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Checking references for intended status: Informational ---------------------------------------------------------------------------- ** Obsolete normative reference: RFC 5996 (Obsoleted by RFC 7296) Summary: 1 error (**), 0 flaws (~~), 1 warning (==), 1 comment (--). Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 Network Working Group J. Merkle 3 Internet-Draft secunet Security Networks 4 Intended status: Informational M. Lochter 5 Expires: October 25, 2013 Bundesamt fuer Sicherheit in der 6 Informationstechnik (BSI) 7 April 23, 2013 9 Using the ECC Brainpool Curves for IKEv2 Key Exchange 10 draft-merkle-ikev2-ke-brainpool-06 12 Abstract 14 This document specifies the use of ECC Brainpool elliptic curve 15 groups for key exchange in the Internet Key Exchange version 2 16 (IKEv2) protocol. 18 Status of This Memo 20 This Internet-Draft is submitted in full conformance with the 21 provisions of BCP 78 and BCP 79. 23 Internet-Drafts are working documents of the Internet Engineering 24 Task Force (IETF). Note that other groups may also distribute 25 working documents as Internet-Drafts. The list of current Internet- 26 Drafts is at http://datatracker.ietf.org/drafts/current/. 28 Internet-Drafts are draft documents valid for a maximum of six months 29 and may be updated, replaced, or obsoleted by other documents at any 30 time. It is inappropriate to use Internet-Drafts as reference 31 material or to cite them other than as "work in progress." 33 This Internet-Draft will expire on October 25, 2013. 35 Copyright Notice 37 Copyright (c) 2013 IETF Trust and the persons identified as the 38 document authors. All rights reserved. 40 This document is subject to BCP 78 and the IETF Trust's Legal 41 Provisions Relating to IETF Documents 42 (http://trustee.ietf.org/license-info) in effect on the date of 43 publication of this document. Please review these documents 44 carefully, as they describe your rights and restrictions with respect 45 to this document. Code Components extracted from this document must 46 include Simplified BSD License text as described in Section 4.e of 47 the Trust Legal Provisions and are provided without warranty as 48 described in the Simplified BSD License. 50 Table of Contents 52 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 53 1.1. Requirements Language . . . . . . . . . . . . . . . . . . 3 54 2. IKEv2 Key Exchange using the ECC Brainpool Curves . . . . . . 4 55 2.1. Diffie-Hellman Group Transform IDs . . . . . . . . . . . . 4 56 2.2. Using the Twisted Brainpool Curves Internally . . . . . . 4 57 2.3. Key Exchange Payload and Shared Secret . . . . . . . . . . 4 58 3. Security Considerations . . . . . . . . . . . . . . . . . . . 6 59 4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 7 60 5. References . . . . . . . . . . . . . . . . . . . . . . . . . . 8 61 5.1. Normative References . . . . . . . . . . . . . . . . . . . 8 62 5.2. Informative References . . . . . . . . . . . . . . . . . . 8 63 Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . 10 64 A.1. 224 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 10 65 A.2. 256 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 11 66 A.3. 384 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 11 67 A.4. 