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Checking references for intended status: Informational ---------------------------------------------------------------------------- -- Looks like a reference, but probably isn't: '1' on line 717 ** Obsolete normative reference: RFC 4492 (Obsoleted by RFC 8422) ** Obsolete normative reference: RFC 5226 (Obsoleted by RFC 8126) ** Obsolete normative reference: RFC 5246 (Obsoleted by RFC 8446) Summary: 3 errors (**), 0 flaws (~~), 1 warning (==), 7 comments (--). Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 Internet Engineering Task Force D. Gillmor 3 Internet-Draft ACLU 4 Updates: 4492, 5246, 4346, 2246 (if March 28, 2015 5 approved) 6 Intended status: Informational 7 Expires: September 29, 2015 9 Negotiated Finite Field Diffie-Hellman Ephemeral Parameters for TLS 10 draft-ietf-tls-negotiated-ff-dhe-08 12 Abstract 14 Traditional finite-field-based Diffie-Hellman (DH) key exchange 15 during the TLS handshake suffers from a number of security, 16 interoperability, and efficiency shortcomings. These shortcomings 17 arise from lack of clarity about which DH group parameters TLS 18 servers should offer and clients should accept. This document offers 19 a solution to these shortcomings for compatible peers by using a 20 section of the TLS "EC Named Curve Registry" to establish common 21 finite-field DH parameters with known structure and a mechanism for 22 peers to negotiate support for these groups. 24 Status of This Memo 26 This Internet-Draft is submitted in full conformance with the 27 provisions of BCP 78 and BCP 79. 29 Internet-Drafts are working documents of the Internet Engineering 30 Task Force (IETF). Note that other groups may also distribute 31 working documents as Internet-Drafts. The list of current Internet- 32 Drafts is at http://datatracker.ietf.org/drafts/current/. 34 Internet-Drafts are draft documents valid for a maximum of six months 35 and may be updated, replaced, or obsoleted by other documents at any 36 time. It is inappropriate to use Internet-Drafts as reference 37 material or to cite them other than as "work in progress." 39 This Internet-Draft will expire on September 29, 2015. 41 Copyright Notice 43 Copyright (c) 2015 IETF Trust and the persons identified as the 44 document authors. All rights reserved. 46 This document is subject to BCP 78 and the IETF Trust's Legal 47 Provisions Relating to IETF Documents 48 (http://trustee.ietf.org/license-info) in effect on the date of 49 publication of this document. Please review these documents 50 carefully, as they describe your rights and restrictions with respect 51 to this document. Code Components extracted from this document must 52 include Simplified BSD License text as described in Section 4.e of 53 the Trust Legal Provisions and are provided without warranty as 54 described in the Simplified BSD License. 56 Table of Contents 58 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 59 1.1. Requirements Language . . . . . . . . . . . . . . . . . . 3 60 1.2. Vocabulary . . . . . . . . . . . . . . . . . . . . . . . 4 61 2. Named Group Overview . . . . . . . . . . . . . . . . . . . . 4 62 3. Client Behavior . . . . . . . . . . . . . . . . . . . . . . . 5 63 4. Server Behavior . . . . . . . . . . . . . . . . . . . . . . . 6 64 5. Optimizations . . . . . . . . . . . . . . . . . . . . . . . . 7 65 5.1. Checking the Peer's Public Key . . . . . . . . . . . . . 7 66 5.2. Short Exponents . . . . . . . . . . . . . . . . . . . . . 7 67 5.3. Table Acceleration . . . . . . . . . . . . . . . . . . . 8 68 6. Operational Considerations . . . . . . . . . . . . . . . . . 8 69 6.1. Preference Ordering . . . . . . . . . . . . . . . . . . . 8 70 7. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 9 71 8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 9 72 9. Security Considerations . . . . . . . . . . . . . . . . . . . 9 73 9.1. Negotiation resistance to active attacks . . . . . . . . 10 74 9.2. Group strength considerations . . . . . . . . . . . . . . 11 75 9.3. Finite-Field DHE only . . . . . . . . . . . . . . . . . . 11 76 9.4. Deprecating weak groups . . . . . . . . . . . . . . . . . 11 77 9.5. Choice of groups . . . . . . . . . . . . . . . . . . . . 12 78 9.6. Timing attacks . . . . . . . . . . . . . . . . . . . . . 12 79 9.7. Replay attacks from non-negotiated FFDHE . . . . . . . . 12 80 9.8. Forward Secrecy . . . . . . . . . . . . . . . . . . . . . 13 81 9.9. False Start . . . . . . . . . . . . . . . . . . . . . . . 13 82 10. Privacy Considerations . . . . . . . . . . . . . . . . . . . 14 83 10.1. Client fingerprinting . . . . . . . . . . . . . . . . . 14 84 11. References . . . . . . . . . . . . . . . . . . . . . . . . . 14 85 11.1. Normative References . . . . . . . . . . . . . . . . . . 14 86 11.2. Informative References . . . . . . . . . . . . . . . . . 14 87 11.3. URIs . . . . . . . . . . . . . . . . . . . . . . . . . . 16 88 Appendix A. Named Group Registry . . . . . . . . . . . . . . . . 16 89 A.1. ffdhe2048 . . . . . . . . . . . . . . . . . . . . . . . . 16 90 A.2. ffdhe3072 . . . . . . . . . . . . . . . . . . . . . . . . 17 91 A.3. ffdhe4096 . . . . . . . . . . . . . . . . . . . . . . . . 19 92 A.4. ffdhe6144 . . . . . . . . . . . . . . . . . . . . . . . . 20 93 A.5. ffdhe8192 . . . . . . . . . . . . . . . . . . . . . . . . 22 94 Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 25 96 1. Introduction 98 Traditional TLS [RFC5246] offers a Diffie-Hellman ephemeral (DHE) key 99 exchange mode which provides Forward Secrecy for the connection. The 100 client offers a ciphersuite in the ClientHello that includes DHE, and 101 the server offers the client group parameters generator g and modulus 102 p. If the client does not consider the group strong enough (e.g. if 103 p is too small, or if p is not prime, or there are small subgroups), 104 or if it is unable to process the group for other reasons, the client 105 has no recourse but to terminate the connection. 107 Conversely, when a TLS server receives a suggestion for a DHE 108 ciphersuite from a client, it has no way of knowing what kinds of DH 109 groups the client is capable of handling, or what the client's 110 security requirements are for this key exchange session. For 111 example, some widely-distributed TLS clients are not capable of DH 112 groups where p > 1024 bits. Other TLS clients may by policy wish to 113 use DHE only if the server can offer a stronger group (and are 114 willing to use a non-PFS key-exchange mechanism otherwise). The 115 server has no way of knowing which type of client is connecting, but 116 must select DH parameters with insufficient knowledge. 