Network Working Group A. Jivsov Internet Draft Symantec Corporation Intended status: Standards March 26, 2012 Expires: September 22, 2012 ECC in OpenPGP draft-jivsov-openpgp-ecc-11.txt 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 NIST standards. The document aims to standardize an optimal but narrow set of parameters for easier interoperability between compliant OpenPGP implementations. Status of this Memo This Internet-Draft is submitted to IETF in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as Internet-Drafts. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at http://www.ietf.org/ietf/1id-abstracts.txt. The list of Internet-Draft Shadow Directories can be accessed at http://www.ietf.org/shadow.html. This Internet-Draft will expire on September 22, 2012. Copyright Notice A. Jivsov Expires September 22, 2012 [Page 1]

Internet-Draft ECC in OpenPGP March 2012 Copyright (c) 2011 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.................................................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..........................8 10. Message encoding with public keys...........................9 11. ECC curve OID...............................................9 12. Compatibility profiles.....................................10 12.1. OpenPGP ECC profile...................................10 12.2. Suite-B profile.......................................10 12.2.1. Security strength at 192 bits....................10 12.2.2. Security strength at 128 bits....................11 13. Security Considerations....................................11 14. IANA Considerations........................................13 15. References.................................................13 15.1. Normative references..................................13 15.2. Informative references................................14 1. Introduction The OpenPGP protocol [RFC4880] 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]. A. Jivsov Expires September 22, 2012 [Page 2]

Internet-Draft ECC in OpenPGP March 2012 Any implementation MAY adhere to the format and methods specified in this document, in which case such an implementation is called a compliant application. Note that any [RFC2119] keyword within this document applies to an OpenPGP application only if it chooses to be a compliant application. 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. National Security Agency (NSA) of the United States specifies ECC for use in its [Suite B] 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 this document 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) [FIPS 186-3] and Elliptic Curve Diffie- Hellman (ECDH), defined in section 8. A compatible specification of ECDSA is given in [RFC6090] as "KT-I Signatures" and in [SEC1]. The following public key algorithm IDs are added to expand the section 9.1. Public-Key Algorithms of [RFC4880]: A. Jivsov Expires September 22, 2012 [Page 3]

Internet-Draft ECC in OpenPGP March 2012 ID Description of algorithm [to be ECDH public key algorithm ASSIGNED] presumably 18 19 ECDSA public key algorithm Compliant applications MUST support ECDSA and ECDH. 6. Conversion primitives This document only defines uncompressed point format. The point is encoded in the Multiprecision Integer (MPI) format [RFC4880]. 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 adjusted underlying field size. The adjusted underlying field size is the underlying field size that is rounded up to the nearest 8-bit boundary. 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 the point O shall not appear in a public or a private key. 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". This encoding is compatible with the definition given in [SEC1]. If other conversion methods are defined in the future, a compliant application MAY use them only when it is certain that every recipient can support another format. 7. Key Derivation Function A key derivation function (KDF) is necessary to implement EC encryption. The Concatenation Key Derivation Function (Approved A. Jivsov Expires September 22, 2012 [Page 4]

Internet-Draft ECC in OpenPGP March 2012 Alternative 1) [NIST SP800-56A] is REQUIRED with the following restriction: the KDF hash function MAY be based on any of the following hash functions specified by [FIPS 180-3]: 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 with significant simplifications applicable to the choice of hash function. However, [NIST SP800-56A] is the normative source of the definition. // 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 // Assumes that oBits <= 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; MB = Hash ( 00 || 00 || 00 || 01 || ZB || P ); 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, 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. One-Pass Diffie-Hellman method C(1, 1, ECC CDH) [NIST SP800-56A] MUST 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 function parameters MUST be encoded as concatenation of the following 5 variable-length and fixed-length fields: o a variable-length field containing curve OID, formatted as follows o a one-octet size of the following field A. Jivsov Expires September 22, 2012 [Page 5]

Internet-Draft ECC in OpenPGP March 2012 o octets representing curve OID, defined in section 11 o a one-octet public key algorithm ID defined in section 5 o a variable-length field containing KDF parameters, identical to the corresponding filed in the ECDH public key, formatted as follows o a one-octet size of the following fields; values 0 and 0xff are reserved for future extensions 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 20 octets representing the UTF-8 encoding of the string "Anonymous Sender " 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 document the size of the key derivation parameters sequence, defined above, is either 54 or 51. The key wrapping method is based on [RFC3394]. KDF produces a symmetric key that is used as 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. The input to the 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 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, A. Jivsov Expires September 22, 2012 [Page 6]

