Network Working Group A. Jivsov
Internet Draft PGP Corporation
Intended status: Internet Draft December 26, 2009
Expires: June 24, 2010
ECC in OpenPGP
draft-jivsov-openpgp-ecc-04.txt
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Abstract
This document proposes an Elliptic Curve Cryptography extension to
the OpenPGP public key format and specifies three Elliptic Curves
that enjoy broad support by other standards, including NIST
standards. The document aims to standardize an optimal but narrow
set of parameters for best interoperability and it does so within
the framework it defines that can be expanded in the future to
allow more choices.
Table of Contents
1. Introduction.................................................2
2. Conventions used in this document............................2
3. Elliptic Curve Cryptography..................................3
4. Supported ECC curves.........................................3
5. Supported public key algorithms..............................3
6. Conversion primitives........................................4
7. Key Derivation Function......................................4
8. EC DH Algorithm (ECDH).......................................5
9. Encoding of public and private keys..........................7
10. Data encoding with public keys..............................8
11. ECC curve OID...............................................9
12. Compatibility profiles......................................9
12.1. OpenPGP ECC profile....................................9
12.2. Suite-B profile.......................................10
12.2.1. Secret information...............................10
12.2.2. Top Secret information...........................10
13. Security Considerations....................................10
14. IANA Considerations........................................12
15. Normative references.......................................12
1. Introduction
The OpenPGP protocol supports RSA and DSA public key formats. This
document defines the extension to incorporate support for public
keys that are based on Elliptic Curve Cryptography (ECC).
2. Conventions used in this document
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].
An application MAY implement this draft; note that any [RFC2119]
keyword within this draft applies to an OpenPGP application only if
it chooses to implement this draft.
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3. Elliptic Curve Cryptography
This specification establishes the minimum set of Elliptic Curve
Cryptography public key parameters and cryptographic methods that
will likely satisfy the widest range of platforms and applications
and facilitate interoperability. This specification offers
efficient cryptographic method for applications to match the level
of security of every type of AES algorithm specified in [RFC4880].
This document defines a path to expand ECC support in the future.
National Security Agency (NSA) of the United States specifies ECC
for use in its Suite B set of algorithms [Suite B]. This
specification includes algorithms permitted by Suite B, so it would
be possible to build a Suite B compatible implementation based on a
subset of [RFC4880] and this specification.
4. Supported ECC curves
This standard references three named prime field curves, which are
defined in [FIPS 186-2] as "Curve P-256", "Curve P-384", and "Curve
P-521".
In data structures that this specification defines the named curves
are referenced as a sequence of bytes, called throughout this
specification as Curve OID. Section 11 describes in details how
this sequence of bytes is formed.
5. Supported public key algorithms
Supported public key algorithms are Elliptic Curve Digital
Signature Algorithm (ECDSA), defined in [FIPS 186-2], and Elliptic
Curve Diffie-Hellman (ECDH), defined in section 8.
Other compatible definition of ECDSA can be found in [SEC1].
The section 9.1. Public-Key Algorithms of [RFC4880] is expanded to
define the following public key algorithm IDs:
ID Description of algorithm
19 ECDSA public key algorithm
[to be ECDH public key algorithm
ASSIGNED]
presumably 22
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Applications MUST support ECDSA and ECDH.
6. Conversion primitives
The method to convert an EC point to the octet string is defined in
[SEC1]. This specification only defines uncompressed point
format. For convenience, the synopsis of the encoding method is
given below, however, the [SEC1] is the normative source of the
definition.
The point is encoded in MPI format. The content of the MPI is the
following:
B = B0 || x || y
where x and y are coordinates of the point P = (x, y), each encoded
in big endian format and zero-padded to the underlying field size.
B0 is a byte with following values:
value description
0 Point O. In this case there is no x or y octets present.
4 Uncompressed point. x and y of EC point values follow.
Note that point O shall not appear in a public or a private
key. Therefore, the size of the MPI payload is always curve_size*2
+ 3 bits. For example, for "Curve P-256" the point is represented
as a bit string of length 515 bits.
If other conversion methods are defined in the future, the
application MAY use them only when it is certain that every
recipient of the data supports the other format.
7. Key Derivation Function
A key derivation function (KDF) is necessary to implement EC
encryption. The Concatenation Key Derivation Function (Approved
Alternative 1) defined in [NIST SP800-56A] is REQUIRED with the
following restriction: the KDF hash function MAY be any of the
following hash functions specified by [FIPS 180-2]: SHA2-256,
SHA2-384, SHA2-512. See section 13 for the details regarding the
choice of the hash function.
For convenience, the synopsis of the encoding method is given
below, however, [NIST SP800-56A] is the normative source of the
definition.