118 Additionally, the DH parameters chosen by the server may have a known 119 structure which renders them secure against a small subgroup attack, 120 but a client receiving an arbitrary p and g has no efficient way to 121 verify that the structure of a new group is reasonable for use. 123 This modification to TLS solves these problems by using a section of 124 the "EC Named Curves" registry to select common DH groups with known 125 structure; defining the use of the "elliptic_curves(10)" extension 126 (described here as "Supported Groups" extension) for clients 127 advertising support for DHE with these groups. This document also 128 provides guidance for compliant peers to take advantage of the 129 additional security, availability, and efficiency offered. 131 The use of this mechanism by one compliant peer when interacting with 132 a non-compliant peer should have no detrimental effects. 134 1.1. Requirements Language 136 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 137 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this 138 document are to be interpreted as described in [RFC2119]. The term 139 "PRIVATE USE" is to be interpreted as described in [RFC5226]. 141 1.2. Vocabulary 143 The terms "DHE" or "FFDHE" are used in this document to refer to the 144 finite-field-based Diffie-Hellman ephemeral key exchange mechanism in 145 TLS. TLS also supports elliptic-curve-based Diffie-Hellman (ECDHE) 146 ephemeral key exchanges [RFC4492], but this document does not 147 document their use. A registry previously used only by ECHDE-capable 148 implementations is expanded in this document to cover FFDHE groups as 149 well. "FFDHE ciphersuites" is used in this document to refer 150 exclusively to ciphersuites with FFDHE key exchange mechanisms, but 151 note that these suites are typically labeled with a TLS_DHE_ prefix. 153 2. Named Group Overview 155 We use previously-unallocated codepoints within the extension 156 currently known as "elliptic_curves" (section 5.1.1. of [RFC4492]) to 157 indicate known finite field groups. The extension's semantics are 158 expanded from "Supported Elliptic Curves" to "Supported Groups". The 159 semantics of the extension's data type (enum NamedCurve) is also 160 expanded from "named curve" to "named group". 162 Codepoints in the NamedCurve registry with a high byte of 0x01 (that 163 is, between 256 and 511 inclusive) are set aside for FFDHE groups, 164 though only a small number of them are initially defined and we do 165 not expect many other FFDHE groups to be added to this range. No 166 codepoints outside of this range will be allocated to FFDHE groups. 167 The new code points for the NamedCurve registry are: 169 enum { 170 // other already defined elliptic curves (see RFC 4492) 171 ffdhe2048(256), ffdhe3072(257), ffdhe4096(258), 172 ffdhe6144(259), ffdhe8192(260), 173 // 174 } NamedCurve; 176 These additions to the Named Curve registry are described in detail 177 in Appendix A. They are all safe primes derived from the base of the 178 natural logarithm ("e"), with the high and low 64 bits set to 1 for 179 efficient Montgomery or Barrett reduction. 181 The use of the base of the natural logarithm here is as a "nothing- 182 up-my-sleeve" number. The goal is to guarantee that the bits in the 183 middle of the modulus are effectively random, while avoiding any 184 suspicion that the primes have secretly been selected to be weak 185 according to some secret criteria. [RFC3526] used pi for this value. 186 See Section 9.5 for reasons that this draft does not reuse pi. 188 3. Client Behavior 190 A TLS client that is capable of using strong finite field Diffie- 191 Hellman groups can advertise its capabilities and its preferences for 192 stronger key exchange by using this mechanism. 194 The compatible client that wants to be able to negotiate strong FFDHE 195 SHOULD send a "Supported Groups" extension (identified by type 196 elliptic_curves(10) in [RFC4492]) in the ClientHello, and include a 197 list of known FFDHE groups in the extension data, ordered from most 198 preferred to least preferred. If the client also supports and wants 199 to offer ECDHE key exchange, it MUST use a single "Supported Groups" 200 extension to include all supported groups (both ECDHE and FFDHE 201 groups). The ordering SHOULD be based on client preference, but see 202 Section 6.1 for more nuance. 204 A client that offers any of these values in the elliptic_curves 205 extension SHOULD ALSO include at least one FFDHE ciphersuite in the 206 Client Hello. 208 A client who offers a group MUST be able and willing to perform a DH 209 key exchange using that group. 211 A client that offers one or more FFDHE groups in the "Supported 212 Groups" extension and an FFDHE ciphersuite, and receives an FFDHE 213 ciphersuite from the server SHOULD take the following steps upon 214 receiving the ServerKeyExchange: 216 For non-anonymous ciphersuites where the offered Certificate is 217 valid and appropriate for the peer, validate the signature over 218 the ServerDHParams. If not valid, terminate the connection. 220 If the signature over ServerDHParams is valid, compare the 221 selected dh_p and dh_g with the FFDHE groups offered by the 222 client. If none of the offered groups match, the server is not 223 compatible with this draft. The client MAY decide to continue the 224 connection if the selected group is acceptable under local policy, 225 or it MAY decide to terminate the connection with a fatal 226 insufficient_security(71) alert. 228 If the selected group matches an offered FFDHE group exactly, the 229 the client MUST verify that dh_Ys is in the range 1 < dh_Ys < dh_p 230 - 1. If dh_Ys is not in this range, the client MUST terminate the 231 connection with a fatal handshake_failure(40) alert. 233 If the selected group matches an offered FFDHE group exactly, and 234 dh_Ys is in range, then the client SHOULD continue with the 235 connection as usual. 237 4. Server Behavior 239 If a compatible TLS server receives a Supported Groups extension from 240 a client that includes any FFDHE group (i.e. any codepoint between 241 256 and 511 inclusive, even if unknown to the server), and if none of 242 the client-proposed FFDHE groups are known and acceptable to the 243 server, then the server SHOULD NOT select an FFDHE ciphersuite. In 244 this case, the server SHOULD select an acceptable non-FFDHE 245 ciphersuite from the client's offered list. If the extension is 246 present with FFDHE groups, none of the client's offered groups are 247 acceptable by the server, and none of the client's proposed non-FFDHE 248 ciphersuites are acceptable to the server, the server SHOULD end the 249 connection with a fatal TLS alert of type insufficient_security(71). 