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Checking references for intended status: Informational ---------------------------------------------------------------------------- -- Looks like a reference, but probably isn't: '1' on line 686 ** Obsolete normative reference: RFC 4492 (Obsoleted by RFC 8422) ** Obsolete normative reference: RFC 5246 (Obsoleted by RFC 8446) Summary: 2 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 December 19, 2014 5 approved) 6 Intended status: Informational 7 Expires: June 22, 2015 9 Negotiated Finite Field Diffie-Hellman Ephemeral Parameters for TLS 10 draft-ietf-tls-negotiated-ff-dhe-05 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 June 22, 2015. 41 Copyright Notice 43 Copyright (c) 2014 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 . . . . . . . . 9 74 9.2. Group strength considerations . . . . . . . . . . . . . . 10 75 9.3. Finite-Field DHE only . . . . . . . . . . . . . . . . . . 11 76 9.4. Deprecating weak groups . . . . . . . . . . . . . . . . . 11 77 9.5. Choice of groups . . . . . . . . . . . . . . . . . . . . 11 78 9.6. Timing attacks . . . . . . . . . . . . . . . . . . . . . 12 79 9.7. Replay attacks from non-negotiated FFDHE . . . . . . . . 12 80 9.8. Forward Secrecy . . . . . . . . . . . . . . . . . . . . . 12 81 9.9. False Start . . . . . . . . . . . . . . . . . . . . . . . 13 82 10. Privacy Considerations . . . . . . . . . . . . . . . . . . . 13 83 10.1. Client fingerprinting . . . . . . . . . . . . . . . . . 13 84 11. References . . . . . . . . . . . . . . . . . . . . . . . . . 13 85 11.1. Normative References . . . . . . . . . . . . . . . . . . 13 86 11.2. Informative References . . . . . . . . . . . . . . . . . 14 87 11.3. URIs . . . . . . . . . . . . . . . . . . . . . . . . . . 15 88 Appendix A. Named Group Registry . . . . . . . . . . . . . . . . 15 89 A.1. ffdhe2048 . . . . . . . . . . . . . . . . . . . . . . . . 16 90 A.2. ffdhe3072 . . . . . . . . . . . . . . . . . . . . . . . . 17 91 A.3. ffdhe4096 . . . . . . . . . . . . . . . . . . . . . . . . 18 92 A.4. ffdhe8192 . . . . . . . . . . . . . . . . . . . . . . . . 20 93 Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 23 95 1. Introduction 97 Traditional TLS [RFC5246] offers a Diffie-Hellman ephemeral (DHE) key 98 exchange mode which provides Forward Secrecy for the connection. The 99 client offers a ciphersuite in the ClientHello that includes DHE, and 100 the server offers the client group parameters generator g and modulus 101 p. If the client does not consider the group strong enough (e.g. if 102 p is too small, or if p is not prime, or there are small subgroups), 103 or if it is unable to process the group for other reasons, the client 104 has no recourse but to terminate the connection. 106 Conversely, when a TLS server receives a suggestion for a DHE 107 ciphersuite from a client, it has no way of knowing what kinds of DH 108 groups the client is capable of handling, or what the client's 109 security requirements are for this key exchange session. For 110 example, some widely-distributed TLS clients are not capable of DH 111 groups where p > 1024 bits. Other TLS clients may by policy wish to 112 use DHE only if the server can offer a stronger group (and are 113 willing to use a non-PFS key-exchange mechanism otherwise). The 114 server has no way of knowing which type of client is connecting, but 115 must select DH parameters with insufficient knowledge. 117 Additionally, the DH parameters chosen by the server may have a known 118 structure which renders them secure against a small subgroup attack, 119 but a client receiving an arbitrary p and g has no efficient way to 120 verify that the structure of a new group is reasonable for use. 122 This modification to TLS solves these problems by using a section of 123 the "EC Named Curves" registry to select common DH groups with known 124 structure; defining the use of the "elliptic_curves(10)" extension 125 (described here as "Supported Groups" extension) for clients 126 advertising support for DHE with these groups. This document also 127 provides guidance for compliant peers to take advantage of the 128 additional security, availability, and efficiency offered. 130 The use of this mechanism by one compliant peer when interacting with 131 a non-compliant peer should have no detrimental effects. 133 1.1. Requirements Language 135 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 136 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this 137 document are to be interpreted as described in [RFC2119]. 139 1.2. Vocabulary 141 The terms "DHE" or "FFDHE" are used in this document to refer to the 142 finite-field-based Diffie-Hellman ephemeral key exchange mechanism in 143 TLS. TLS also supports elliptic-curve-based Diffie-Hellman (ECDHE) 144 ephemeral key exchanges [RFC4492], but this document does not 145 document their use. A registry previously used only by ECHDE-capable 146 implementations is expanded in this document to cover FFDHE groups as 147 well. "FFDHE ciphersuites" is used in this document to refer 148 exclusively to ciphersuites with FFDHE key exchange mechanisms, but 149 note that these suites are typically labeled with a TLS_DHE_ prefix. 151 2. Named Group Overview 153 We use previously-unallocated codepoints within the extension 154 currently known as "elliptic_curves" (section 5.1.1. of [RFC4492]) to 155 indicate known finite field groups. The extension's semantics are 156 expanded from "Supported Elliptic Curves" to "Supported Groups". The 157 semantics of the extension's data type (enum NamedCurve) is also 158 expanded from "named curve" to "named group". 