Elliptic Curve Cryptography (ECC) in OpenPGP

Abstract

This document defines an Elliptic Curve Cryptography extension to the OpenPGP public key format and specifies three Elliptic Curves that enjoy broad support by other standards, including standards published by the US National Institute of Standards and Technology. The document specifies the conventions for interoperability between compliant OpenPGP implementations that make use of this extension and these Elliptic Curves.

Status of This Memo

This is an Internet Standards Track document.

This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Further information on Internet Standards is available in Section 2 of RFC 5741.

Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at http://www.rfc-editor.org/info/rfc6637.

Copyright Notice

Copyright © 2012 IETF Trust and the persons identified as the document authors. All rights reserved.

This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.

Table of Contents

   1. Introduction ....................................................3
   2. Conventions used in This Document ...............................3
   3. Elliptic Curve Cryptography .....................................3
   4. Supported ECC Curves ............................................3
   5. Supported Public Key Algorithms .................................4
   6. Conversion Primitives ...........................................4
   7. Key Derivation Function .........................................5
   8. EC DH Algorithm (ECDH) ..........................................5
   9. Encoding of Public and Private Keys .............................8
   10. Message Encoding with Public Keys ..............................9
   11. ECC Curve OID .................................................10
   12. Compatibility Profiles ........................................10
      12.1. OpenPGP ECC Profile ......................................10
      12.2. Suite-B Profile ..........................................11
           12.2.1. Security Strength at 192 Bits .....................11
           12.2.2. Security Strength at 128 Bits .....................11
   13. Security Considerations .......................................12
   14. IANA Considerations ...........................................14
   15. References ....................................................14
      15.1. Normative References .....................................14
      15.2. Informative References ...................................15
   16. Contributors ..................................................15
   17. Acknowledgment ................................................15

1. Introduction

The OpenPGP protocol [RFC4880] supports RSA and DSA (Digital Signature Algorithm) 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]. Any implementation that adheres to the format and methods specified in this document is called a compliant application. Compliant applications are a subset of the broader set of OpenPGP applications described in [RFC4880]. Any [RFC2119] keyword within this document applies to compliant applications only.

3. Elliptic Curve Cryptography

This document establishes the minimum set of Elliptic Curve Cryptography (ECC) public key parameters and cryptographic methods that will likely satisfy the widest range of platforms and applications and facilitate interoperability. It adds a more efficient method for applications to balance the overall level of security with any AES algorithm specified in [RFC4880] than by simply increasing the size of RSA keys. This document defines a path to expand ECC support in the future.

The National Security Agency (NSA) of the United States specifies ECC for use in its [SuiteB] set of algorithms. This document includes algorithms required by Suite B that are not present in [RFC4880].

[KOBLITZ] provides a thorough introduction to ECC.

4. Supported ECC Curves

This document references three named prime field curves, defined in [FIPS-186-3] as "Curve P-256", "Curve P-384", and "Curve P-521".

The named curves are referenced as a sequence of bytes in this document, called throughout, curve OID. Section 11 describes in detail how this sequence of bytes is formed.

5. Supported Public Key Algorithms

The supported public key algorithms are the Elliptic Curve Digital Signature Algorithm (ECDSA) [FIPS-186-3] and the Elliptic Curve Diffie-Hellman (ECDH). A compatible specification of ECDSA is given in [RFC6090] as "KT-I Signatures" and in [SEC1]; ECDH is defined in Section 8 of this document.

The following public key algorithm IDs are added to expand Section 9.1 of [RFC4880], "Public-Key Algorithms":

          ID        Description of Algorithm
          --        --------------------------
          18        ECDH public key algorithm
          19        ECDSA public key algorithm

Compliant applications MUST support ECDSA and ECDH.

6. Conversion Primitives

This document only defines the uncompressed point format. The point is encoded in the Multiprecision Integer (MPI) format [RFC4880]. The content of the MPI is the following:

      B = 04 || x || y

where x and y are coordinates of the point P = (x, y), each encoded in the big-endian format and zero-padded to the adjusted underlying field size. The adjusted underlying field size is the underlying field size that is rounded up to the nearest 8-bit boundary.