251 If at least one FFDHE ciphersuite is present in the client 252 ciphersuite list, and the Supported Groups extension is present in 253 the ClientHello, but the extension does not include any FFDHE groups 254 (i.e. no codepoints between 256 and 511 inclusive), then the server 255 knows that the client is not compatible with this document. In this 256 scenario, a server MAY choose to select a non-FFDHE ciphersuite, or 257 MAY choose an FFDHE ciphersuite and offer an FFDHE group of its 258 choice to the client as part of a traditional ServerKeyExchange. 260 A compatible TLS server that receives the Supported Groups extension 261 with FFDHE codepoints in it, and which selects an FFDHE ciphersuite 262 MUST select one of the client's offered groups. The server indicates 263 the choice of group to the client by sending the group's parameters 264 as usual in the ServerKeyExchange as described in section 7.4.3 of 265 [RFC5246]. 267 A TLS server MUST NOT select a named FFDHE group that was not offered 268 by a compatible client. 270 A TLS server MUST NOT select an FFDHE ciphersuite if the client did 271 not offer one, even if the client offered an FFDHE group in the 272 Supported Groups extension. 274 If a non-anonymous FFDHE ciphersuite is chosen, and the TLS client 275 has used this extension to offer an FFDHE group of comparable or 276 greater strength than the server's public key, the server SHOULD 277 select an FFDHE group at least as strong as the server's public key. 278 For example, if the server has a 3072-bit RSA key, and the client 279 offers only ffdhe2048 and ffdhe4096, the server SHOULD select 280 ffdhe4096. 282 When a compatible server selects an FFDHE group from among a client's 283 Supported Groups, and the client sends a ClientKeyExchange, the 284 server MUST verify that 1 < dh_Yc < dh_p - 1. If it is out of range, 285 the server MUST terminate the connection with fatal 286 handshake_failure(40) alert. 288 5. Optimizations 290 In a key exchange with a successfully negotiated known FFDHE group, 291 both peers know that the group in question uses a safe prime as a 292 modulus, and that the group in use is of size p-1 or (p-1)/2. This 293 allows at least three optimizations that can be used to improve 294 performance. 296 5.1. Checking the Peer's Public Key 298 Peers MUST validate each other's public key Y (dh_Ys offered by the 299 server or dh_Yc offered by the client) by ensuring that 1 < Y < p-1. 300 This simple check ensures that the remote peer is properly behaved 301 and isn't forcing the local system into a small subgroup. 303 To reach the same assurance with an unknown group, the client would 304 need to verify the primality of the modulus, learn the factors of 305 p-1, and test both the generator g and Y against each factor to avoid 306 small subgroup attacks. 308 5.2. Short Exponents 310 Traditional Finite Field Diffie-Hellman has each peer choose their 311 secret exponent from the range [2,p-2]. Using exponentiation by 312 squaring, this means each peer must do roughly 2*log_2(p) 313 multiplications, twice (once for the generator and once for the 314 peer's public key). 316 Peers concerned with performance may also prefer to choose their 317 secret exponent from a smaller range, doing fewer multiplications, 318 while retaining the same level of overall security. Each named group 319 indicates its approximate security level, and provides a lower-bound 320 on the range of secret exponents that should preserve it. For 321 example, rather than doing 2*2*3072 multiplications for a ffdhe3072 322 handshake, each peer can choose to do 2*2*275 multiplications by 323 choosing their secret exponent from the range [2^274,2^275] (that is, 324 a m-bit integer where m is at least 275) and still keep the same 325 approximate security level. 327 A similar short-exponent approach is suggested in SSH's Diffie- 328 Hellman key exchange (See section 6.2 of [RFC4419]). 330 5.3. Table Acceleration 332 Peers wishing to further accelerate FFDHE key exchange can also pre- 333 compute a table of powers of the generator of a known group. This is 334 a memory vs. time tradeoff, and it only accelerates the first 335 exponentiation of the ephemeral DH exchange (the fixed-base 336 exponentiation). The variable-base exponentiation (using the peer's 337 public exponent as a base) still needs to be calculated as normal. 339 6. Operational Considerations 341 6.1. Preference Ordering 343 The ordering of named groups in the Supported Groups extension may 344 contain some ECDHE groups and some FFDHE groups. These SHOULD be 345 ranked in the order preferred by the client. 347 However, the ClientHello also contains list of desired ciphersuites, 348 also ranked in preference order. This presents the possibility of 349 conflicted preferences. For example, if the ClientHello contains a 350 CipherSuite with two choices in order 351 and the Supported Groups 353 Extension contains two choices in order then 354 there is a clear contradiction. Clients SHOULD NOT present such a 355 contradiction since it does not represent a sensible ordering. A 356 server that encounters such an contradiction when selecting between 357 an ECDHE or FFDHE key exchange mechanism while trying to respect 358 client preferences SHOULD give priority to the Supported Groups 359 extension (in the example case, it should select 360 TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA with secp256r1), but MAY resolve 361 the contradiction any way it sees fit. 363 More subtly, clients MAY interleave preferences between ECDHE and 364 FFDHE groups, for example if stronger groups are preferred regardless 365 of cost, but weaker groups are acceptable, the Supported Groups 366 extension could consist of: 367 . In this example, with the 368 same CipherSuite offered as the previous example, a server configured 369 to respect client preferences and with support for all listed groups 370 SHOULD select TLS_DHE_RSA_WITH_AES_128_CBC_SHA with ffdhe8192. A 371 server configured to respect client preferences and with support for 372 only secp384p1 and ffdhe3072 SHOULD select 373 TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA with secp384p1. 375 7. Acknowledgements 377 Thanks to Fedor Brunner, Dave Fergemann, Niels Ferguson, Sandy 378 Harris, Tero Kivinen, Watson Ladd, Nikos Mavrogiannopolous, Niels 379 Moeller, Bodo Moeller, Kenny Paterson, Eric Rescorla, Tom Ritter, 380 Rene Struik, Martin Thomson, Sean Turner, and other members of the 381 TLS Working Group for their comments and suggestions on this draft. 