160 Codepoints in the NamedCurve registry with a high byte of 0x01 (that 161 is, between 256 and 511 inclusive) are set aside for FFDHE groups, 162 though only a small number of them are initially defined and we do 163 not expect many other FFDHE groups to be added to this range. No 164 codepoints outside of this range will be allocated to FFDHE groups. 165 The new code points for the NamedCurve registry are: 167 enum { 168 // other already defined elliptic curves (see RFC 4492) 169 ffdhe2048(256), ffdhe3072(257), ffdhe4096(258), 170 ffdhe8192(259), 171 // 172 } NamedCurve; 174 These additions to the Named Curve registry are described in detail 175 in Appendix A. They are all safe primes derived from the base of the 176 natural logarithm ("e"), with the high and low 64 bits set to 1 for 177 efficient Montgomery or Barrett reduction. 179 The use of the base of the natural logarithm here is as a "nothing- 180 up-my-sleeve" number. The goal is to guarantee that the bits in the 181 middle of the modulus are effectively random, while avoiding any 182 suspicion that the primes have secretly been selected to be weak 183 according to some secret criteria. [RFC3526] used pi for this value. 184 See Section 9.5 for reasons that this draft does not reuse pi. 186 3. Client Behavior 188 A TLS client that is capable of using strong finite field Diffie- 189 Hellman groups can advertise its capabilities and its preferences for 190 stronger key exchange by using this mechanism. 192 The compatible client that wants to be able to negotiate strong FFDHE 193 SHOULD send a "Supported Groups" extension (identified by type 194 elliptic_curves(10) in [RFC4492]) in the ClientHello, and include a 195 list of known FFDHE groups in the extension data, ordered from most 196 preferred to least preferred. If the client also supports and wants 197 to offer ECDHE key exchange, it MUST use a single "Supported Groups" 198 extension to include all supported groups (both ECDHE and FFDHE 199 groups). The ordering SHOULD be based on client preference, but see 200 Section 6.1 for more nuance. 202 A client that offers any of these values in the elliptic_curves 203 extension SHOULD ALSO include at least one FFDHE ciphersuite in the 204 Client Hello. 206 A client who offers a group MUST be able and willing to perform a DH 207 key exchange using that group. 209 A client that offers one or more FFDHE groups in the "Supported 210 Groups" extension and an FFDHE ciphersuite, and receives an FFDHE 211 ciphersuite from the server SHOULD take the following steps upon 212 receiving the ServerKeyExchange: 214 For non-anonymous ciphersuites where the offered Certificate is 215 valid and appropriate for the peer, validate the signature over 216 the ServerDHParams. If not valid, terminate the connection. 218 If the signature over ServerDHParams is valid, compare the 219 selected dh_p and dh_g with the FFDHE groups offered by the 220 client. If none of the offered groups match, the server is not 221 compatible with this draft. The client MAY decide to continue the 222 connection if the selected group is acceptable under local policy, 223 or it MAY decide to terminate the connection with a fatal 224 insufficient_security(71) alert. 226 If the selected group matches an offered FFDHE group exactly, the 227 the client MUST verify that dh_Ys is in the range 1 < dh_Ys < dh_p 228 - 1. If dh_Ys is not in this range, the client MUST terminate the 229 connection with a fatal handshake_failure(40) alert. 231 If the selected group matches an offered FFDHE group exactly, and 232 dh_Ys is in range, then the client SHOULD continue with the 233 connection as usual. 235 4. Server Behavior 237 If a compatible TLS server receives a Supported Groups extension from 238 a client that includes any FFDHE group (i.e. any codepoint between 239 256 and 511 inclusive, even if unknown to the server), and if none of 240 the client-proposed FFDHE groups are known and acceptable to the 241 server, then the server SHOULD NOT select an FFDHE ciphersuite. In 242 this case, the server SHOULD select an acceptable non-FFDHE 243 ciphersuite from the client's offered list. If the extension is 244 present with FFDHE groups, none of the client's offered groups are 245 acceptable by the server, and none of the client's proposed non-FFDHE 246 ciphersuites are acceptable to the server, the server SHOULD end the 247 connection with a fatal TLS alert of type insufficient_security(71). 249 If at least one FFDHE ciphersuite is present in the client 250 ciphersuite list, and the Supported Groups extension is present in 251 the ClientHello, but the extension does not include any FFDHE groups 252 (i.e. no codepoints between 256 and 511 inclusive), then the server 253 knows that the client is not compatible with this document. In this 254 scenario, a server MAY choose to select a non-FFDHE ciphersuite, or 255 MAY choose an FFDHE ciphersuite and offer an FFDHE group of its 256 choice to the client as part of a traditional ServerKeyExchange. 258 A compatible TLS server that receives the Supported Groups extension 259 with FFDHE codepoints in it, and which selects an FFDHE ciphersuite 260 MUST select one of the client's offered groups. The server indicates 261 the choice of group to the client by sending the group's parameters 262 as usual in the ServerKeyExchange as described in section 7.4.3 of 263 [RFC5246]. 