512 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 12 69 1. Introduction 71 In [RFC5639], a new set of elliptic curve groups over finite prime 72 fields for use in cryptographic applications was specified. These 73 groups, denoted as ECC Brainpool curves, were generated in a 74 verifiably pseudo-random way and comply with the security 75 requirements of relevant standards from ISO [ISO1] [ISO2], ANSI 76 [ANSI1], NIST [FIPS], and SecG [SEC2]. 78 While the ASN.1 object identifiers defined in RFC 5639 allow usage of 79 the ECC Brainpool curves in certificates and certificate revocation 80 lists, their utilization for key exchange in IKEv2 [RFC5996] requires 81 the definition and assignment of additional Diffie-Hellman Group 82 Transform IDs in the respective IANA registry. This document 83 specifies tranform IDs for four curves from RFC 5639 as well as the 84 encoding of the key exchange payload and derivation of the shared 85 secret when using one of these curves. 87 1.1. Requirements Language 89 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 90 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this 91 document are to be interpreted as described in [RFC2119]. 93 2. IKEv2 Key Exchange using the ECC Brainpool Curves 95 2.1. Diffie-Hellman Group Transform IDs 97 In order to use the ECC Brainpool curves for key exchange within 98 IKEv2, the Diffie-Hellman Group Transform IDs (Transform Type 4) 99 listed in the following table are to be registered with IANA 100 [IANA-IKE2]. The parameters associated with these curves are defined 101 in RFC 5639 [RFC5639]. 103 +-----------------+--------------+ 104 | Curve | Transform ID | 105 +-----------------+--------------+ 106 | brainpoolP224r1 | 27 | 107 | | | 108 | brainpoolP256r1 | 28 | 109 | | | 110 | brainpoolP384r1 | 29 | 111 | | | 112 | brainpoolP512r1 | 30 | 113 +-----------------+--------------+ 115 Table 1 117 Test vectors for the groups defined by the ECC Brainpool curves are 118 provided in Appendix A 120 2.2. Using the Twisted Brainpool Curves Internally 122 In [RFC5639] for each random curve, a "twisted curve" (defined by a 123 quadratic twist, see [HMV]) is defined offering the same level of 124 security but potentially allowing more efficient arithmetic due to 125 the curve parameter A = -3. The transform IDs listed in Table 1 also 126 allow using the twisted curve corresponding to the specified random 127 curve: points (x,y) of any curve listed in can be efficiently 128 transformed to the corresponding point (x',y') on the twisted curve 129 of same bit length - and vice versa - by setting (x',y') = (x*Z^2, 130 y*Z^3) with the coefficient Z specified for that curve in [RFC5639]. 132 2.3. Key Exchange Payload and Shared Secret 134 For the encoding of the key exchange payload and the derivation of 135 the shared secret, the methods specified in [RFC5903] are adopted. 137 In an ECP key exchange in IKEv2, the Diffie-Hellman public value 138 passed in a KE payload consists of two components, x and y, 139 corresponding to the coordinates of an elliptic curve point. Each 140 component MUST be computed from the corresponding coordinate using 141 the FieldElement-to-OctetString conversion method specified in [SEC1] 142 and MUST have bit length as indicated in Table 2. This length is 143 enforced by the FieldElement-to-OctetString conversion method, if 144 necessary, by prepending the value with zeros. 146 Note: The FieldElement-to-OctetString conversion method specified in 147 [SEC1] is equivalent to applying the conversion between integers and 148 octet strings of Section 6 of [RFC6090] after representing the field 149 element as integer in the interval [0, p-1]. 