The Elliptic Curve Diffie-Hellman key exchange is defined by a family
of method names. Each method name is the concatenation of the string
"ecdh-sha2" with the elliptic curve domain parameter identifier as
defined in Section Section 6.1. A list of the required and
recommended curves and their OIDs can be found in Section 9.
For example: The method name for ECDH key exchange with ephemeral
keys generated on the sect409k1 curve would be "ecdh-sha2-m/
FtSAmrV4j/Wy6RVUaK7A==".
The hashing algorithm defined by this family of method names is the
SHA2 family of hashing algorithms [RFC4634]. The hashing algorithm
is defined in the method name to allow room for other algorithms to
be defined in future documents. The algorithm from the SHA2 family
that will be used is chosen based on the size of the named curve
specified in the method name according to the table in Section
Section 6.2.1.
The concatenation of any so encoded ASN.1 OID specifying a set of
elliptic curve domain parameters with "ecdh-sha2-" is implicitly
registered under this specification.
6.4. ECMQV Key Exchange and Verification Method Name (ecmqv-sha2)
The Elliptic Curve Menezes-Qu-Vanstone key exchange is defined by the
method name "ecmqv-sha2". Unlike the ECDH key exchange method, ECMQV
relies on a public key algorithm that uses ECC keys: it does not need
a family of method names because the curve information can be gained
from the public key algorithm.
The hashing and message authentication code algorithms are defined by
the method name to allow room for other algorithms to be defined for
use with ECMQV in future documents.
The hashing algorithm defined by this method name is the SHA2 family
of hashing algorithms [RFC4634]. The algorithm from the SHA2 family
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that will be used is chosen based on the size of the named curve
specified for use with ECMQV by the chosen public key algorithm
according to the table in Section Section 6.2.1.
The keyed-hash message authentication code that is used to identify
the server and verify communications is based on the hash chosen
above. The information on implementing the HMAC based on the chosen
hash algorithm can be found in [RFC4634].
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7. Key Exchange Messages
The message numbers 30-49 are key exchange-specific and in a private
namespace defined in [RFC4250] that may be redefined by any key
exchange method [RFC4253] without being granted IANA permission.
The following message numbers have been defined in this document:
7.1. ECDH Message Numbers
#define SSH_MSG_KEX_ECDH_INIT 30
#define SSH_MSG_KEX_ECDH_REPLY 31
7.2. ECMQV Message Numbers
#define SSH_MSG_ECMQV_INIT 30
#define SSH_MSG_ECMQV_REPLY 31
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8. Security Considerations
The Elliptic Curve Diffie-Hellman key agreement algorithm is defined
in [SEC1], [IEEE1363] and [ANSI-X9.63]. The appropriate security
considerations of those documents apply.
The Elliptic Curve Menezes-Qu-Vanstone key agreement algorithm is
defined in [SEC1]. The security considerations raised in that
document also apply. A more detailed discussion of security
considerations can be found in Section 4.7 of the Guide to Elliptic
Curve Cryptography [HMV04].
The server's host key is used in the ECMQV key exchange algorithm.
This means that the strength of the server's ECC host key determines
the strength of the ECMQV key exchange algorithm. This should be
taken into consideration when generating ECC keys for a server.
The methods defined in Section Section 6 rely on the SHA2 family of
hashing functions as defined in [FIPS-180-2]. The appropriate
security considerations of that document apply.
The hashing algorithms defined for use with ECDH and ECMQV are
defined by their method names so that if security problems are found
with the SHA2 family of hashing algorithms or more secure hashing
algorithms become the standard then future documents can extend this
document to include new hashing algorithms by defining new method
names.
Additionally a good general discussion of the security considerations
that must be taken into account when creating an ECC implementation
can be found in Section 5 of the Guide to Elliptic Curve Cryptography
[HMV04].