382 Any mistakes here are not theirs. 384 8. IANA Considerations 386 IANA maintains the registry currently known as EC Named Curves 387 (originally defined in [RFC4492] and updated by [RFC7027]) at [1]. 389 This document expands the semantics of this registry slightly, to 390 include groups based on finite fields in addition to groups based on 391 elliptic curves. It should add a range designation to that registry, 392 indicating that values from 256-511 (inclusive) are set aside for 393 "Finite Field Diffie-Hellman groups", and that all other entries in 394 the registry are "Elliptic curve groups". 396 This document allocates five well-defined codepoints in the registry 397 for specific Finite Field Diffie-Hellman groups defined in 398 Appendix A. 400 In addition, the four highest codepoints in this range (508-511, 401 inclusive) are designated for PRIVATE USE by peers who have custom 402 Finite Field Diffie-Hellman groups that they wish to signal 403 internally. 405 The updated registry section should be as follows: 407 +---------------------+-------------+---------+-----------------+ 408 | Value | Description | DTLS-OK | Reference | 409 +---------------------+-------------+---------+-----------------+ 410 | 256 | ffdhe2048 | Y | [this document] | 411 | 257 | ffdhe3072 | Y | [this document] | 412 | 258 | ffdhe4096 | Y | [this document] | 413 | 259 | ffdhe6144 | Y | [this document] | 414 | 260 | ffdhe8192 | Y | [this document] | 415 | 508-511 (inclusive) | PRIVATE USE | - | - | 416 +---------------------+-------------+---------+-----------------+ 418 9. Security Considerations 419 9.1. Negotiation resistance to active attacks 421 Because the contents of the Supported Groups extension is hashed in 422 the finished message, an active MITM that tries to filter or omit 423 groups will cause the handshake to fail, but possibly not before 424 getting the peer to do something they would not otherwise have done. 426 An attacker who impersonates the server can try to do any of the 427 following: 429 Pretend that a non-compatible server is actually capable of this 430 extension, and select a group from the client's list, causing the 431 client to select a group it is willing to negotiate. It is 432 unclear how this would be an effective attack. 434 Pretend that a compatible server is actually non-compatible by 435 negotiating a non-FFDHE ciphersuite. This is no different than 436 MITM ciphersuite filtering. 438 Pretend that a compatible server is actually non-compatible by 439 negotiating a DHE ciphersuite, with a custom (perhaps weak) group 440 chosen by the attacker. This is no worse than the current 441 scenario, and would require the attacker to be able to sign the 442 ServerDHParams, which should not be possible without access to the 443 server's secret key. 445 An attacker who impersonates the client can try to do the following: 447 Pretend that a compatible client is not compatible (e.g. by not 448 offering the Supported Groups extension, or by replacing the 449 Supported Groups extension with one that includes no FFDHE 450 groups). This could cause the server to negotiate a weaker DHE 451 group during the handshake, or to select a non-FFDHE ciphersuite, 452 but it would fail to complete during the final check of the 453 Finished message. 455 Pretend that a non-compatible client is compatible (e.g. by . 456 This could cause the server to select a particular named group in 457 the ServerKeyExchange, or to avoid selecting an FFDHE ciphersuite. 458 The peers would fail to compute the final check of the Finished 459 message. 461 Change the list of groups offered by the client (e.g. by removing 462 the stronger of the set of groups offered). This could cause the 463 server to negotiate a weaker group than desired, but again should 464 be caught by the check in the Finished message. 466 9.2. Group strength considerations 468 TLS implementations using FFDHE key exchange should consider the 469 strength of the group they negotiate. The strength of the selected 470 group is one of the factors which defines the connection's resiliance 471 against attacks on the session's confidentiality and integrity, since 472 the session keys are derived from the DHE handshake. 474 While attacks on integrity must generally happen while the session is 475 in progress, attacks against session confidentiality can happen 476 significantly later, if the entire TLS session is stored for offline 477 analysis. Therefore, FFDHE groups should be selected by clients and 478 servers based on confidentiality guarantees they need. Sessions 479 which need extremely long-term confidentiality should prefer stronger 480 groups. 482 [ENISA] provides rough estimates of group resistance to attack, and 483 recommends that forward-looking implementations ("future systems") 484 should use FFDHE group sizes of at least 3072 bits. ffdhe3072 is 485 intended for use in these implementations. 487 Other sources (e.g. [NIST]) estimate the security levels of the DLOG 488 problem to be slightly more difficult than [ENISA]. This document's 489 suggested minimum exponent sizes in Appendix A for implementations 490 that use the short exponents optimization (Section 5.2) are 491 deliberately conservative to account for the range of these 492 estimates. 494 9.3. Finite-Field DHE only 496 Note that this document specifically targets only finite field-based 497 Diffie-Hellman ephemeral key exchange mechanisms. It does not cover 498 the non-ephemeral DH key exchange mechanisms, nor does it address 499 elliptic curve DHE (ECDHE) key exchange, which is defined in 500 [RFC4492]. 502 Measured by computational cost to the TLS peers, ECDHE appears today 503 to offer much a stronger key exchange than FFDHE. 505 9.4. Deprecating weak groups 507 Advances in hardware or in finite field cryptanalysis may cause some 508 of the negotiated groups to not provide the desired security margins, 509 as indicated by the estimated work factor of an adversary to discover 510 the premaster secret (and may therefore compromise the 511 confidentiality and integrity of the TLS session). 513 Revisions of this document should mark known-weak groups as 514 explicitly deprecated for use in TLS, and should update the estimated 515 work factor needed to break the group, if the cryptanalysis has 516 changed. Implementations that require strong confidentiality and 517 integrity guarantees should avoid using deprecated groups and should 518 be updated when the estimated security margins are updated. 