265 A TLS server MUST NOT select a named FFDHE group that was not offered 266 by a compatible client. 268 A TLS server MUST NOT select an FFDHE ciphersuite if the client did 269 not offer one, even if the client offered an FFDHE group in the 270 Supported Groups extension. 272 If a non-anonymous FFDHE ciphersuite is chosen, and the TLS client 273 has used this extension to offer an FFDHE group of comparable or 274 greater strength than the server's public key, the server SHOULD 275 select an FFDHE group at least as strong as the server's public key. 276 For example, if the server has a 3072-bit RSA key, and the client 277 offers only ffdhe2048 and ffdhe4096, the server SHOULD select 278 ffdhe4096. 280 When a compatible server selects an FFDHE group from among a client's 281 Supported Groups, and the client sends a ClientKeyExchange, the 282 server MUST verify that 1 < dh_Yc < dh_p - 1. If it is out of range, 283 the server MUST terminate the connection with fatal 284 handshake_failure(40) alert. 286 5. Optimizations 288 In a key exchange with a successfully negotiated known FFDHE group, 289 both peers know that the group in question uses a safe prime as a 290 modulus, and that the group in use is of size p-1 or (p-1)/2. This 291 allows at least three optimizations that can be used to improve 292 performance. 294 5.1. Checking the Peer's Public Key 296 Peers MUST validate each other's public key Y (dh_Ys offered by the 297 server or dh_Yc offered by the client) by ensuring that 1 < Y < p-1. 298 This simple check ensures that the remote peer is properly behaved 299 and isn't forcing the local system into a small subgroup. 301 To reach the same assurance with an unknown group, the client would 302 need to verify the primality of the modulus, learn the factors of 303 p-1, and test both the generator g and Y against each factor to avoid 304 small subgroup attacks. 306 5.2. Short Exponents 308 Traditional Finite Field Diffie-Hellman has each peer choose their 309 secret exponent from the range [2,p-2]. Using exponentiation by 310 squaring, this means each peer must do roughly 2*log_2(p) 311 multiplications, twice (once for the generator and once for the 312 peer's public key). 314 Peers concerned with performance may also prefer to choose their 315 secret exponent from a smaller range, doing fewer multiplications, 316 while retaining the same level of overall security. Each named group 317 indicates its approximate security level, and provides a lower-bound 318 on the range of secret exponents that should preserve it. For 319 example, rather than doing 2*2*3072 multiplications for a ffdhe3072 320 handshake, each peer can choose to do 2*2*250 multiplications by 321 choosing their secret exponent from the range [2^249,2^250] (that is, 322 a m-bit integer where m is at least 224) and still keep the 323 approximate 125-bit security level. 325 A similar short-exponent approach is suggested in SSH's Diffie- 326 Hellman key exchange (See section 6.2 of [RFC4419]). 328 5.3. Table Acceleration 330 Peers wishing to further accelerate FFDHE key exchange can also pre- 331 compute a table of powers of the generator of a known group. This is 332 a memory vs. time tradeoff, and it only accelerates the first 333 exponentiation of the ephemeral DH exchange (the fixed-base 334 exponentiation). The variable-base exponentiation (using the peer's 335 public exponent as a base) still needs to be calculated as normal. 337 6. Operational Considerations 339 6.1. Preference Ordering 341 The ordering of named groups in the Supported Groups extension may 342 contain some ECDHE groups and some FFDHE groups. These SHOULD be 343 ranked in the order preferred by the client. 345 However, the ClientHello also contains list of desired ciphersuites, 346 also ranked in preference order. This presents the possibility of 347 conflicted preferences. For example, if the ClientHello contains a 348 CipherSuite with two choices in order 349 and the Supported Groups 351 Extension contains two choices in order then 352 there is a clear contradiction. Clients SHOULD NOT present such a 353 contradiction since it does not represent a sensible ordering. A 354 server that encounters such an contradiction when selecting between 355 an ECDHE or FFDHE key exchange mechanism while trying to respect 356 client preferences SHOULD give priority to the Supported Groups 357 extension (in the example case, it should select 358 TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA with secp256r1), but MAY resolve 359 the contradiction any way it sees fit. 361 More subtly, clients MAY interleave preferences between ECDHE and 362 FFDHE groups, for example if stronger groups are preferred regardless 363 of cost, but weaker groups are acceptable, the Supported Groups 364 extension could consist of: 365 . In this example, with the 366 same CipherSuite offered as the previous example, a server configured 367 to respect client preferences and with support for all listed groups 368 SHOULD select TLS_DHE_RSA_WITH_AES_128_CBC_SHA with ffdhe8192. A 369 server configured to respect client preferences and with support for 370 only secp384p1 and ffdhe3072 SHOULD select 371 TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA with secp384p1. 