Since ECDH and ECMQV allow for elliptic curves of arbitrary sizes and
thus arbitrary security strength, it is important that the size of
elliptic curve be chosen to match the security strength of other
elements of the SSH handshake. In particular, host key sizes,
hashing algorithms and bulk encryption algorithms must be chosen
appropriately. Information regarding estimated equivalence of key
sizes is available in [NIST-800-57]. We note in particular that when
ECDSA is used as the signature algorithm and ECDH is used as the key
exchange method, if curves of different sizes are used, then it is
possible that different hash functions from the SHA2 family could be
used.
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9. Named Elliptic Curve Domain Parameters
Implementations may support any ASN.1 object identifier (OID) in the
ASN.1 object tree that defines a set of elliptic curve domain
parameters [ASN1].
9.1. Required and Recommended Curves
Every SSH ECC implementation MUST support the named curves below,
these curves are defined in [SEC2]. These curves should always be
enabled unless specifically disabled by local security policy.
o secp256r1
o secp384r1
o secp521r1
It is RECOMMENDED that SSH ECC implementations also support the
following curves.
o sect163k1
o sect233k1
o sect233r1
o sect283k1
o sect409k1
o sect409r1
o sect571k1
o secp192r1
o secp224r1
9.2. SEC Equivalent NIST Curves and Encoded OIDs
The following table lists common curves by their equivalent SEC and
NIST names. The named NIST curves are specified in [NIST-CURVES].
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+-----------+----------+
| SEC | NIST |
+-----------+----------+
| sect163k1 | nistk163 |
| | |
| secp192r1 | nistp192 |
| | |
| secp224r1 | nistp224 |
| | |
| sect233k1 | nistk233 |
| | |
| sect233r1 | nistb233 |
| | |
| secp256r1 | nistp256 |
| | |
| sect283k1 | nistk283 |
| | |
| secp384r1 | nistp384 |
| | |
| sect409k1 | nistk409 |
| | |
| sect409r1 | nistb409 |
| | |
| secp521r1 | nistp521 |
| | |
| sect571k1 | nistk571 |
+-----------+----------+
The following table lists the above SEC curves, their OID, and the
encoding of their OID as appropriate for the identifiers and method
names defined in Section Section 6. The encoding is the Base64
encoding of the MD5 hash [RFC1321] of the ASN.1 Distinguished
Encoding Rules (DER) encoding [ASN1] of the ASN.1 Object Identifier
(OID) of the named curve domain parameters that are associated with
the ephemeral keys. Base64 encoding is described in Section 6.8 of
[RFC2045].
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+-----------+---------------------+--------------------------+
| SEC | OID | Base64(MD5(DER(OID))) |
+-----------+---------------------+--------------------------+
| sect163k1 | 1.3.132.0.1 | 4MHB+NBt3AlaSRQ7MnB4cg== |
| | | |
| secp192r1 | 1.2.840.10045.3.1.1 | 5pPrSUQtIaTjUSt5VZNBjg== |
| | | |
| secp224r1 | 1.3.132.0.33 | VqBg4QRPjxx1EXZdV0GdWQ== |
| | | |
| sect233k1 | 1.3.132.0.26 | zD/b3hu/71952ArpUG4OjQ== |
| | | |
| sect233r1 | 1.3.132.0.27 | qCbG5Cn/jjsZ7nBeR7EnOA== |
| | | |
| secp256r1 | 1.2.840.10045.3.1.7 | 9UzNcgwTlEnSCECZa7V1mw== |
| | | |
| sect283k1 | 1.3.132.0.16 | wiRIU8TKjMZ418sMqlqtvQ== |
| | | |
| secp384r1 | 1.3.132.0.34 | qcFQaMAMGhTziMT0z+Tuzw== |
| | | |
| sect409k1 | 1.3.132.0.36 | m/FtSAmrV4j/Wy6RVUaK7A== |
| | | |
| sect409r1 | 1.3.132.0.37 | D3FefCjYoJ/kfXgAyLddYA== |
| | | |
| secp521r1 | 1.3.132.0.35 | h/SsxnLCtRBh7I9ATyeB3A== |
| | | |
| sect571k1 | 1.3.132.0.38 | mNVwCXAoS1HGmHpLvBC94w== |
+-----------+---------------------+--------------------------+
The following sequence of commands can be used on many Unix-type
systems to generated the encoding of the OID as above. The command
oid below is an OID converter such as [OID.C].