520 9.5. Choice of groups 522 Other lists of named finite field Diffie-Hellman groups 523 [STRONGSWAN-IKE] exist. This draft chooses to not reuse them for 524 several reasons: 526 Using the same groups in multiple protocols increases the value 527 for an attacker with the resources to crack any single group. 529 The IKE groups include weak groups like MODP768 which are 530 unacceptable for secure TLS traffic. 532 Mixing group parameters across multiple implementations leaves 533 open the possibility of some sort of cross-protocol attack. This 534 shouldn't be relevant for ephemeral scenarios, and even with non- 535 ephemeral keying, services shouldn't share keys; however, using 536 different groups avoids these failure modes entirely. 538 9.6. Timing attacks 540 Any implementation of finite field Diffie-Hellman key exchange should 541 use constant-time modular-exponentiation implementations. This is 542 particularly true for those implementations that ever re-use DHE 543 secret keys (so-called "semi-static" ephemeral keying) or share DHE 544 secret keys across a multiple machines (e.g. in a load-balancer 545 situation). 547 9.7. Replay attacks from non-negotiated FFDHE 549 [SECURE-RESUMPTION], [CROSS-PROTOCOL], and [SSL3-ANALYSIS] all show a 550 malicious peer using a bad FFDHE group to maneuver a client into 551 selecting a pre-master secret of the peer's choice, which can be 552 replayed to another server using a non-FFDHE key exchange, and can 553 then be bootstrapped to replay client authentication. 555 To prevent this attack (barring the fixes proposed in 556 [SESSION-HASH]), a client would need not only to implement this 557 draft, but also to reject non-negotiated FFDHE ciphersuites whose 558 group structure it cannot afford to verify. Such a client would need 559 to abort the initial handshake and reconnect to the server in 560 question without listing any FFDHE ciphersuites on the subsequent 561 connection. 563 This tradeoff may be too costly for most TLS clients today, but may 564 be a reasonable choice for clients performing client certificate 565 authentication, or who have other reason to be concerned about 566 server-controlled pre-master secrets. 568 9.8. Forward Secrecy 570 One of the main reasons to prefer FFDHE ciphersuites is Forward 571 Secrecy, the ability to resist decryption even if when the endpoint's 572 long-term secret key (usually RSA) is revealed in the future. 574 This property depends on both sides of the connection discarding 575 their ephemeral keys promptly. Implementations should wipe their 576 FFDHE secret key material from memory as soon as it is no longer 577 needed, and should never store it in persistent storage. 579 Forward secrecy also depends on the strength of the Diffie-Hellman 580 group; using a very strong symmetric cipher like AES256 with a 581 forward-secret ciphersuite, but generating the keys with a much 582 weaker group like dhe2048 simply moves the adversary's cost from 583 attacking the symmetric cipher to attacking the dh_Ys or dh_Yc 584 ephemeral keyshares. 586 If the goal is to provide forward secrecy, attention should be paid 587 to all parts of the ciphersuite selection process, both key exchange 588 and symmetric cipher choice. 590 9.9. False Start 592 Clients capable of TLS False Start [FALSE-START] may receive a 593 proposed FFDHE group from a server that is attacker-controlled. In 594 particular, the attacker can modify the ClientHello to strip the 595 proposed FFDHE groups, which may cause the server to offer a weaker 596 FFDHE group than it should, and this will not be detected until 597 receipt of the server's Finished message. This could cause the a 598 client using the False Start protocol modification to send data 599 encrypted under a weak key agreement. 601 Clients should have their own classification of FFDHE groups that are 602 "cryptographically strong" in the same sense described in the 603 description of symmetric ciphers in [FALSE-START], and SHOULD offer 604 at least one of these in the initial handshake if they contemplate 605 using the False Start protocol modification with an FFDHE 606 ciphersuite. 608 Compatible clients performing a full handshake MUST NOT use the False 609 Start protocol modification if the server selects an FFDHE 610 ciphersuite but sends a group that is not cryptographically strong 611 from the client's perspective. 613 10. Privacy Considerations 615 10.1. Client fingerprinting 617 This extension provides a few additional bits of information to 618 distinguish between classes of TLS clients (see e.g. 619 [PANOPTICLICK]). To minimize this sort of fingerprinting, clients 620 SHOULD support all named groups at or above their minimum security 621 threshhold. New named groups SHOULD NOT be added to the registry 622 without consideration of the cost of browser fingerprinting. 624 11. References 626 11.1. Normative References 628 [FALSE-START] 629 Langley, A., Modadugu, N., and B. Moeller, "Transport 630 Layer Security (TLS) False Start", Work in Progress, 631 draft-bmoeller-tls-falsestart-01, November 2014. 633 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate 634 Requirement Levels", BCP 14, RFC 2119, March 1997. 636 [RFC4492] Blake-Wilson, S., Bolyard, N., Gupta, V., Hawk, C., and B. 637 Moeller, "Elliptic Curve Cryptography (ECC) Cipher Suites 638 for Transport Layer Security (TLS)", RFC 4492, May 2006. 640 [RFC5226] Narten, T. and H. Alvestrand, "Guidelines for Writing an 641 IANA Considerations Section in RFCs", BCP 26, RFC 5226, 642 May 2008. 644 [RFC5246] Dierks, T. and E. Rescorla, "The Transport Layer Security 645 (TLS) Protocol Version 1.2", RFC 5246, August 2008. 647 11.2. Informative References 649 [CROSS-PROTOCOL] 650 Mavrogiannopolous, N., Vercauteren, F., Velichkov, V., and 651 B. Preneel, "A Cross-Protocol Attack on the TLS Protocol", 652 October 2012, 653 . 656 [ECRYPTII] 657 European Network of Excellence in Cryptology II, "ECRYPT 658 II Yearly Report on Algorithms and Keysizes (2011-2012)", 659 September 2012, 660 . 662 [ENISA] European Union Agency for Network and Information Security 663 Agency, "Algorithms, Key Sizes and Parameters Report, 664 version 1.0", October 2013, 665 . 669 [NIST] National Institute of Standards and Technology, "NIST 670 Special Publication 800-57. Recommendation for key 671 management - Part 1: General (Revision 3)", 2012, 672 . 675 [PANOPTICLICK] 676 Electronic Frontier Foundation, "Panopticlick: How Unique 677 - and Trackable - Is Your Browser?", 2010, 678 . 