Therefore, the exact size of the MPI payload is 515 bits for "Curve P-256", 771 for "Curve P-384", and 1059 for "Curve P-521".

Even though the zero point, also called the point at infinity, may occur as a result of arithmetic operations on points of an elliptic curve, it SHALL NOT appear in data structures defined in this document.

This encoding is compatible with the definition given in [SEC1].

If other conversion methods are defined in the future, a compliant application MUST NOT use a new format when in doubt that any recipient can support it. Consider, for example, that while both the public key and the per-recipient ECDH data structure, respectively defined in Sections 9 and 10, contain an encoded point field, the format changes to the field in Section 10 only affect a given recipient of a given message.

7. Key Derivation Function

A key derivation function (KDF) is necessary to implement the EC encryption. The Concatenation Key Derivation Function (Approved Alternative 1) [NIST-SP800-56A] with the KDF hash function that is SHA2-256 [FIPS-180-3] or stronger is REQUIRED. See Section 12 for the details regarding the choice of the hash function.

For convenience, the synopsis of the encoding method is given below with significant simplifications attributable to the restricted choice of hash functions in this document. However, [NIST-SP800-56A] is the normative source of the definition.

          //   Implements KDF( X, oBits, Param );
          //   Input: point X = (x,y)
          //   oBits - the desired size of output
          //   hBits - the size of output of hash function Hash
          //   Param - octets representing the parameters
          //   Assumes that oBits <= hBits
         // Convert the point X to the octet string, see section 6:
         //   ZB' = 04 || x || y
         // and extract the x portion from ZB'
         ZB = x;
         MB = Hash ( 00 || 00 || 00 || 01 || ZB || Param );
         return oBits leftmost bits of MB.

Note that ZB in the KDF description above is the compact representation of X, defined in Section 4.2 of [RFC6090].

8. EC DH Algorithm (ECDH)

The method is a combination of an ECC Diffie-Hellman method to establish a shared secret, a key derivation method to process the shared secret into a derived key, and a key wrapping method that uses the derived key to protect a session key used to encrypt a message.

The One-Pass Diffie-Hellman method C(1, 1, ECC CDH) [NIST-SP800-56A] MUST be implemented with the following restrictions: the ECC CDH primitive employed by this method is modified to always assume the cofactor as 1, the KDF specified in Section 7 is used, and the KDF parameters specified below are used.

The KDF parameters are encoded as a concatenation of the following 5 variable-length and fixed-length fields, compatible with the definition of the OtherInfo bitstring [NIST-SP800-56A]:

• a variable-length field containing a curve OID, formatted as follows:

• a one-octet size of the following field

• the octets representing a curve OID, defined in Section 11

• a one-octet public key algorithm ID defined in Section 5

• a variable-length field containing KDF parameters, identical to the corresponding field in the ECDH public key, formatted as follows:

• a one-octet size of the following fields; values 0 and 0xff are reserved for future extensions

- a one-octet value 01, reserved for future extensions

- a one-octet hash function ID used with the KDF

• a one-octet algorithm ID for the symmetric algorithm used to wrap the symmetric key for message encryption; see Section 8 for details

• 20 octets representing the UTF-8 encoding of the string "Anonymous Sender ", which is the octet sequence 41 6E 6F 6E 79 6D 6F 75 73 20 53 65 6E 64 65 72 20 20 20 20

• 20 octets representing a recipient encryption subkey or a master key fingerprint, identifying the key material that is needed for the decryption

The size of the KDF parameters sequence, defined above, is either 54 or 51 for the three curves defined in this document.

The key wrapping method is described in [RFC3394]. KDF produces a symmetric key that is used as a key-encryption key (KEK) as specified in [RFC3394]. Refer to Section 13 for the details regarding the choice of the KEK algorithm, which SHOULD be one of three AES algorithms. Key wrapping and unwrapping is performed with the default initial value of [RFC3394].