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// Implements KDF( X, oBits, P );
// Input: point X = (x,y)
// oBits - the desired size of output
// hBits - the size of output of hash function Hash
// P - octets representing the parameters
counter=1;
threshold = (oBits + hBits - 1) / hBits;
// Convert the point P to octet string as defined in section 6:
// ZB' = 04 || x || y
// and extract the x portion from ZB':
ZB = x;
do {
C32 = (uint32)big_endian(counter);
HB = Hash ( C32 || ZB || P );
MB = MB || HB;
counter = counter + 1;
} while( counter <= threshold );
return oBits leftmost bits of MB
8. EC DH Algorithm (ECDH)
The method is a combination of ECC Diffie-Hellman method to
establish a shared secret and a key wrapping method that uses the
shared secret to protect symmetric encryption key.
One-Pass Diffie-Hellman method C(1, 1, ECC CDH), defined in [NIST
SP800-56A], SHOULD be implemented with the following restrictions:
ECC CDH primitive employed by this method is modified to always
assume the cofactor as 1, KDF specified in section 7 is used, and
KDF parameters specified below are used.
Key derivation parameters MUST be encoded as concatenation of the
following 7 fields, each of them, except the first one, is
considered a fixed-length field of corresponding size:
o a variable-length field containing curve OID, formatted as
follows
o a one-octet size of the following field
o octets representing curve OID, defined in section 11
o a one-octet public key algorithm ID defined in section 5
o a one-octet value 01, reserved for future extensions
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o a one-octet hash function ID used in KDF; according to section
7, this octet is 08 for SHA2-256, 09 for SHA2-384, or 10 for
SHA2-512
o a one-octet algorithm ID for the symmetric algorithm used to
wrap the symmetric key for message encryption; the method is
defined later in this section
o 15 octets representing the UTF-8 encoding of the string
"AnonymousSender"
o 20 octets representing recipient encryption subkey or master key
fingerprint, identifying the key material that is needed for
decryption
For three curves defined in this specification the size of the key
derivation parameters sequence, defined above, is either 48 or 45.
The key wrapping method is based on [RFC3394]. KDF produces the
AES key that is used as KEK according to [RFC3394]. Refer to
section 13 for the details regarding the choice of the KEK
algorithm, which MUST be one of three AES algorithms.
The input to key wrapping method is the value "m" derived from the
session key as described in section 5.1. Public-Key Encrypted
Session Key Packets (Tag 1) of [RFC4880], except, the PKCS#1.5
padding step is omitted. The result is padded using the method
described in [PKCS5] to the 8-byte granularity. For example, a
following AES-256 session key which 32 octets are denoted from k0
to k31 is composed as described bellow to form a 40 octet sequence:
09 k0 k1 ... k31 c0 c1 05 05 05 05 05
The octets c0 and c1 above denote the checksum. This encoding
allows the sender to obfuscate size of the symmetric encryption key
used to encrypt the data. To do this the sender MAY use 21, 13,
and 5 bytes of padding for AES-128, AES-192, and AES-256,
respectfully, to provide the same number of octets, 40 total, as an
input to the key wrapping method.
The output of the method consists of two fields. The first field
is the MPI with the ephemeral key used to establish shared
secret. The second field is composed of the following two fields:
o a one octet, encoding the size in octets of the result of the
key wrapping method; the value 255 is reserved for future
extensions
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o up to 254 octets representing the result of the key wrapping
method applied to session key encoded as described above
Note that for session key sizes 128, 192, and 256 bits the size of
the result of the key wrapping method is, respectfully, 32, 40, and
48 octets.
For convenience, the synopsis of the encoding method is given
below, however, this section, [NIST SP800-56A], and [RFC3394] are
the normative sources of the definition.
Obtain authenticated recipient public key R
Generate ephemeral key pair {v, V=vG}
Compute shared point S = vR;
m = symm_alg_ID || session key || checksum || pkcs5_padding;
curve_OID_len = (byte)len(curve_OID);
Param = curve_OID_len || curve_OID || public_key_alg_ID ||
01 || KDF_hash_ID || AES_alg_ID for AESKeyWrap ||
"AnonymousSender" || recipient_fingerprint;
Z_len = key size for AES_alg_ID to be used with AESKeyWrap
Compute Z = KDF( S, Z_len, Param );
Compute C = AESKeyWrap( Z, m ) as per [RFC3394]
VB = convert point V to octet string
Output (MPI(VB) || len(C) || C).
The decryption is the inverse of the method given. Note that the
recipient obtains the shared secret by calculating
S = rV = rvG, where (r,R) is the recipient's key pair.
Consistent with section 5.13 Sym. Encrypted Integrity Protected
Data Packet (Tag 18) of [RFC4880], the MDC SHOULD be used anytime
symmetric key is protected by ECDH.
9. Encoding of public and private keys
The following algorithm-specific packets are added to Section 5.5.2
Public-Key Packet Formats of [RFC4880] to support ECDH and ECDSA.