373 7. Acknowledgements 375 Thanks to Fedor Brunner, Dave Fergemann, Sandy Harris, Watson Ladd, 376 Nikos Mavrogiannopolous, Niels Moeller, Bodo Moeller, Kenny Paterson, 377 Eric Rescorla, Tom Ritter, Rene Struik, Martin Thomson, Sean Turner, 378 and other members of the TLS Working Group for their comments and 379 suggestions on this draft. Any mistakes here are not theirs. 381 8. IANA Considerations 383 IANA maintains the registry currently known as EC Named Curves 384 (originally defined in [RFC4492] and updated by [RFC7027]) at [1]. 386 This document expands the semantics of this registry slightly, to 387 include groups based on finite fields in addition to groups based on 388 elliptic curves. It should add a range designation to that registry, 389 indicating that values from 256-511 (inclusive) are set aside for 390 "Finite Field Diffie-Hellman groups", and that all other entries in 391 the registry are "Elliptic curve groups". 393 This document allocates five codepoints in the registry, as follows: 395 +-------+-------------+---------+-----------------+ 396 | Value | Description | DTLS-OK | Reference | 397 +-------+-------------+---------+-----------------+ 398 | 256 | ffdhe2048 | Y | [this document] | 399 | 257 | ffdhe3072 | Y | [this document] | 400 | 258 | ffdhe4096 | Y | [this document] | 401 | 259 | ffdhe8192 | Y | [this document] | 402 +-------+-------------+---------+-----------------+ 404 9. Security Considerations 406 9.1. Negotiation resistance to active attacks 408 Because the contents of the Supported Groups extension is hashed in 409 the finished message, an active MITM that tries to filter or omit 410 groups will cause the handshake to fail, but possibly not before 411 getting the peer to do something they would not otherwise have done. 413 An attacker who impersonates the server can try to do any of the 414 following: 416 Pretend that a non-compatible server is actually capable of this 417 extension, and select a group from the client's list, causing the 418 client to select a group it is willing to negotiate. It is 419 unclear how this would be an effective attack. 421 Pretend that a compatible server is actually non-compatible by 422 negotiating a non-FFDHE ciphersuite. This is no different than 423 MITM ciphersuite filtering. 425 Pretend that a compatible server is actually non-compatible by 426 negotiating a DHE ciphersuite, with a custom (perhaps weak) group 427 chosen by the attacker. This is no worse than the current 428 scenario, and would require the attacker to be able to sign the 429 ServerDHParams, which should not be possible without access to the 430 server's secret key. 432 An attacker who impersonates the client can try to do the following: 434 Pretend that a compatible client is not compatible (e.g. by not 435 offering the Supported Groups extension, or by replacing the 436 Supported Groups extension with one that includes no FFDHE 437 groups). This could cause the server to negotiate a weaker DHE 438 group during the handshake, or to select a non-FFDHE ciphersuite, 439 but it would fail to complete during the final check of the 440 Finished message. 442 Pretend that a non-compatible client is compatible (e.g. by . 443 This could cause the server to select a particular named group in 444 the ServerKeyExchange, or to avoid selecting an FFDHE ciphersuite. 445 The peers would fail to compute the final check of the Finished 446 message. 448 Change the list of groups offered by the client (e.g. by removing 449 the stronger of the set of groups offered). This could cause the 450 server to negotiate a weaker group than desired, but again should 451 be caught by the check in the Finished message. 453 9.2. Group strength considerations 455 TLS implementations using FFDHE key exchange should consider the 456 strength of the group they negotiate. The strength of the selected 457 group is one of the factors which defines the connection's resiliance 458 against attacks on the session's confidentiality and integrity, since 459 the session keys are derived from the DHE handshake. 461 While attacks on integrity must generally happen while the session is 462 in progress, attacks against session confidentiality can happen 463 significantly later, if the entire TLS session is stored for offline 464 analysis. Therefore, FFDHE groups should be selected by clients and 465 servers based on confidentiality guarantees they need. Sessions 466 which need extremely long-term confidentiality should prefer stronger 467 groups. 469 [ENISA] provides rough estimates of group resistance to attack, and 470 recommends that forward-looking implementations ("future systems") 471 should use FFDHE group sizes of at least 3072 bits. ffdhe3072 is 472 intended for use in these implementations. 474 9.3. Finite-Field DHE only 476 Note that this document specifically targets only finite field-based 477 Diffie-Hellman ephemeral key exchange mechanisms. It does not cover 478 the non-ephemeral DH key exchange mechanisms, nor does it address 479 elliptic curve DHE (ECDHE) key exchange, which is defined in 480 [RFC4492]. 482 Measured by computational cost to the TLS peers, ECDHE appears today 483 to offer much a stronger key exchange than FFDHE. 485 9.4. Deprecating weak groups 487 Advances in hardware or in finite field cryptanalysis may cause some 488 of the negotiated groups to not provide the desired security margins, 489 as indicated by the estimated work factor of an adversary to discover 490 the premaster secret (and may therefore compromise the 491 confidentiality and integrity of the TLS session). 