The input to the key wrapping method is the value "m" derived from the session key, as described in Section 5.1 of [RFC4880], "Public- Key Encrypted Session Key Packets (Tag 1)", except that the PKCS #1.5 (Public-Key Cryptography Standards version 1.5) padding step is omitted. The result is padded using the method described in [PKCS5] to the 8-byte granularity. For example, the following AES-256 session key, in which 32 octets are denoted from k0 to k31, is composed to form the following 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 the size of the symmetric encryption key used to encrypt the data. For example, assuming that an AES algorithm is used for the session key, the sender MAY use 21, 13, and 5 bytes of padding for AES-128, AES-192, and AES-256, respectively, 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 containing the ephemeral key used to establish the shared secret. The second field is composed of the following two fields:

• a one-octet encoding the size in octets of the result of the key wrapping method; the value 255 is reserved for future extensions

• up to 254 octets representing the result of the key wrapping method, applied to the 8-byte padded session key, 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, respectively, 32, 40, and 48 octets, unless the size obfuscation is used.

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 the authenticated recipient public key R
         Generate an ephemeral key pair {v, V=vG}
         Compute the 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 || 03
         || 01 || KDF_hash_ID || KEK_alg_ID for AESKeyWrap || "Anonymous
         Sender    " || recipient_fingerprint;
         Z_len = the key size for the KEK_alg_ID used with AESKeyWrap
         Compute Z = KDF( S, Z_len, Param );
         Compute C = AESKeyWrap( Z, m ) as per [RFC3394]
         VB = convert point V to the 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 of [RFC4880], "Sym. Encrypted Integrity Protected Data Packet (Tag 18)", a Modification Detection Code (MDC) MUST be used anytime the 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 of [RFC4880], "Public-Key Packet Formats", to support ECDH and ECDSA.

This algorithm-specific portion is:

Algorithm-Specific Fields for ECDSA keys:

• a variable-length field containing a curve OID, formatted as follows:

• a one-octet size of the following field; values 0 and 0xFF are reserved for future extensions

- octets representing a curve OID, defined in Section 11

• MPI of an EC point representing a public key

Algorithm-Specific Fields for ECDH keys:

• a variable-length field containing a curve OID, formatted as follows:

• a one-octet size of the following field; values 0 and 0xFF are reserved for future extensions

• the octets representing a curve OID, defined in Section 11

• MPI of an EC point representing a public key

• a variable-length field containing KDF parameters, formatted as follows:

• a one-octet size of the following fields; values 0 and 0xff are reserved for future extensions

- a one-octet value 01, reserved for future extensions

• a one-octet hash function ID used with a KDF

- a one-octet algorithm ID for the symmetric algorithm

used to wrap the symmetric key used for the message

encryption; see Section 8 for details

Observe that an ECDH public key is composed of the same sequence of fields that define an ECDSA key, plus the KDF parameters field.

The following algorithm-specific packets are added to Section 5.5.3. of [RFC4880], "Secret-Key Packet Formats", to support ECDH and ECDSA.

Algorithm-Specific Fields for ECDH or ECDSA secret keys:

• an MPI of an integer representing the secret key, which is a scalar of the public EC point

10. Message Encoding with Public Keys

Section 5.2.2 of [RFC4880], "Version 3 Signature Packet Format" defines signature formats. No changes in the format are needed for ECDSA.

Section 5.1 of [RFC4880], "Public-Key Encrypted Session Key Packets (Tag 1)" is extended to support ECDH. The following two fields are the result of applying the KDF, as described in Section 8.

Algorithm-Specific Fields for ECDH:

• an MPI of an EC point representing an ephemeral public key

o a one-octet size, followed by a symmetric key encoded using the

method described in Section 8

11. ECC Curve OID

The parameter curve OID is an array of octets that define a named curve. The table below specifies the exact sequence of bytes for each named curve referenced in this document:

   ASN.1 Object          OID Curve OID bytes in         Curve name in
   Identifier            len hexadecimal                [FIPS-186-3]
                             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 the Distinguished Encoding Rules (DER) to the ASN.1 Object Identifier with subsequent truncation. The truncation removes the 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 OID is "06 08 2A 86 48 CE 3D 03 01 07", from which the first entry in the table above is constructed by omitting the first two octets. Only the truncated sequence of octets is the valid representation of a curve OID.