680 [RFC3526] Kivinen, T. and M. Kojo, "More Modular Exponential (MODP) 681 Diffie-Hellman groups for Internet Key Exchange (IKE)", 682 RFC 3526, May 2003. 684 [RFC4419] Friedl, M., Provos, N., and W. Simpson, "Diffie-Hellman 685 Group Exchange for the Secure Shell (SSH) Transport Layer 686 Protocol", RFC 4419, March 2006. 688 [RFC7027] Merkle, J. and M. Lochter, "Elliptic Curve Cryptography 689 (ECC) Brainpool Curves for Transport Layer Security 690 (TLS)", RFC 7027, October 2013. 692 [SECURE-RESUMPTION] 693 Delignat-Lavaud, A., Bhargavan, K., and A. Pironti, 694 "Triple Handshakes Considered Harmful: Breaking and Fixing 695 Authentication over TLS", March 2014, . 698 [SESSION-HASH] 699 Bhargavan, K., Delignat-Lavaud, A., Pironti, A., Langley, 700 A., and M. Ray, "Triple Handshakes Considered Harmful: 701 Breaking and Fixing Authentication over TLS", March 2014, 702 . 705 [SSL3-ANALYSIS] 706 Schneier, B. and D. Wagner, "Analysis of the SSL 3.0 707 protocol", 1996, . 709 [STRONGSWAN-IKE] 710 Brunner, T. and A. Steffen, "Diffie Hellman Groups in 711 IKEv2 Cipher Suites", October 2013, 712 . 715 11.3. URIs 717 [1] https://www.iana.org/assignments/tls-parameters/tls- 718 parameters.xhtml#tls-parameters-8 720 Appendix A. Named Group Registry 722 Each description below indicates the group itself, its derivation, 723 its expected strength (estimated roughly from guidelines in 724 [ECRYPTII]), and whether it is recommended for use in TLS key 725 exchange at the given security level. It is not recommended to add 726 further finite field groups to the NamedCurves registry; any attempt 727 to do so should consider Section 10.1. 729 The primes in these finite field groups are all safe primes, that is, 730 a prime p is a safe prime when q = (p-1)/2 is also prime. Where e is 731 the base of the natural logarithm, and square brackets denote the 732 floor operation, the groups which initially populate this registry 733 are derived for a given bitlength b by finding the lowest positive 734 integer X that creates a safe prime p where: 736 p = 2^b - 2^{b-64} + {[2^{b-130} e] + X } * 2^64 - 1 738 New additions of FFDHE groups to this registry may use this same 739 derivation (e.g. with different bitlengths) or may choose their 740 parameters in a different way, but must be clear about how the 741 parameters were derived. 743 New additions of FFDHE groups MUST use a safe prime as the modulus to 744 enable the inexpensive peer verification described in Section 5.1. 746 A.1. ffdhe2048 748 The 2048-bit group has registry value 256, and is calcluated from the 749 following formula: 751 The modulus is: p = 2^2048 - 2^1984 + {[2^1918 * e] + 560316 } * 2^64 752 - 1 753 The hexadecimal representation of p is: 755 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 756 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 757 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 758 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 759 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 760 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 761 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 762 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 763 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 764 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 765 886B4238 61285C97 FFFFFFFF FFFFFFFF 767 The generator is: g = 2 769 The group size is: q = (p-1)/2 771 The hexadecimal representation of q is: 773 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 774 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 775 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 776 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 777 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 778 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 779 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 780 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 781 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 782 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 783 4435A11C 30942E4B FFFFFFFF FFFFFFFF 785 The estimated symmetric-equivalent strength of this group is 103 786 bits. 788 Peers using ffdhe2048 that want to optimize their key exchange with a 789 short exponent (Section 5.2) should choose a secret key of at least 790 225 bits. 792 A.2. ffdhe3072 794 The 3072-bit prime has registry value 257, and is calcluated from the 795 following formula: 797 The modulus is: p = 2^3072 - 2^3008 + {[2^2942 * e] + 2625351} * 2^64 798 -1 800 The hexadecimal representation of p is: 802 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 803 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 804 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 805 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 806 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 807 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 808 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 809 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 810 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 811 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 812 886B4238 611FCFDC DE355B3B 6519035B BC34F4DE F99C0238 813 61B46FC9 D6E6C907 7AD91D26 91F7F7EE 598CB0FA C186D91C 814 AEFE1309 85139270 B4130C93 BC437944 F4FD4452 E2D74DD3 815 64F2E21E 71F54BFF 5CAE82AB 9C9DF69E E86D2BC5 22363A0D 816 ABC52197 9B0DEADA 1DBF9A42 D5C4484E 0ABCD06B FA53DDEF 817 3C1B20EE 3FD59D7C 25E41D2B 66C62E37 FFFFFFFF FFFFFFFF 819 The generator is: g = 2 821 The group size is: q = (p-1)/2 823 The hexadecimal representation of q is: 825 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 826 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 827 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 828 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 829 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 830 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 831 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 832 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 833 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 834 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 835 4435A11C 308FE7EE 6F1AAD9D B28C81AD DE1A7A6F 7CCE011C 836 30DA37E4 EB736483 BD6C8E93 48FBFBF7 2CC6587D 60C36C8E 837 577F0984 C289C938 5A098649 DE21BCA2 7A7EA229 716BA6E9 838 B279710F 38FAA5FF AE574155 CE4EFB4F 743695E2 911B1D06 839 D5E290CB CD86F56D 0EDFCD21 6AE22427 055E6835 FD29EEF7 840 9E0D9077 1FEACEBE 12F20E95 B363171B FFFFFFFF FFFFFFFF 842 The estimated symmetric-equivalent strength of this group is 125 843 bits. 845 Peers using ffdhe3072 that want to optimize their key exchange with a 846 short