493 Revisions of this document should mark known-weak groups as 494 explicitly deprecated for use in TLS, and should update the estimated 495 work factor needed to break the group, if the cryptanalysis has 496 changed. Implementations that require strong confidentiality and 497 integrity guarantees should avoid using deprecated groups and should 498 be updated when the estimated security margins are updated. 500 9.5. Choice of groups 502 Other lists of named finite field Diffie-Hellman groups 503 [STRONGSWAN-IKE] exist. This draft chooses to not reuse them for 504 several reasons: 506 Using the same groups in multiple protocols increases the value 507 for an attacker with the resources to crack any single group. 509 The IKE groups include weak groups like MODP768 which are 510 unacceptable for secure TLS traffic. 512 Mixing group parameters across multiple implementations leaves 513 open the possibility of some sort of cross-protocol attack. This 514 shouldn't be relevant for ephemeral scenarios, and even with non- 515 ephemeral keying, services shouldn't share keys; however, using 516 different groups avoids these failure modes entirely. 518 9.6. Timing attacks 520 Any implementation of finite field Diffie-Hellman key exchange should 521 use constant-time modular-exponentiation implementations. This is 522 particularly true for those implementations that ever re-use DHE 523 secret keys (so-called "semi-static" ephemeral keying) or share DHE 524 secret keys across a multiple machines (e.g. in a load-balancer 525 situation). 527 9.7. Replay attacks from non-negotiated FFDHE 529 [SECURE-RESUMPTION], [CROSS-PROTOCOL], and [SSL3-ANALYSIS] all show a 530 malicious peer using a bad FFDHE group to maneuver a client into 531 selecting a pre-master secret of the peer's choice, which can be 532 replayed to another server using a non-FFDHE key exchange, and can 533 then be bootstrapped to replay client authentication. 535 To prevent this attack (barring the fixes proposed in 536 [SESSION-HASH]), a client would need not only to implement this 537 draft, but also to reject non-negotiated FFDHE ciphersuites whose 538 group structure it cannot afford to verify. Such a client would need 539 to abort the initial handshake and reconnect to the server in 540 question without listing any FFDHE ciphersuites on the subsequent 541 connection. 543 This tradeoff may be too costly for most TLS clients today, but may 544 be a reasonable choice for clients performing client certificate 545 authentication, or who have other reason to be concerned about 546 server-controlled pre-master secrets. 548 9.8. Forward Secrecy 550 One of the main reasons to prefer FFDHE ciphersuites is Forward 551 Secrecy, the ability to resist decryption even if when the endpoint's 552 long-term secret key (usually RSA) is revealed in the future. 554 This property depends on both sides of the connection discarding 555 their ephemeral keys promptly. Implementations should wipe their 556 FFDHE secret key material from memory as soon as it is no longer 557 needed, and should never store it in persistent storage. 559 Forward secrecy also depends on the strength of the Diffie-Hellman 560 group; using a very strong symmetric cipher like AES256 with a 561 forward-secret ciphersuite, but generating the keys with a much 562 weaker group like dhe2048 simply moves the adversary's cost from 563 attacking the symmetric cipher to attacking the dh_Ys or dh_Yc 564 ephemeral keyshares. 566 If the goal is to provide forward secrecy, attention should be paid 567 to all parts of the ciphersuite selection process, both key exchange 568 and symmetric cipher choice. 570 9.9. False Start 572 Clients capable of TLS False Start [FALSE-START] may receive a 573 proposed FFDHE group from a server that is attacker-controlled. In 574 particular, the attacker can modify the ClientHello to strip the 575 proposed FFDHE groups, which may cause the server to offer a weaker 576 FFDHE group than it should, and this will not be detected until 577 receipt of the server's Finished message. This could cause the a 578 client using the False Start protocol modification to send data 579 encrypted under a weak key agreement. 581 Clients should have their own classification of FFDHE groups that are 582 "cryptographically strong" in the same sense described in the 583 description of symmetric ciphers in [FALSE-START], and MUST offer at 584 least one of these in the initial handshake if they contemplate using 585 the False Start protocol modification. 587 Compatible clients performing a full handshake MUST NOT use the False 588 Start protocol modification if the server selects an FFDHE 589 ciphersuite but sends a group that is not cryptographically strong 590 from the client's perspective. 592 10. Privacy Considerations 594 10.1. Client fingerprinting 596 This extension provides a few additional bits of information to 597 distinguish between classes of TLS clients (see e.g. 598 [PANOPTICLICK]). To minimize this sort of fingerprinting, clients 599 SHOULD support all named groups at or above their minimum security 600 threshhold. New named groups SHOULD NOT be added to the registry 601 without consideration of the cost of browser fingerprinting. 603 11. References 605 11.1. Normative References 607 [FALSE-START] 608 Langley, A., Modadugu, N., and B. Moeller, "Transport 609 Layer Security (TLS) False Start", Work in Progress, 610 draft-bmoeller-tls-falsestart-01, November 2014. 612 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate 613 Requirement Levels", BCP 14, RFC 2119, March 1997. 