151 +-----------------+------------------------+------------------------+ 152 | Curves | Bit length of each | Bit length of key | 153 | | component (x or y) | exchange payload | 154 +-----------------+------------------------+------------------------+ 155 | brainpoolP224r1 | 224 | 448 | 156 | | | | 157 | brainpoolP256r1 | 256 | 512 | 158 | | | | 159 | brainpoolP384r1 | 384 | 768 | 160 | | | | 161 | brainpoolP512r1 | 512 | 1024 | 162 +-----------------+------------------------+------------------------+ 164 Table 2 166 From these components, the key exchange payload MUST be computed as 167 the concatenation of the x and y coordinates. Hence, the key 168 exchange payload has the bit length indicated in Table 2. 170 The Diffie-Hellman shared secret value consists only of the x value. 171 In particular, the shared secret value MUST be computed from the x 172 coordinate of the Diffie-Hellman common value using the FieldElement- 173 to-OctetString conversion method specified in [SEC1] and MUST have 174 bit length as indicated in the Table 2. 176 3. Security Considerations 178 The security considerations of [RFC5996] apply accordingly. 180 In order to thwart certain active attacks, the validity of the other 181 peer's public Diffie-Hellmann value (x,y) recovered from the received 182 key exchange payload needs to be verified. In particular, it MUST be 183 verified that the coordinates x and y of the public value satisfy the 184 curve equation. For additional information we refer to [IKE_DH_Req]. 186 The confidentiality, authenticity and integrity of a secure 187 communication based on IKEv2 is limited by the weakest cryptographic 188 primitive applied. In order to achieve a maximum security level when 189 using one of the elliptic curves from Table 1 for key exchange, the 190 key derivation function, the algorithms and key lengths of symmetric 191 encryption and message authentication as well as the algorithm, bit 192 length and hash function used for signature generation should be 193 chosen according to the recommendations of [NIST800-57] and 194 [RFC5639]. Furthermore, the private Diffie-Hellman keys should be 195 selected with the same bit length as the order of the group generated 196 by the base point G and with approximately maximum entropy. 198 Implementations of elliptic curve cryptography for IKEv2 could be 199 susceptible to side-channel attacks. Particular care should be taken 200 for implementations that internally use the corresponding twisted 201 curve to take advantage of an efficient arithmetic for the special 202 parameters (A = -3): although the twisted curve itself offers the 203 same level of security as the corresponding random curve (through 204 mathematical equivalence), an arithmetic based on small curve 205 parameters could be harder to protect against side-channel attacks. 206 General guidance on resistence of elliptic curve cryptography 207 implementations against side-channel-attacks is given in [BSI1] and 208 [HMV]. 210 4. IANA Considerations 212 IANA has updated its Transform Type 4 (Diffie-Hellman Group 213 Transform) registry in [IANA-IKE2] to include the groups listed in 214 Table 1. 216 5. References 218 5.1. Normative References 220 [IANA-IKE2] Internet Assigned Numbers Authority, "Internet Key 221 Exchange Version 2 (IKEv2) Parameters", 222 . 224 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate 225 Requirement Levels", BCP 14, RFC 2119, March 1997. 227 [RFC5996] Kaufman, C., Hoffman, P., Nir, Y., and P. Eronen, 228 "Internet Key Exchange Protocol Version 2 (IKEv2)", 229 RFC 5996, September 2010. 