exponent (Section 5.2) should choose a secret key of at least 847 275 bits. 849 A.3. ffdhe4096 851 The 4096-bit group has registry value 258, and is calcluated from the 852 following formula: 854 The modulus is: p = 2^4096 - 2^4032 + {[2^3966 * e] + 5736041} * 2^64 855 - 1 857 The hexadecimal representation of p is: 859 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 860 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 861 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 862 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 863 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 864 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 865 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 866 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 867 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 868 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 869 886B4238 611FCFDC DE355B3B 6519035B BC34F4DE F99C0238 870 61B46FC9 D6E6C907 7AD91D26 91F7F7EE 598CB0FA C186D91C 871 AEFE1309 85139270 B4130C93 BC437944 F4FD4452 E2D74DD3 872 64F2E21E 71F54BFF 5CAE82AB 9C9DF69E E86D2BC5 22363A0D 873 ABC52197 9B0DEADA 1DBF9A42 D5C4484E 0ABCD06B FA53DDEF 874 3C1B20EE 3FD59D7C 25E41D2B 669E1EF1 6E6F52C3 164DF4FB 875 7930E9E4 E58857B6 AC7D5F42 D69F6D18 7763CF1D 55034004 876 87F55BA5 7E31CC7A 7135C886 EFB4318A ED6A1E01 2D9E6832 877 A907600A 918130C4 6DC778F9 71AD0038 092999A3 33CB8B7A 878 1A1DB93D 7140003C 2A4ECEA9 F98D0ACC 0A8291CD CEC97DCF 879 8EC9B55A 7F88A46B 4DB5A851 F44182E1 C68A007E 5E655F6A 880 FFFFFFFF FFFFFFFF 882 The generator is: g = 2 884 The group size is: q = (p-1)/2 886 The hexadecimal representation of q is: 888 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 889 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 890 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 891 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 892 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 893 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 894 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 895 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 896 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 897 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 898 4435A11C 308FE7EE 6F1AAD9D B28C81AD DE1A7A6F 7CCE011C 899 30DA37E4 EB736483 BD6C8E93 48FBFBF7 2CC6587D 60C36C8E 900 577F0984 C289C938 5A098649 DE21BCA2 7A7EA229 716BA6E9 901 B279710F 38FAA5FF AE574155 CE4EFB4F 743695E2 911B1D06 902 D5E290CB CD86F56D 0EDFCD21 6AE22427 055E6835 FD29EEF7 903 9E0D9077 1FEACEBE 12F20E95 B34F0F78 B737A961 8B26FA7D 904 BC9874F2 72C42BDB 563EAFA1 6B4FB68C 3BB1E78E AA81A002 905 43FAADD2 BF18E63D 389AE443 77DA18C5 76B50F00 96CF3419 906 5483B005 48C09862 36E3BC7C B8D6801C 0494CCD1 99E5C5BD 907 0D0EDC9E B8A0001E 15276754 FCC68566 054148E6 E764BEE7 908 C764DAAD 3FC45235 A6DAD428 FA20C170 E345003F 2F32AFB5 909 7FFFFFFF FFFFFFFF 911 The estimated symmetric-equivalent strength of this group is 150 912 bits. 914 Peers using ffdhe4096 that want to optimize their key exchange with a 915 short exponent (Section 5.2) should choose a secret key of at least 916 325 bits. 918 A.4. ffdhe6144 920 The 6144-bit group has registry value 259, and is calcluated from the 921 following formula: 923 The modulus is: p = 2^6144 - 2^6080 + {[2^6014 * e] + 15705020} * 924 2^64 - 1 926 The hexadecimal representation of p is: 928 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 929 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 930 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 931 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 932 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 933 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 934 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 935 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 936 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 937 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 938 886B4238 611FCFDC DE355B3B 6519035B BC34F4DE F99C0238 939 61B46FC9 D6E6C907 7AD91D26 91F7F7EE 598CB0FA C186D91C 940 AEFE1309 85139270 B4130C93 BC437944 F4FD4452 E2D74DD3 941 64F2E21E 71F54BFF 5CAE82AB 9C9DF69E E86D2BC5 22363A0D 942 ABC52197 9B0DEADA 1DBF9A42 D5C4484E 0ABCD06B FA53DDEF 943 3C1B20EE 3FD59D7C 25E41D2B 669E1EF1 6E6F52C3 164DF4FB 944 7930E9E4 E58857B6 AC7D5F42 D69F6D18 7763CF1D 55034004 945 87F55BA5 7E31CC7A 7135C886 EFB4318A ED6A1E01 2D9E6832 946 A907600A 918130C4 6DC778F9 71AD0038 092999A3 33CB8B7A 947 1A1DB93D 7140003C 2A4ECEA9 F98D0ACC 0A8291CD CEC97DCF 948 8EC9B55A 7F88A46B 4DB5A851 F44182E1 C68A007E 5E0DD902 949 0BFD64B6 45036C7A 4E677D2C 38532A3A 23BA4442 CAF53EA6 950 3BB45432 9B7624C8 917BDD64 B1C0FD4C B38E8C33 4C701C3A 951 CDAD0657 FCCFEC71 9B1F5C3E 4E46041F 388147FB 4CFDB477 952 A52471F7 A9A96910 B855322E DB6340D8 A00EF092 350511E3 953 0ABEC1FF F9E3A26E 7FB29F8C 183023C3 587E38DA 0077D9B4 954 763E4E4B 94B2BBC1 94C6651E 77CAF992 EEAAC023 2A281BF6 955 B3A739C1 22611682 0AE8DB58 47A67CBE F9C9091B 462D538C 956 D72B0374 6AE77F5E 62292C31 1562A846 505DC82D B854338A 957 E49F5235 C95B9117 8CCF2DD5 CACEF403 EC9D1810 C6272B04 958 5B3B71F9 DC6B80D6 3FDD4A8E 9ADB1E69 62A69526 D43161C1 959 A41D570D 7938DAD4 A40E329C D0E40E65 FFFFFFFF FFFFFFFF 961 The generator is: g = 2 963 The group size is: q = (p-1)/2 965 The hexadecimal representation of q is: 967 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 968 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 969 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 970 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 971 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 972 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 973 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 974 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 975 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 976 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 977 4435A11C 308FE7EE 6F1AAD9D B28C81AD DE1A7A6F 7CCE011C 978 30DA37E4 EB736483 BD6C8E93 48FBFBF7 2CC6587D 60C36C8E 979 577F0984 C289C938 5A098649 DE21BCA2 7A7EA229 716BA6E9 980 B279710F 38FAA5FF AE574155 CE4EFB4F 743695E2 911B1D06 981 D5E290CB CD86F56D 0EDFCD21 6AE22427 055E6835 FD29EEF7 982 9E0D9077 1FEACEBE 12F20E95 B34F0F78 B737A961 8B26FA7D 983 BC9874F2 72C42BDB 563EAFA1 6B4FB68C 3BB1E78E AA81A002 984 43FAADD2 BF18E63D 389AE443 77DA18C5 76B50F00 96CF3419 985 5483B005 48C09862 36E3BC7C B8D6801C 0494CCD1 99E5C5BD 986 0D0EDC9E B8A0001E 15276754 FCC68566 054148E6 E764BEE7 987 C764DAAD 3FC45235 A6DAD428 FA20C170 E345003F 2F06EC81 988 05FEB25B 2281B63D 2733BE96 1C29951D 11DD2221 657A9F53 