This algorithm-specific portion is:
Algorithm-Specific Fields for ECDH keys:
o a variable-length field containing curve OID, formatted as
follows
o a one-octet size of the following field; values 0 and
0xFF are reserved for future extensions
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o octets representing curve OID, defined in section 11
o a one-octet value 01, reserved for future extension
o a one-octet hash function ID used with KDF
o a one-octet algorithm ID for the symmetric algorithm used
to wrap the symmetric key for message encryption, see
section 8 for details
o MPI of EC point representing public key
Algorithm-Specific Fields for ECDSA keys:
o a variable-length field containing curve OID, formatted as
follows
o a one-octet size of the following field; values 0 and
0xFF are reserved for future extensions
o octets representing curve OID, defined in section 11
o MPI of EC point representing public key
The following algorithm-specific packets are added to section
5.5.3. Secret-Key Packet Formats of [RFC4880] to support ECDH and
ECDSA.
Algorithm-Specific Fields for ECDH or ECDSA secret keys:
o MPI of an integer representing the secret key, which is a
scalar of the EC point
10. Data encoding with public keys
Section 5.2.2. Version 3 Signature Packet Format defines signature
formats. No changes in format are needed for ECDSA.
Section 5.1. Public-Key Encrypted Session Key Packets (Tag 1) is
extended to support ECDH. The following two fields are result of
applying KDF, as described in section 8.
Algorithm Specific Fields for ECDH:
o an MPI of EC point representing ephemeral public key
o a one octet size, followed by a symmetric key encoded using
the method described in section 8.
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11. ECC curve OID
The parameter curve OID is an array of octets that define the named
curve. The table bellow specifies the exact sequence of bytes for
each named curve referenced in this specification:
ASN.1 Object OID Curve OID bytes in Curve name in
Identifier len hexadecimal [FIPS 186-2]
representation
1.2.840.10045.3.1.7 8 2A 86 48 CE 3D 03 01 07 NIST curve P-256
1.3.132.0.34 5 2B 81 04 00 22 NIST curve P-384
1.3.132.0.35 5 2B 81 04 00 23 NIST curve P-521
The sequence of octets in the third column is the result of
applying Distinguished Encoding Rules (DER) to the ASN.1 Object
Identifier with subsequent truncation. The truncation removes two
fields of encoded Object Identifier. The first omitted field is
one octet representing the Object Identifier tag and the second
omitted field is the length of the Object Identifier body. For
example, the complete ASN.1 DER encoding for the NIST P-256 curve
is "06 08 2A 86 48 CE 3D 03 01 07", from which the entry in the
table above is constructed by omitting two first octets.
12. Compatibility profiles
12.1. OpenPGP ECC profile
Application MUST implement NIST curve P-256, MAY implement NIST
curve P-384, and SHOULD implement NIST curve P-521, defined in
section 11. Application MUST implement SHA2-256 and SHOULD
implement SHA2-512. Application MUST implement AES-128 and SHOULD
implement AES-256.
Application SHOULD follow section 13 regarding the choice of the
following algorithms for each curve
o the KDF hash algorithm
o KEK algorithm
o message digest algorithm and hash algorithm used in key
certifications
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o message encryption symmetric algorithm.
It is recommended that the chosen symmetric algorithm for message
encryption be no less secure than the KEK algorithm.
12.2. Suite-B profile
A subset of algorithms allowed by this specification can be used to
achieve [Suite B] compatibility. The references to [Suite B] in
this document are informative. This document is primarily
concerned with format specification, leaving unspecified additional
security restrictions, such as matching security level of
information with authorized recipients or interoperability concerns
arising from fewer allowed algorithms in [Suite B] than in
[RFC4880].
12.2.1. Secret information
Applications MUST use NIST curves P-256 or P-384. KEK MUST be used
with AES-128 or AES-256. KDF MUST be used with SHA2-256 or
SHA2-384.
Note that the most secure algorithm in of each of 3 categories
above is also listed in the section 12.2.2.
12.2.2. Top Secret information
Application MUST use NIST curve P-384. KEK MUST be used with
AES-256. SHA2-384 MUST be used for KDF.
13. Security Considerations
The curves proposed in this document correspond to the symmetric
key sizes 128 bits, 192 bits, and 256 bits as described in the
table below. This allows OpenPGP application to offer security
comparable with the strength of each AES algorithms allowed by
[RFC4880].
The following table defines the hash and symmetric encryption
algorithm that SHOULD be used with specific curve for ECDSA or
ECDH. Stronger hash algorithm or symmetric key algorithm MAY be
used for a given ECC curve. However, note that the increase in the
strength of the hash algorithm or symmetric key algorithm may not
increase the overall security offered by the given ECC key.