615 [RFC4492] Blake-Wilson, S., Bolyard, N., Gupta, V., Hawk, C., and B. 616 Moeller, "Elliptic Curve Cryptography (ECC) Cipher Suites 617 for Transport Layer Security (TLS)", RFC 4492, May 2006. 619 [RFC5246] Dierks, T. and E. Rescorla, "The Transport Layer Security 620 (TLS) Protocol Version 1.2", RFC 5246, August 2008. 622 11.2. Informative References 624 [CROSS-PROTOCOL] 625 Mavrogiannopolous, N., Vercauteren, F., Velichkov, V., and 626 B. Preneel, "A Cross-Protocol Attack on the TLS Protocol", 627 October 2012, 628 . 631 [ECRYPTII] 632 European Network of Excellence in Cryptology II, "ECRYPT 633 II Yearly Report on Algorithms and Keysizes (2011-2012)", 634 September 2012, 635 . 637 [ENISA] European Union Agency for Network and Information Security 638 Agency, "Algorithms, Key Sizes and Parameters Report, 639 version 1.0", October 2013, 640 . 644 [PANOPTICLICK] 645 Electronic Frontier Foundation, "Panopticlick: How Unique 646 - and Trackable - Is Your Browser?", 2010, 647 . 649 [RFC3526] Kivinen, T. and M. Kojo, "More Modular Exponential (MODP) 650 Diffie-Hellman groups for Internet Key Exchange (IKE)", 651 RFC 3526, May 2003. 653 [RFC4419] Friedl, M., Provos, N., and W. Simpson, "Diffie-Hellman 654 Group Exchange for the Secure Shell (SSH) Transport Layer 655 Protocol", RFC 4419, March 2006. 657 [RFC7027] Merkle, J. and M. Lochter, "Elliptic Curve Cryptography 658 (ECC) Brainpool Curves for Transport Layer Security 659 (TLS)", RFC 7027, October 2013. 661 [SECURE-RESUMPTION] 662 Delignat-Lavaud, A., Bhargavan, K., and A. Pironti, 663 "Triple Handshakes Considered Harmful: Breaking and Fixing 664 Authentication over TLS", March 2014, . 667 [SESSION-HASH] 668 Bhargavan, K., Delignat-Lavaud, A., Pironti, A., Langley, 669 A., and M. Ray, "Triple Handshakes Considered Harmful: 670 Breaking and Fixing Authentication over TLS", March 2014, 671 . 674 [SSL3-ANALYSIS] 675 Schneier, B. and D. Wagner, "Analysis of the SSL 3.0 676 protocol", 1996, . 678 [STRONGSWAN-IKE] 679 Brunner, T. and A. Steffen, "Diffie Hellman Groups in 680 IKEv2 Cipher Suites", October 2013, 681 . 684 11.3. URIs 686 [1] https://www.iana.org/assignments/tls-parameters/tls- 687 parameters.xhtml#tls-parameters-8 689 Appendix A. Named Group Registry 691 Each description below indicates the group itself, its derivation, 692 its expected strength (estimated roughly from guidelines in 693 [ECRYPTII]), and whether it is recommended for use in TLS key 694 exchange at the given security level. It is not recommended to add 695 further finite field groups to the NamedCurves registry; any attempt 696 to do so should consider Section 10.1. 698 The primes in these finite field groups are all safe primes, that is, 699 a prime p is a safe prime when q = (p-1)/2 is also prime. Where e is 700 the base of the natural logarithm, and square brackets denote the 701 floor operation, the groups which initially populate this registry 702 are derived for a given bitlength b by finding the lowest positive 703 integer X that creates a safe prime p where: 705 p = 2^b - 2^{b-64} + {[2^{b-130} e] + X } * 2^64 - 1 707 New additions of FFDHE groups to this registry may use this same 708 derivation (e.g. with different bitlengths) or may choose their 709 parameters in a different way, but must be clear about how the 710 parameters were derived. 712 New additions of FFDHE groups MUST use a safe prime as the modulus to 713 enable the inexpensive peer verification described in Section 5.1. 715 A.1. ffdhe2048 717 The 2048-bit group has registry value 256, and is calcluated from the 718 following formula: 720 The modulus is: p = 2^2048 - 2^1984 + {[2^1918 * e] + 560315 } * 2^64 721 - 1 723 The hexadecimal representation of p is: 725 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 726 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 727 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 728 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 729 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 730 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 731 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 732 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 733 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 734 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 735 886B4238 61285C97 FFFFFFFF FFFFFFFF 737 The generator is: g = 2 739 The group size is: q = (p-1)/2 741 The hexadecimal representation of q is: 743 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 744 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 745 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 746 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 747 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 748 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 749 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 750 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 751 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 752 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 753 4435A11C 30942E4B FFFFFFFF FFFFFFFF 755 The estimated symmetric-equivalent strength of this group is 103 756 bits. 758 Peers using ffdhe2048 that want to optimize their key exchange with a 759 short exponent (Section 5.2) should choose a secret key of at least 760 206 bits. 762 A.2. ffdhe3072 764 The 3072-bit prime has registry value 257, and is calcluated from the 765 following formula: 767 The modulus is: p = 2^3072 - 2^3008 + {[2^2942 * e] + 2625351} * 2^64 768 -1 