Internet-Draft ECC in OpenPGP March 2012 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 o 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, respectfully, 32, 40, and 48 octets, unless 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 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 || 03 || 01 || KDF_hash_ID || KEK_alg_ID for AESKeyWrap || "Anonymous Sender " || recipient_fingerprint; Z_len = key size for KEK_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 MUST be used anytime symmetric key is protected by ECDH. A. Jivsov Expires September 22, 2012 [Page 7]

Internet-Draft ECC in OpenPGP March 2012 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 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 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 o octets representing curve OID, defined in section 11 o MPI of EC point representing public key o a variable-length field containing KDF parameters, formatted as follows o a one-octet size of the following fields; values 0 and 0xff are reserved for future extensions 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 used for 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 and the KDF parameters field. A. Jivsov Expires September 22, 2012 [Page 8]

Internet-Draft ECC in OpenPGP March 2012 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. Message 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. 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 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 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 A. Jivsov Expires September 22, 2012 [Page 9]

Internet-Draft ECC in OpenPGP March 2012 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 first entry in the table above is constructed by omitting the first two octets. 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, defined in section 11. A compliant application MUST implement SHA2-256 and SHOULD implement 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: o the KDF hash algorithm o KEK algorithm o message digest algorithm and hash algorithm used in key certifications o 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 [Suite B] compatibility. The references to [Suite B] in this document are informative. This document is primarily concerned with format specification, leaving additional security restrictions unspecified, such as matching assigned security level of information to authorized recipients or interoperability concerns arising from fewer allowed algorithms in [Suite B] than allowed by [RFC4880]. 12.2.1. Security strength at 192 bits To achieve the security strength of 192 bits [Suite B] requires NIST curve P-384, AES-256, and SHA2-384. Symmetric algorithm restriction means that the algorithm of KEK used for key wrapping in section 8 and a [RFC4880] session key used for message encryption must be AES-256. Hash algorithm restriction means that the hash algorithms of KDF and [RFC4880] message digest calculation must be SHA-384. A. Jivsov Expires September 22, 2012 [Page 10]

Internet-Draft ECC in OpenPGP March 2012 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 symmetric key strength for 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. 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 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 AES KEK algorithm MAY be used for a given ECC curve. A. Jivsov Expires September 22, 2012 [Page 11]

Internet-Draft ECC in OpenPGP March 2012 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. 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 as 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] 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 the corresponding public key. For example, the presence of symmetric key algorithms and their order in the key preference list affects the algorithm choices available to the encoding side, which in turn may make unfeasible the adherence to the table above. Therefore, compliance with this specification is a concern 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 a symmetric algorithm of strength matching the public key at the head of the key preference list. Often encryption to multiple recipients results in an unordered intersection subset. For example, given two recipients, if the first recipient's set is {A, B} and the second's is {B, A}, the intersection is unordered set of two algorithms A and B. In this case a compliant 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 applications are expected to fall into either of two categories. A A. Jivsov Expires September 22, 2012 [Page 12]

Internet-Draft ECC in OpenPGP March 2012 compliant application in the second or strongest category SHOULD prefer AES-256 to AES-192. While some statements in this document refer to TripleDES algorithm, this is only done to help interoperability with existing OpenPGP applications 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 with KDF in 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. A compliant 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 suggested to be 18; there is an implementation advantage in having consecutive ID values for two complementary algorithms). 15. References 15.1. Normative references [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", March 1997 [RFC4880] Callas, J., Donnerhacke, L., Finney, H., Shaw, D., and R. Thayer, "OpenPGP Message Format", November 2007 [Suite B] NSA, US Government, NSA Suite B Cryptography, March 11, 2010, http://www.nsa.gov/ia/programs/suiteb_cryptography/ [FIPS 186-3] US Dept. of Commerce / NIST, "Digital Signature Standard (DSS)", June 2009 [NIST SP800-56A] Elaine Barker, Don Johnson, and Miles Smid, "Recommendation for Pair-WiseKey Establishment Schemes Using Discrete Logarithm Cryptography (Revised)", March 2007 [FIPS 180-3] NIST, "Secure Hash Standard (SHS)", October 2008 A. Jivsov Expires September 22, 2012 [Page 13]

Internet-Draft ECC in OpenPGP March 2012 [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 [RFC2434] Narten, T., Alvestrand, H., "Guidelines for Writing IANA Considerations Section in RFCs", October 1998 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", February 2011, [SEC1] Certicom Research, "SEC 1: Elliptic Curve Cryptography", September 20, 2000 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, Marko Kreen. Author's Address Andrey Jivsov Symantec Corporation Email: Andrey_Jivsov@symantec.com A. Jivsov Expires September 22, 2012 [Page 14]