231 [RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography 232 (ECC) Brainpool Standard Curves and Curve Generation", 233 RFC 5639, March 2010. 235 [SEC1] Certicom Research, "Elliptic Curve Cryptography", 236 Standards for Efficient Cryptography (SEC) 1, 237 September 2000. 239 5.2. Informative References 241 [ANSI1] American National Standards Institute, "Public Key 242 Cryptography For The Financial Services Industry: The 243 Elliptic Curve Digital Signature Algorithm (ECDSA)", 244 ANSI X9.62, 2005. 246 [BSI1] Bundesamt fuer Sicherheit in der Informationstechnik, 247 "Minimum Requirements for Evaluating Side-Channel 248 Attack Resistance of Elliptic Curve Implementations", 249 July 2011. 251 [FIPS] National Institute of Standards and Technology, 252 "Digital Signature Standard (DSS)", FIPS PUB 186-2, 253 December 1998. 255 [HMV] Hankerson, D., Menezes, A., and S. Vanstone, "Guide to 256 Elliptic Curve Cryptography", Springer Verlag, 2004. 258 [IKE_DH_Req] Sheffer, Y. and S. Fluhrer, "Additional Diffie-Hellman 259 Tests for IKEv2 (work in progress)", 260 draft-ietf-ipsecme-dh-checks-00 (work in progress), 261 January 2013. 263 [ISO1] International Organization for Standardization, 264 "Information Technology - Security Techniques - Digital 265 Signatures with Appendix - Part 3: Discrete Logarithm 266 Based Mechanisms", ISO/IEC 14888-3, 2006. 268 [ISO2] International Organization for Standardization, 269 "Information Technology - Security Techniques - 270 Cryptographic Techniques Based on Elliptic Curves - 271 Part 2: Digital signatures", ISO/IEC 15946-2, 2002. 273 [NIST800-57] National Institute of Standards and Technology, 274 "Recommendation for Key Management - Part 1: General 275 (Revised)", NIST Special Publication 800-57, 276 March 2007. 278 [RFC5903] Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a 279 Prime (ECP Groups) for IKE and IKEv2", RFC 5903, 280 June 2010. 282 [RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental 283 Elliptic Curve Cryptography Algorithms", RFC 6090, 284 February 2011. 286 [SEC2] Certicom Research, "Recommended Elliptic Curve Domain 287 Parameters", Standards for Efficient Cryptography 288 (SEC) 2, September 2000. 290 Appendix A. Test Vectors 292 This section provides some test vectors for example Diffie-Hellman 293 key exchanges using each of the curves defined in Section 2 . In all 294 of the following sections the following notation is used: 296 d_A: the secret key of party A 298 x_qA: the x-coordinate of the public key of party A 300 y_qA: the y-coordinate of the public key of party A 302 d_B: the secret key of party B 304 x_qB: the x-coordinate of the public key of party B 306 y_qB: the y-coordinate of the public key of party B 308 x_Z: the x-coordinate of the shared secret that results from 309 completion of the Diffie-Hellman computation 311 y_Z: the y-coordinate of the shared secret that results from 312 completion of the Diffie-Hellman computation 314 The field elements x_qA, y_qA, x_qB, y_qB, x_Z, y_Z are represented 315 as hexadecimal values using the FieldElement-to-OctetString 316 conversion method specified in [SEC1]. 318 A.1. 224 Bit Curve 320 Curve brainpoolP224r1 322 dA = 39F155483CEE191FBECFE9C81D8AB1A03CDA6790E7184ACE44BCA161 324 x_qA = A9C21A569759DA95E0387041184261440327AFE33141CA04B82DC92E 326 y_qA = 98A0F75FBBF61D8E58AE5511B2BCDBE8E549B31E37069A2825F590C1 328 dB = 6060552303899E2140715816C45B57D9B42204FB6A5BF5BEAC10DB00 330 x_qB = 034A56C550FF88056144E6DD56070F54B0135976B5BF77827313F36B 332 y_qB = 75165AD99347DC86CAAB1CBB579E198EAF88DC35F927B358AA683681 334 x_Z = 1A4BFE705445120C8E3E026699054104510D119757B74D5FE2462C66 336 y_Z = BB6802AC01F8B7E91B1A1ACFB9830A95C079CEC48E52805DFD7D2AFE 338 A.2. 