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Curve name ECC RSA Hash size Symmetric
strength strength, key size
informative
NIST curve P-256 256 3072 256 128
NIST curve P-384 384 7680 384 192
NIST curve P-521 521 15360 512 256
Requirement levels indicated elsewhere in this document result in
the effective support for the following combinations of algorithms
in OpenPGP profile: MUST implement NIST curve P-256 / SHA2-256 /
AES-128, SHOULD implement NIST curve P-521 / SHA2-512 / AES-256,
MAY implement NIST curve P-384 / SHA2-384 / AES-256, among other
allowed combinations.
Consistent with the table above, the following table defines the
KDF hash algorithm and AES KEK encryption algorithm that SHOULD be
used with specific curve for ECDH. Stronger KDF hash algorithm or
KEK algorithm MAY be used for a given ECC curve.
Curve name Recommended KDF Recommended KEK
hash algorithm encryption algorithm
NIST curve P-256 SHA2-256 AES-128
NIST curve P-384 SHA2-384 AES-192
NIST curve P-521 SHA2-512 AES-256
Applications SHOULD implement, advertise through key preferences,
and use in compliance with [RFC4880] strongest algorithms specified
in this document.
Note that [RFC4880] symmetric algorithm preference list may
restrict the use of balanced strength of symmetric key algorithms
for corresponding public key. For example, the presence of
symmetric key algorithms and their order in key preference list
affects the choices available to encoding side for compliance with
the table above. Therefore, applications need to be concerned with
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this compliance throughout the life of the key, starting
immediately after key generation when the key preferences are first
added to a key. It is generally advisable to have at the head of
the key preference list a symmetric algorithm of strength
corresponding to the public key.
Often encryption to multiple recipients results in an unordered
intersection subset. For example, given two recipients, if first
recipient's set is {A, B} and second's is {B, A}, the intersection
is unordered set of two algorithms A and B. In this case
application SHOULD choose stronger encryption algorithm.
Resource constraint, such as limited computational power, is the
likely reason why an application might prefer to use weakest
algorithms. On the other side of the spectrum are applications
that can implement every algorithm defined in this document. Most
of applications are expected to fall into either of two
categories. An application in the second or strongest category
SHOULD prefer AES-256 to AES-192.
While some statements in this specification refer to TripleDES
algorithm, this is only done to help interoperability with existing
application and already generated keys; AES-256 is the recommended
alternative to TripleDES in all circumstances when AES-256 is
available.
SHA-1 MUST NOT be used for ECDSA or as part of ECDH method.
MDC MUST be used when symmetric encryption key is protected by
ECDH. None of the ECC methods described in this document are
allowed with deprecated V3 keys. The application MUST only use
Iterated and Salted S2K to protect private keys, as defined in
section 3.7.1.3 Iterated and Salted S2K of [RFC4880].
14. IANA Considerations
This document asks IANA to assign an algorithm number from OpenPGP
Public-Key Algorithms range, or "name space" in the terminology of
[RFC2434], that was created by [RFC4880]. Two ID numbers are
requested, as defined in section 5. The first one with value 19 is
already designated for ECDSA and currently unused, while another
one is new (and expected to be 22).
15. Normative references
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", March 1997
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[RFC4880] Callas, J., Donnerhacke, L., Finney, H., Shaw, D., and R.
Thayer, "OpenPGP Message Format", November 2007
[Suite B] NSA, US Government, Fact Sheet NSA Suite B Cryptography,
2005, http://www.nsa.gov/ia/Industry/crypto_suite_b.cfm
[FIPS 186-2] US Dept. of Commerce / NIST, "DIGITAL SIGNATURE
STANDARD (DSS)", 2001 October 5
[SEC1] Certicom Research, "SEC 1: Elliptic Curve Cryptography",
September 20, 2000
[NIST SP800-56A] Elaine Barker, Don Johnson, and Miles Smid,
"Recommendation for Pair-WiseKey Establishment Schemes Using
Discrete Logarithm Cryptography (Revised)", March, 2007
[FIPS 180-2] NIST, SECURE HASH STANDARD, 2002 August 1
[RFC3394] J. Schaad, R. Housley, "Advanced Encryption Standard
(AES) Key Wrap Algorithm", September 2002
[PKCS5] RSA Laboratories, PKCS #5 v2.0: Password-Based Cryptography
Standard, March 25, 1999
Contributors
Hal Finney provided important criticism on compliance with [NIST
SP800-56A] and [Suite B], and pointed out a few other mistakes.
Acknowledgment
The author would like to acknowledge the help of many individuals
who kindly voiced their opinions on IETF OpenPGP Working Group
mailing list and, in particular the help of Jon Callas, David
Crick, Ian G, Werner Koch. [to be continued]
Author's Address
Andrey Jivsov
PGP Corporation
Email: ajivsov@pgp.com
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