12. Compatibility Profiles

12.1. OpenPGP ECC Profile

A compliant application MUST implement NIST curve P-256, MAY implement NIST curve P-384, and SHOULD implement NIST curve P-521, as defined in Section 11. A compliant application MUST implement SHA2-256 and SHOULD implement SHA2-384 and SHA2-512. A compliant application MUST implement AES-128 and SHOULD implement AES-256.

A compliant application SHOULD follow Section 13 regarding the choice of the following algorithms for each curve:

• the KDF hash algorithm

• the KEK algorithm

• the message digest algorithm and the hash algorithm used in the key certifications

• the symmetric algorithm used for message encryption.

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 document can be used to achieve [SuiteB] compatibility. The references to [SuiteB] in this document are informative. This document is primarily concerned with format specification, leaving additional security restrictions unspecified, such as matching the assigned security level of information to authorized recipients or interoperability concerns arising from fewer allowed algorithms in [SuiteB] than allowed by [RFC4880].

12.2.1. Security Strength at 192 Bits

To achieve the security strength of 192 bits, [SuiteB] requires NIST curve P-384, AES-256, and SHA2-384. The symmetric algorithm restriction means that the algorithm of KEK used for key wrapping in Section 8 and an [RFC4880] session key used for message encryption must be AES-256. The hash algorithm restriction means that the hash algorithms of KDF and the [RFC4880] message digest calculation must be SHA-384.

12.2.2. Security Strength at 128 Bits

The set of algorithms in Section 12.2.1 is extended to allow NIST curve P-256, AES-128, and SHA2-256.

13. Security Considerations

Refer to [FIPS-186-3], B.4.1, for the method to generate a uniformly distributed ECC private key.

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 a compliant application to offer balanced public key security, which is compatible with the symmetric key strength for each AES algorithm allowed by [RFC4880].

The following table defines the hash and the symmetric encryption algorithm that SHOULD be used with a given curve for ECDSA or ECDH. A stronger hash algorithm or a symmetric key algorithm MAY be used for a given ECC curve. However, note that the increase in the strength of the hash algorithm or the symmetric key algorithm may not increase the overall security offered by the given ECC key.

   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 lead to the following combinations of algorithms in the 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 the AES KEK encryption algorithm that SHOULD be used with a given curve for ECDH. A stronger KDF hash algorithm or AES 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

This document explicitly discourages the use of algorithms other than AES as a KEK algorithm because backward compatibility of the ECDH format is not a concern. The KEK algorithm is only used within the scope of a Public-Key Encrypted Session Key Packet, which represents an ECDH key recipient of a message. Compare this with the algorithm used for the session key of the message, which MAY be different from a KEK algorithm.

Compliant applications SHOULD implement, advertise through key preferences, and use in compliance with [RFC4880], the strongest algorithms specified in this document.

Note that the [RFC4880] symmetric algorithm preference list may make it impossible to use the balanced strength of symmetric key algorithms for a corresponding public key. For example, the presence of the symmetric key algorithm IDs and their order in the key preference list affects the algorithm choices available to the encoding side, which in turn may make the adherence to the table above infeasible. Therefore, compliance with this specification is a concern throughout the life of the key, starting immediately after the key generation when the key preferences are first added to a key. It is generally advisable to position a symmetric algorithm ID of strength matching the public key at the head of the key preference list.

Encryption to multiple recipients often results in an unordered intersection subset. For example, if the first recipient's set is {A, B} and the second's is {B, A}, the intersection is an unordered set of two algorithms, A and B. In this case, a compliant application SHOULD choose the stronger encryption algorithm.

Resource constraints, such as limited computational power, is a likely reason why an application might prefer to use the weakest algorithm. On the other side of the spectrum are applications that can implement every algorithm defined in this document. Most applications are expected to fall into either of two categories. A compliant application in the second, or strongest, category SHOULD prefer AES-256 to AES-192.

SHA-1 MUST NOT be used with the ECDSA or the KDF in the ECDH method.