256 Bit Curve 340 Curve brainpoolP256r1 342 dA = 343 81DB1EE100150FF2EA338D708271BE38300CB54241D79950F77B063039804F1D 345 x_qA = 346 44106E913F92BC02A1705D9953A8414DB95E1AAA49E81D9E85F929A8E3100BE5 348 y_qA = 349 8AB4846F11CACCB73CE49CBDD120F5A900A69FD32C272223F789EF10EB089BDC 351 dB = 352 55E40BC41E37E3E2AD25C3C6654511FFA8474A91A0032087593852D3E7D76BD3 354 x_qB = 355 8D2D688C6CF93E1160AD04CC4429117DC2C41825E1E9FCA0ADDD34E6F1B39F7B 357 y_qB = 358 990C57520812BE512641E47034832106BC7D3E8DD0E4C7F1136D7006547CEC6A 360 x_Z = 361 89AFC39D41D3B327814B80940B042590F96556EC91E6AE7939BCE31F3A18BF2B 363 y_Z = 364 49C27868F4ECA2179BFD7D59B1E3BF34C1DBDE61AE12931648F43E59632504DE 366 A.3. 384 Bit Curve 368 Curve brainpoolP384r1 370 dA = 1E20F5E048A5886F1F157C74E91BDE2B98C8B52D58E5003D57053FC4B0BD6 371 5D6F15EB5D1EE1610DF870795143627D042 373 x_qA = 68B665DD91C195800650CDD363C625F4E742E8134667B767B1B47679358 374 8F885AB698C852D4A6E77A252D6380FCAF068 376 y_qA = 55BC91A39C9EC01DEE36017B7D673A931236D2F1F5C83942D049E3FA206 377 07493E0D038FF2FD30C2AB67D15C85F7FAA59 379 dB = 032640BC6003C59260F7250C3DB58CE647F98E1260ACCE4ACDA3DD869F74E 380 01F8BA5E0324309DB6A9831497ABAC96670 382 x_qB = 4D44326F269A597A5B58BBA565DA5556ED7FD9A8A9EB76C25F46DB69D19 383 DC8CE6AD18E404B15738B2086DF37E71D1EB4 384 y_qB = 62D692136DE56CBE93BF5FA3188EF58BC8A3A0EC6C1E151A21038A42E91 385 85329B5B275903D192F8D4E1F32FE9CC78C48 387 x_Z = 0BD9D3A7EA0B3D519D09D8E48D0785FB744A6B355E6304BC51C229FBBCE2 388 39BBADF6403715C35D4FB2A5444F575D4F42 390 y_Z = 0DF213417EBE4D8E40A5F76F66C56470C489A3478D146DECF6DF0D94BAE9 391 E598157290F8756066975F1DB34B2324B7BD 393 A.4. 512 Bit Curve 395 Curve brainpoolP512r1 397 dA = 16302FF0DBBB5A8D733DAB7141C1B45ACBC8715939677F6A56850A38BD87B 398 D59B09E80279609FF333EB9D4C061231FB26F92EEB04982A5F1D1764CAD5766542 399 2 401 x_qA = 0A420517E406AAC0ACDCE90FCD71487718D3B953EFD7FBEC5F7F27E28C6 402 149999397E91E029E06457DB2D3E640668B392C2A7E737A7F0BF04436D11640FD0 403 9FD 405 y_qA = 72E6882E8DB28AAD36237CD25D580DB23783961C8DC52DFA2EC138AD472 406 A0FCEF3887CF62B623B2A87DE5C588301EA3E5FC269B373B60724F5E82A6AD147F 407 DE7 409 dB = 230E18E1BCC88A362FA54E4EA3902009292F7F8033624FD471B5D8ACE49D1 410 2CFABBC19963DAB8E2F1EBA00BFFB29E4D72D13F2224562F405CB80503666B2542 411 9 413 x_qB = 9D45F66DE5D67E2E6DB6E93A59CE0BB48106097FF78A081DE781CDB31FC 414 E8CCBAAEA8DD4320C4119F1E9CD437A2EAB3731FA9668AB268D871DEDA55A54731 415 99F 417 y_qB = 2FDC313095BCDD5FB3A91636F07A959C8E86B5636A1E930E8396049CB48 418 1961D365CC11453A06C719835475B12CB52FC3C383BCE35E27EF194512B7187628 419 5FA 421 x_Z = A7927098655F1F9976FA50A9D566865DC530331846381C87256BAF322624 422 4B76D36403C024D7BBF0AA0803EAFF405D3D24F11A9B5C0BEF679FE1454B21C4CD 423 1F 425 y_Z = 7DB71C3DEF63212841C463E881BDCF055523BD368240E6C3143BD8DEF8B3 426 B3223B95E0F53082FF5E412F4222537A43DF1C6D25729DDB51620A832BE6A26680 427 A2 429 Authors' Addresses 431 Johannes Merkle 432 secunet Security Networks 433 Mergenthaler Allee 77 434 65760 Eschborn 435 Germany 437 Phone: +49 201 5454 3091 438 EMail: johannes.merkle@secunet.com 440 Manfred Lochter 441 Bundesamt fuer Sicherheit in der Informationstechnik (BSI) 442 Postfach 200363 443 53133 Bonn 444 Germany 446 Phone: +49 228 9582 5643 447 EMail: manfred.lochter@bsi.bund.de