770 The hexadecimal representation of p is: 772 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 773 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 774 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 775 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 776 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 777 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 778 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 779 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 780 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 781 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 782 886B4238 611FCFDC DE355B3B 6519035B BC34F4DE F99C0238 783 61B46FC9 D6E6C907 7AD91D26 91F7F7EE 598CB0FA C186D91C 784 AEFE1309 85139270 B4130C93 BC437944 F4FD4452 E2D74DD3 785 64F2E21E 71F54BFF 5CAE82AB 9C9DF69E E86D2BC5 22363A0D 786 ABC52197 9B0DEADA 1DBF9A42 D5C4484E 0ABCD06B FA53DDEF 787 3C1B20EE 3FD59D7C 25E41D2B 66C62E37 FFFFFFFF FFFFFFFF 789 The generator is: g = 2 791 The group size is: q = (p-1)/2 793 The hexadecimal representation of q is: 795 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 796 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 797 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 798 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 799 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 800 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 801 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 802 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 803 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 804 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 805 4435A11C 308FE7EE 6F1AAD9D B28C81AD DE1A7A6F 7CCE011C 806 30DA37E4 EB736483 BD6C8E93 48FBFBF7 2CC6587D 60C36C8E 807 577F0984 C289C938 5A098649 DE21BCA2 7A7EA229 716BA6E9 808 B279710F 38FAA5FF AE574155 CE4EFB4F 743695E2 911B1D06 809 D5E290CB CD86F56D 0EDFCD21 6AE22427 055E6835 FD29EEF7 810 9E0D9077 1FEACEBE 12F20E95 B363171B FFFFFFFF FFFFFFFF 812 The estimated symmetric-equivalent strength of this group is 125 813 bits. 815 Peers using ffdhe3072 that want to optimize their key exchange with a 816 short exponent (Section 5.2) should choose a secret key of at least 817 250 bits. 819 A.3. ffdhe4096 821 The 4096-bit group has registry value 258, and is calcluated from the 822 following formula: 824 The modulus is: p = 2^4096 - 2^4032 + {[2^3966 * e] + 5736041} * 2^64 825 - 1 827 The hexadecimal representation of p is: 829 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 830 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 831 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 832 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 833 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 834 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 835 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 836 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 837 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 838 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 839 886B4238 611FCFDC DE355B3B 6519035B BC34F4DE F99C0238 840 61B46FC9 D6E6C907 7AD91D26 91F7F7EE 598CB0FA C186D91C 841 AEFE1309 85139270 B4130C93 BC437944 F4FD4452 E2D74DD3 842 64F2E21E 71F54BFF 5CAE82AB 9C9DF69E E86D2BC5 22363A0D 843 ABC52197 9B0DEADA 1DBF9A42 D5C4484E 0ABCD06B FA53DDEF 844 3C1B20EE 3FD59D7C 25E41D2B 669E1EF1 6E6F52C3 164DF4FB 845 7930E9E4 E58857B6 AC7D5F42 D69F6D18 7763CF1D 55034004 846 87F55BA5 7E31CC7A 7135C886 EFB4318A ED6A1E01 2D9E6832 847 A907600A 918130C4 6DC778F9 71AD0038 092999A3 33CB8B7A 848 1A1DB93D 7140003C 2A4ECEA9 F98D0ACC 0A8291CD CEC97DCF 849 8EC9B55A 7F88A46B 4DB5A851 F44182E1 C68A007E 5E655F6A 850 FFFFFFFF FFFFFFFF 852 The generator is: g = 2 854 The group size is: q = (p-1)/2 856 The hexadecimal representation of q is: 858 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 859 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 860 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 861 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 862 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 863 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 864 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 865 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 866 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 867 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 868 4435A11C 308FE7EE 6F1AAD9D B28C81AD DE1A7A6F 7CCE011C 869 30DA37E4 EB736483 BD6C8E93 48FBFBF7 2CC6587D 60C36C8E 870 577F0984 C289C938 5A098649 DE21BCA2 7A7EA229 716BA6E9 871 B279710F 38FAA5FF AE574155 CE4EFB4F 743695E2 911B1D06 872 D5E290CB CD86F56D 0EDFCD21 6AE22427 055E6835 FD29EEF7 873 9E0D9077 1FEACEBE 12F20E95 B34F0F78 B737A961 8B26FA7D 874 BC9874F2 72C42BDB 563EAFA1 6B4FB68C 3BB1E78E AA81A002 875 43FAADD2 BF18E63D 389AE443 77DA18C5 76B50F00 96CF3419 876 5483B005 48C09862 36E3BC7C B8D6801C 0494CCD1 99E5C5BD 877 0D0EDC9E B8A0001E 15276754 FCC68566 054148E6 E764BEE7 878 C764DAAD 3FC45235 A6DAD428 FA20C170 E345003F 2F32AFB5 879 7FFFFFFF FFFFFFFF 881 The estimated symmetric-equivalent strength of this group is 150 882 bits. 884 Peers using ffdhe4096 that want to optimize their key exchange with a 885 short exponent (Section 5.2) should choose a secret key of at least 886 300 bits. 888 A.4. ffdhe8192 890 The 8192-bit group has registry value 259, and is calcluated from the 891 following formula: 893 The modulus is: p = 2^8192 - 2^8128 + {[2^8062 * e] + 10965728} * 894 