MDC MUST be used when a symmetric encryption key is protected by ECDH. None of the ECC methods described in this document are allowed with deprecated V3 keys. A compliant application MUST only use iterated and salted S2K to protect private keys, as defined in Section 3.7.1.3 of [RFC4880], "Iterated and Salted S2K".

Side channel attacks are a concern when a compliant application's use of the OpenPGP format can be modeled by a decryption or signing oracle model, for example, when an application is a network service performing decryption to unauthenticated remote users. ECC scalar multiplication operations used in ECDSA and ECDH are vulnerable to side channel attacks. Countermeasures can often be taken at the higher protocol level, such as limiting the number of allowed failures or time-blinding of the operations associated with each network interface. Mitigations at the scalar multiplication level seek to eliminate any measurable distinction between the ECC point addition and doubling operations.

14. IANA Considerations

Per this document, IANA has assigned an algorithm number from the "Public Key Algorithms" range (or the "name space" in the terminology of [RFC5226]) of the "Pretty Good Privacy (PGP)" registry, created by [RFC4880]. Two ID numbers have been assigned, as defined in Section 5. The first one, value 19, is already designated for ECDSA and is currently unused, while the other one, value 18, is new.

15. References

15.1. Normative References

   [RFC2119]        Bradner, S., "Key words for use in RFCs to Indicate
                    Requirement Levels", BCP 14, RFC 2119, March 1997.
   
   [RFC4880]        Callas, J., Donnerhacke, L., Finney, H., Shaw, D.,
                    and R. Thayer, "OpenPGP Message Format", RFC 4880,
                    November 2007.
   
   [SuiteB]         National Security Agency, "NSA Suite B
                    Cryptography", March 11, 2010,
                    http://www.nsa.gov/ia/programs/suiteb_cryptography/.
   
   [FIPS-186-3]     National Institute of Standards and Technology, U.S.
                    Department of Commerce, "Digital Signature
                    Standard", FIPS 186-3, June 2009.
   
   [NIST-SP800-56A] Barker, E., Johnson, D., and M. Smid,
                    "Recommendation for Pair-Wise Key Establishment
                    Schemes Using Discrete Logarithm Cryptography", NIST
                    Special Publication 800-56A Revision 1, March 2007.
   
   [FIPS-180-3]     National Institute of Standards and Technology, U.S.
                    Department of Commerce, "Secure Hash Standard
                    (SHS)", FIPS 180-3, October 2008.
   
   [RFC3394]        Schaad, J. and R. Housley, "Advanced Encryption
                    Standard (AES) Key Wrap Algorithm", RFC 3394,
                    September 2002.
   
   [PKCS5]          RSA Laboratories, "PKCS #5 v2.0: Password-Based
                    Cryptography Standard", March 25, 1999.
   
   [RFC5226]        Narten, T. and H. Alvestrand, "Guidelines for
                    Writing an IANA Considerations Section in RFCs", BCP
                    26, RFC 5226, May 2008.

15.2. Informative References

   [KOBLITZ]        N. Koblitz, "A course in number theory and
                    cryptography", Chapter VI. Elliptic Curves, ISBN:
                    0-387-96576-9, Springer-Verlag, 1987
   
   [RFC6090]        McGrew, D., Igoe, K., and M. Salter, "Fundamental
                    Elliptic Curve Cryptography Algorithms", RFC 6090,
                    February 2011.
   
   [SEC1]           Standards for Efficient Cryptography Group, "SEC 1:
                    Elliptic Curve Cryptography", September 2000.

16. Contributors

Hal Finney provided important criticism on compliance with [NIST-SP800-56A] and [SuiteB], and pointed out a few other mistakes.

17. Acknowledgment

The author would like to acknowledge the help of many individuals who kindly voiced their opinions on the IETF OpenPGP Working Group mailing list, in particular, the help of Jon Callas, David Crick, Ian G, Werner Koch, and Marko Kreen.

Author's Address

   Andrey Jivsov
   Symantec Corporation
   EMail: Andrey_Jivsov@symantec.com