Network Working Group A. Jivsov Internet Draft Symantec Corporation Intended status: Standards April 11, 2012 Expires: October 8, 2012 ECC in OpenPGP draft-jivsov-openpgp-ecc-14.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 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. 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 October 8, 2012. Copyright Notice A. Jivsov Expires October 8, 2012 [Page 1]

Internet-Draft ECC in OpenPGP April 2012 Copyright (c) 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.................................................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 October 8, 2012 [Page 2]

Internet-Draft ECC in OpenPGP April 2012 Any implementation that adheres to the format and methods specified in this document is called a compliant application. Compliant applications is a subset of the the broader set of [RFC4880] OpenPGP applications. 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. 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 The supported public key algorithms are Elliptic Curve Digital Signature Algorithm (ECDSA) [FIPS 186-3] and 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. The following public key algorithm IDs are added to expand the section 9.1. Public-Key Algorithms of [RFC4880]: A. Jivsov Expires October 8, 2012 [Page 3]

Internet-Draft ECC in OpenPGP April 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 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 A. Jivsov Expires October 8, 2012 [Page 4]

Internet-Draft ECC in OpenPGP April 2012 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 is the compact representation of X, defined in section 4.2 of [RFC6090] 8. EC DH Algorithm (ECDH) The method is a combination of a 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 concatenation of the following 5 variable-length and fixed-length fields, compatible with the definition of the OtherInfo bitstring [NIST SP800-56A]: o a variable-length field containing a curve OID, formatted as follows o a one-octet size of the following field o the octets representing a curve OID, defined in section 11 A. Jivsov Expires October 8, 2012 [Page 5]

Internet-Draft ECC in OpenPGP April 2012 o a one-octet public key algorithm ID defined in section 5 o a variable-length field containing KDF parameters, identical to the corresponding field 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 extensions o a one-octet hash function ID used with the 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 ", 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 o 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 pameters 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 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. 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 October 8, 2012 [Page 6]

Internet-Draft ECC in OpenPGP April 2012 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: 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, 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 Sym. Encrypted Integrity Protected Data Packet (Tag 18) of [RFC4880], MDC MUST be used anytime symmetric key is protected by ECDH. A. Jivsov Expires October 8, 2012 [Page 7]

Internet-Draft ECC in OpenPGP April 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 a 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 a curve OID, defined in section 11 o MPI of an EC point representing a public key Algorithm-Specific Fields for ECDH keys: o a variable-length field containing a curve OID, formatted as follows o a one-octet size of the following field; values 0 and 0xFF are reserved for future extensions o the octets representing a 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 extensions o a one-octet hash function ID used with a KDF o 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. A. Jivsov Expires October 8, 2012 [Page 8]

Internet-Draft ECC in OpenPGP April 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 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. Version 3 Signature Packet Format defines signature formats. No changes in the 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 the result of applying the KDF, as described in section 8. Algorithm Specific Fields for ECDH: o an MPI of 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 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 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 A. Jivsov Expires October 8, 2012 [Page 9]

Internet-Draft ECC in OpenPGP April 2012 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, 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: o the KDF hash algorithm o the KEK algorithm o the message digest algorithm and the hash algorithm used in the key certifications o 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 [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. The 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. The hash algorithm restriction means A. Jivsov Expires October 8, 2012 [Page 10]

Internet-Draft ECC in OpenPGP April 2012 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 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. Stronger KDF hash algorithm or AES KEK algorithm MAY be used for a given ECC curve. A. Jivsov Expires October 8, 2012 [Page 11]

Internet-Draft ECC in OpenPGP April 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. 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 unfeasible. 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 A. Jivsov Expires October 8, 2012 [Page 12]

Internet-Draft ECC in OpenPGP April 2012 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 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]. Side channel attacks are a concern when a compliant application's use of 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 ECC point addition and doubling operations. 14. IANA Considerations This document asks IANA to assign an algorithm number from the OpenPGP Public-Key Algorithms range, or the "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 is currently unused, while another one is new (and suggested to be 18; there is an implementation advantage in having consecutive ID values for the 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 A. Jivsov Expires October 8, 2012 [Page 13]

Internet-Draft ECC in OpenPGP April 2012 [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 [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 October 8, 2012 [Page 14]