2^64 - 1 896 The hexadecimal representation of p is: 898 FFFFFFFF FFFFFFFF ADF85458 A2BB4A9A AFDC5620 273D3CF1 899 D8B9C583 CE2D3695 A9E13641 146433FB CC939DCE 249B3EF9 900 7D2FE363 630C75D8 F681B202 AEC4617A D3DF1ED5 D5FD6561 901 2433F51F 5F066ED0 85636555 3DED1AF3 B557135E 7F57C935 902 984F0C70 E0E68B77 E2A689DA F3EFE872 1DF158A1 36ADE735 903 30ACCA4F 483A797A BC0AB182 B324FB61 D108A94B B2C8E3FB 904 B96ADAB7 60D7F468 1D4F42A3 DE394DF4 AE56EDE7 6372BB19 905 0B07A7C8 EE0A6D70 9E02FCE1 CDF7E2EC C03404CD 28342F61 906 9172FE9C E98583FF 8E4F1232 EEF28183 C3FE3B1B 4C6FAD73 907 3BB5FCBC 2EC22005 C58EF183 7D1683B2 C6F34A26 C1B2EFFA 908 886B4238 611FCFDC DE355B3B 6519035B BC34F4DE F99C0238 909 61B46FC9 D6E6C907 7AD91D26 91F7F7EE 598CB0FA C186D91C 910 AEFE1309 85139270 B4130C93 BC437944 F4FD4452 E2D74DD3 911 64F2E21E 71F54BFF 5CAE82AB 9C9DF69E E86D2BC5 22363A0D 912 ABC52197 9B0DEADA 1DBF9A42 D5C4484E 0ABCD06B FA53DDEF 913 3C1B20EE 3FD59D7C 25E41D2B 669E1EF1 6E6F52C3 164DF4FB 914 7930E9E4 E58857B6 AC7D5F42 D69F6D18 7763CF1D 55034004 915 87F55BA5 7E31CC7A 7135C886 EFB4318A ED6A1E01 2D9E6832 916 A907600A 918130C4 6DC778F9 71AD0038 092999A3 33CB8B7A 917 1A1DB93D 7140003C 2A4ECEA9 F98D0ACC 0A8291CD CEC97DCF 918 8EC9B55A 7F88A46B 4DB5A851 F44182E1 C68A007E 5E0DD902 919 0BFD64B6 45036C7A 4E677D2C 38532A3A 23BA4442 CAF53EA6 920 3BB45432 9B7624C8 917BDD64 B1C0FD4C B38E8C33 4C701C3A 921 CDAD0657 FCCFEC71 9B1F5C3E 4E46041F 388147FB 4CFDB477 922 A52471F7 A9A96910 B855322E DB6340D8 A00EF092 350511E3 923 0ABEC1FF F9E3A26E 7FB29F8C 183023C3 587E38DA 0077D9B4 924 763E4E4B 94B2BBC1 94C6651E 77CAF992 EEAAC023 2A281BF6 925 B3A739C1 22611682 0AE8DB58 47A67CBE F9C9091B 462D538C 926 D72B0374 6AE77F5E 62292C31 1562A846 505DC82D B854338A 927 E49F5235 C95B9117 8CCF2DD5 CACEF403 EC9D1810 C6272B04 928 5B3B71F9 DC6B80D6 3FDD4A8E 9ADB1E69 62A69526 D43161C1 929 A41D570D 7938DAD4 A40E329C CFF46AAA 36AD004C F600C838 930 1E425A31 D951AE64 FDB23FCE C9509D43 687FEB69 EDD1CC5E 931 0B8CC3BD F64B10EF 86B63142 A3AB8829 555B2F74 7C932665 932 CB2C0F1C C01BD702 29388839 D2AF05E4 54504AC7 8B758282 933 2846C0BA 35C35F5C 59160CC0 46FD8251 541FC68C 9C86B022 934 BB709987 6A460E74 51A8A931 09703FEE 1C217E6C 3826E52C 935 51AA691E 0E423CFC 99E9E316 50C1217B 624816CD AD9A95F9 936 D5B80194 88D9C0A0 A1FE3075 A577E231 83F81D4A 3F2FA457 937 1EFC8CE0 BA8A4FE8 B6855DFE 72B0A66E DED2FBAB FBE58A30 938 FAFABE1C 5D71A87E 2F741EF8 C1FE86FE A6BBFDE5 30677F0D 939 97D11D49 F7A8443D 0822E506 A9F4614E 011E2A94 838FF88C 940 D68C8BB7 C5C6424C FFFFFFFF FFFFFFFF 942 The generator is: g = 2 944 The group size is: q = (p-1)/2 945 The hexadecimal representation of q is: 947 7FFFFFFF FFFFFFFF D6FC2A2C 515DA54D 57EE2B10 139E9E78 948 EC5CE2C1 E7169B4A D4F09B20 8A3219FD E649CEE7 124D9F7C 949 BE97F1B1 B1863AEC 7B40D901 576230BD 69EF8F6A EAFEB2B0 950 9219FA8F AF833768 42B1B2AA 9EF68D79 DAAB89AF 3FABE49A 951 CC278638 707345BB F15344ED 79F7F439 0EF8AC50 9B56F39A 952 98566527 A41D3CBD 5E0558C1 59927DB0 E88454A5 D96471FD 953 DCB56D5B B06BFA34 0EA7A151 EF1CA6FA 572B76F3 B1B95D8C 954 8583D3E4 770536B8 4F017E70 E6FBF176 601A0266 941A17B0 955 C8B97F4E 74C2C1FF C7278919 777940C1 E1FF1D8D A637D6B9 956 9DDAFE5E 17611002 E2C778C1 BE8B41D9 6379A513 60D977FD 957 4435A11C 308FE7EE 6F1AAD9D B28C81AD DE1A7A6F 7CCE011C 958 30DA37E4 EB736483 BD6C8E93 48FBFBF7 2CC6587D 60C36C8E 959 577F0984 C289C938 5A098649 DE21BCA2 7A7EA229 716BA6E9 960 B279710F 38FAA5FF AE574155 CE4EFB4F 743695E2 911B1D06 961 D5E290CB CD86F56D 0EDFCD21 6AE22427 055E6835 FD29EEF7 962 9E0D9077 1FEACEBE 12F20E95 B34F0F78 B737A961 8B26FA7D 963 BC9874F2 72C42BDB 563EAFA1 6B4FB68C 3BB1E78E AA81A002 964 43FAADD2 BF18E63D 389AE443 77DA18C5 76B50F00 96CF3419 965 5483B005 48C09862 36E3BC7C B8D6801C 0494CCD1 99E5C5BD 966 0D0EDC9E B8A0001E 15276754 FCC68566 054148E6 E764BEE7 967 C764DAAD 3FC45235 A6DAD428 FA20C170 E345003F 2F06EC81 968 05FEB25B 2281B63D 2733BE96 1C29951D 11DD2221 657A9F53 969 1DDA2A19 4DBB1264 48BDEEB2 58E07EA6 59C74619 A6380E1D 970 66D6832B FE67F638 CD8FAE1F 2723020F 9C40A3FD A67EDA3B 971 D29238FB D4D4B488 5C2A9917 6DB1A06C 50077849 1A8288F1 972 855F60FF FCF1D137 3FD94FC6 0C1811E1 AC3F1C6D 003BECDA 973 3B1F2725 CA595DE0 CA63328F 3BE57CC9 77556011 95140DFB 974 59D39CE0 91308B41 05746DAC 23D33E5F 7CE4848D A316A9C6 975 6B9581BA 3573BFAF 31149618 8AB15423 282EE416 DC2A19C5 976 724FA91A E4ADC88B C66796EA E5677A01 F64E8C08 63139582 977 2D9DB8FC EE35C06B 1FEEA547 4D6D8F34 B1534A93 6A18B0E0 978 D20EAB86 BC9C6D6A 5207194E 67FA3555 1B568026 7B00641C 979 0F212D18 ECA8D732 7ED91FE7 64A84EA1 B43FF5B4 F6E8E62F 980 05C661DE FB258877 C35B18A1 51D5C414 AAAD97BA 3E499332 981 E596078E 600DEB81 149C441C E95782F2 2A282563 C5BAC141 982 1423605D 1AE1AFAE 2C8B0660 237EC128 AA0FE346 4E435811 983 5DB84CC3 B523073A 28D45498 84B81FF7 0E10BF36 1C137296 984 28D5348F 07211E7E 4CF4F18B 286090BD B1240B66 D6CD4AFC 985 EADC00CA 446CE050 50FF183A D2BBF118 C1FC0EA5 1F97D22B 986 8F7E4670 5D4527F4 5B42AEFF 39585337 6F697DD5 FDF2C518 987 7D7D5F0E 2EB8D43F 17BA0F7C 60FF437F 535DFEF2 9833BF86 988 CBE88EA4 FBD4221E 84117283 54FA30A7 008F154A 41C7FC46 989 6B4645DB E2E32126 7FFFFFFF FFFFFFFF 991 The estimated symmetric-equivalent strength of this group is 192 992 bits. 994 Peers using ffdhe8192 that want to optimize their key exchange with a 995 short exponent (Section 5.2) should choose a secret key of at least 996 384 bits. 998 Author's Address 1000 Daniel Kahn Gillmor 1001 ACLU 1002 125 Broad Street, 18th Floor 1003 New York, NY 10004 1004 USA 1006 Email: dkg@fifthhorseman.net