echo -n ${i} > tmp.oid
echo -n 0000: > tmp.hex
oid -i tmp.oid >> tmp.hex
xxd -r tmp.hex tmp.der
openssl md5 -binary < tmp.der > tmp.md5
openssl base64 < tmp.md5 > tmp.b64
cat tmp.b64
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10. References
10.1. Normative References
[ASN1] International Telecommunications Union, "Abstract Syntax
Notation One (ASN.1): Specification of basic notation",
X.680, July 2002.
[RFC1321] Rivest, R., "The MD5 Message-Digest Algorithm", RFC 1321,
April 1992.
[RFC2045] Freed, N. and N. Borenstein, "Multipurpose Internet Mail
Extensions (MIME) Part One: Format of Internet Message
Bodies", RFC 2045, November 1996.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC4250] Lehtinen, S. and C. Lonvick, "The Secure Shell (SSH)
Protocol Assigned Numbers", RFC 4250, January 2006.
[RFC4251] Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
Protocol Architecture", RFC 4251, January 2006.
[RFC4253] Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
Transport Layer Protocol", RFC 4253, January 2006.
[RFC4634] Eastlake, D. and T. Hansen, "US Secure Hash Algorithms
(SHA and HMAC-SHA)", RFC 4634, July 2006.
[SEC1] Standards for Efficient Cryptography Group, "Elliptic
Curve Cryptography", SEC 1, September 2000,
.
[SEC2] Standards for Efficient Cryptography Group, "Recommended
Elliptic Curve Domain Parameters", SEC 2, September 2000,
.
10.2. Informative References
[ANSI-X9.62]
American National Standards Institute, "Public Key
Cryptography For The Financial Services Industry: The
Elliptic Curve Digital Signature Algorithm (ECDSA)",
ANSI X9.62, 1998.
[ANSI-X9.63]
American National Standards Institute, "Public Key
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Cryptography For The Financial Services Industry: Key
Agreement and Key Transport Using Elliptic Curve
Cryptography", ANSI X9.63, January 1999.
[FIPS-180-2]
National Institute of Standards and Technology, "Secure
Hash Standard", FIPS 180-2, August 2002.
[HMV04] Hankerson, D., Menezes, A., and S. Vanstone, "Guide to
Elliptic Curve Cryptography", 2004.
Springer, ISBN 038795273X
[IEEE1363]
Institute of Electrical and Electronics Engineers,
"Standard Specifications for Public Key Cryptography",
IEEE 1363, 2000.
[LMQSV98] Law, L., Menezes, A., Qu, M., Solinas, J., and S.
Vanstone, "An Efficient Protocol for Authenticated Key
Agreement", University of Waterloo Technical Report
CORR 98-05, August 1998, .
[NIST-800-57]
National Institute of Standards and Technology,
"Recommendation for Key Management - Part 1: General
(Revised)", NIST Special Publication 800-57, March 2007.
[NIST-CURVES]
National Institute of Standards and Technology,
"Recommended Elliptic Curves for Federal Government Use",
August 1999.
[OID.C] Gartner, M., "OID Converter", 2006,
.
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Appendix A. Acknowledgements
The authors acknowledge helpful comments from Alfred Hines, Russ
Housley, Jeffrey Hutzelman, and Rob Lambert.
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Authors' Addresses
Douglas Stebila
University of Waterloo
Department of Combinatorics and Optimization
Waterloo, Ontario N2L 3G1
Canada
Email: douglas@stebila.ca
Jon Green
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