989 1DDA2A19 4DBB1264 48BDEEB2 58E07EA6 59C74619 A6380E1D 990 66D6832B FE67F638 CD8FAE1F 2723020F 9C40A3FD A67EDA3B 991 D29238FB D4D4B488 5C2A9917 6DB1A06C 50077849 1A8288F1 992 855F60FF FCF1D137 3FD94FC6 0C1811E1 AC3F1C6D 003BECDA 993 3B1F2725 CA595DE0 CA63328F 3BE57CC9 77556011 95140DFB 994 59D39CE0 91308B41 05746DAC 23D33E5F 7CE4848D A316A9C6 995 6B9581BA 3573BFAF 31149618 8AB15423 282EE416 DC2A19C5 996 724FA91A E4ADC88B C66796EA E5677A01 F64E8C08 63139582 997 2D9DB8FC EE35C06B 1FEEA547 4D6D8F34 B1534A93 6A18B0E0 998 D20EAB86 BC9C6D6A 5207194E 68720732 FFFFFFFF FFFFFFFF 1000 The estimated symmetric-equivalent strength of this group is 175 1001 bits. 1003 Peers using ffdhe6144 that want to optimize their key exchange with a 1004 short exponent (Section 5.2) should choose a secret key of at least 1005 375 bits. 1007 A.5. ffdhe8192 1009 The 8192-bit group has registry value 260, and is calcluated from the 1010 following formula: 1012 The modulus is: p = 2^8192 - 2^8128 + {[2^8062 * e] + 10965728} * 1013 2^64 - 1 1014 The hexadecimal representation of p is: 1016 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 1017 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 1018 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 1019 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 1020 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 1021 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 1022 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 1023 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 1024 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 1025 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 1026 886B4238 611FCFDC DE355B3B 6519035B BC34F4DE F99C0238 1027 61B46FC9 D6E6C907 7AD91D26 91F7F7EE 598CB0FA C186D91C 1028 AEFE1309 85139270 B4130C93 BC437944 F4FD4452 E2D74DD3 1029 64F2E21E 71F54BFF 5CAE82AB 9C9DF69E E86D2BC5 22363A0D 1030 ABC52197 9B0DEADA 1DBF9A42 D5C4484E 0ABCD06B FA53DDEF 1031 3C1B20EE 3FD59D7C 25E41D2B 669E1EF1 6E6F52C3 164DF4FB 1032 7930E9E4 E58857B6 AC7D5F42 D69F6D18 7763CF1D 55034004 1033 87F55BA5 7E31CC7A 7135C886 EFB4318A ED6A1E01 2D9E6832 1034 A907600A 918130C4 6DC778F9 71AD0038 092999A3 33CB8B7A 1035 1A1DB93D 7140003C 2A4ECEA9 F98D0ACC 0A8291CD CEC97DCF 1036 8EC9B55A 7F88A46B 4DB5A851 F44182E1 C68A007E 5E0DD902 1037 0BFD64B6 45036C7A 4E677D2C 38532A3A 23BA4442 CAF53EA6 1038 3BB45432 9B7624C8 917BDD64 B1C0FD4C B38E8C33 4C701C3A 1039 CDAD0657 FCCFEC71 9B1F5C3E 4E46041F 388147FB 4CFDB477 1040 A52471F7 A9A96910 B855322E DB6340D8 A00EF092 350511E3 1041 0ABEC1FF F9E3A26E 7FB29F8C 183023C3 587E38DA 0077D9B4 1042 763E4E4B 94B2BBC1 94C6651E 77CAF992 EEAAC023 2A281BF6 1043 B3A739C1 22611682 0AE8DB58 47A67CBE F9C9091B 462D538C 1044 D72B0374 6AE77F5E 62292C31 1562A846 505DC82D B854338A 1045 E49F5235 C95B9117 8CCF2DD5 CACEF403 EC9D1810 C6272B04 1046 5B3B71F9 DC6B80D6 3FDD4A8E 9ADB1E69 62A69526 D43161C1 1047 A41D570D 7938DAD4 A40E329C CFF46AAA 36AD004C F600C838 1048 1E425A31 D951AE64 FDB23FCE C9509D43 687FEB69 EDD1CC5E 1049 0B8CC3BD F64B10EF 86B63142 A3AB8829 555B2F74 7C932665 1050 CB2C0F1C C01BD702 29388839 D2AF05E4 54504AC7 8B758282 1051 2846C0BA 35C35F5C 59160CC0 46FD8251 541FC68C 9C86B022 1052 BB709987 6A460E74 51A8A931 09703FEE 1C217E6C 3826E52C 1053 51AA691E 0E423CFC 99E9E316 50C1217B 624816CD AD9A95F9 1054 D5B80194 88D9C0A0 A1FE3075 A577E231 83F81D4A 3F2FA457 1055 1EFC8CE0 BA8A4FE8 B6855DFE 72B0A66E DED2FBAB FBE58A30 1056 FAFABE1C 5D71A87E 2F741EF8 C1FE86FE A6BBFDE5 30677F0D 1057 97D11D49 F7A8443D 0822E506 A9F4614E 011E2A94 838FF88C 1058 D68C8BB7 C5C6424C FFFFFFFF FFFFFFFF 1060 The generator is: g = 2 1061 The group size is: q = (p-1)/2 1063 The hexadecimal representation of q is: 1065 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 1066 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 1067 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 1068 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 1069 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 1070 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 1071 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 1072 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 1073 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 1074 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 1075 4435A11C 308FE7EE 6F1AAD9D B28C81AD DE1A7A6F 7CCE011C 1076 30DA37E4 EB736483 BD6C8E93 48FBFBF7 2CC6587D 60C36C8E 1077 577F0984 C289C938 5A098649 DE21BCA2 7A7EA229 716BA6E9 1078 B279710F 38FAA5FF AE574155 CE4EFB4F 743695E2 911B1D06 1079 D5E290CB CD86F56D 0EDFCD21 6AE22427 055E6835 FD29EEF7 1080 9E0D9077 1FEACEBE 12F20E95 B34F0F78 B737A961 8B26FA7D 1081 BC9874F2 72C42BDB 563EAFA1 6B4FB68C 3BB1E78E AA81A002 1082 43FAADD2 BF18E63D 389AE443 77DA18C5 76B50F00 96CF3419 1083 5483B005 48C09862 36E3BC7C B8D6801C 0494CCD1 99E5C5BD 1084 0D0EDC9E B8A0001E 15276754 FCC68566 054148E6 E764BEE7 1085 C764DAAD 3FC45235 A6DAD428 FA20C170 E345003F 2F06EC81 1086 05FEB25B 2281B63D 2733BE96 1C29951D 11DD2221 657A9F53 1087 1DDA2A19 4DBB1264 48BDEEB2 58E07EA6 59C74619 A6380E1D 1088 66D6832B FE67F638 CD8FAE1F 2723020F 9C40A3FD A67EDA3B 1089 D29238FB D4D4B488 5C2A9917 6DB1A06C 50077849 1A8288F1 1090 855F60FF FCF1D137 3FD94FC6 0C1811E1 AC3F1C6D 003BECDA 1091 3B1F2725 CA595DE0 CA63328F 3BE57CC9 77556011 95140DFB 1092 59D39CE0 91308B41 05746DAC 23D33E5F 7CE4848D A316A9C6 1093 6B9581BA 3573BFAF 31149618 8AB15423 282EE416 DC2A19C5 1094 724FA91A E4ADC88B C66796EA E5677A01 F64E8C08 63139582 1095 2D9DB8FC EE35C06B 1FEEA547 4D6D8F34 B1534A93 6A18B0E0 1096 D20EAB86 BC9C6D6A 5207194E 67FA3555 1B568026 7B00641C 1097 0F212D18 ECA8D732 7ED91FE7 64A84EA1 B43FF5B4 F6E8E62F 1098 05C661DE FB258877 C35B18A1 51D5C414 AAAD97BA 3E499332 1099 E596078E 600DEB81 149C441C E95782F2 2A282563 C5BAC141 1100 1423605D 1AE1AFAE 2C8B0660 237EC128 AA0FE346 4E435811 1101 5DB84CC3 B523073A 28D45498 84B81FF7 0E10BF36 1C137296 1102 28D5348F 07211E7E 4CF4F18B 286090BD B1240B66 D6CD4AFC 1103 EADC00CA 446CE050 50FF183A D2BBF118 C1FC0EA5 1F97D22B 1104 8F7E4670 5D4527F4 5B42AEFF 39585337 6F697DD5 FDF2C518 1105 7D7D5F0E 2EB8D43F 17BA0F7C 60FF437F 535DFEF2 9833BF86 1106 CBE88EA4 FBD4221E 84117283 54FA30A7 008F154A 41C7FC46 1107 6B4645DB E2E32126 7FFFFFFF FFFFFFFF 1109 The estimated symmetric-equivalent strength of this group is 192 1110 bits. 1112 Peers using ffdhe8192 that want to optimize their key exchange with a 1113 short exponent (Section 5.2) should choose a secret key of at least 1114 400 bits. 1116 Author's Address 1118 Daniel Kahn Gillmor 1119 ACLU 1120 125 Broad Street, 18th Floor 1121 New York, NY 10004 1122 USA 1124 Email: dkg@fifthhorseman.net