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Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 Internet Engineering Task Force N. McCallum 3 Internet-Draft S. Sorce 4 Intended status: Standards Track R. Harwood 5 Expires: November 1, 2020 Red Hat, Inc. 6 G. Hudson 7 MIT 8 April 30, 2020 10 SPAKE Pre-Authentication 11 draft-ietf-kitten-krb-spake-preauth-07 13 Abstract 15 This document defines a new pre-authentication mechanism for the 16 Kerberos protocol that uses a password authenticated key exchange. 17 This document has three goals. First, increase the security of 18 Kerberos pre-authentication exchanges by making offline brute-force 19 attacks infeasible. Second, enable the use of second factor 20 authentication without relying on FAST. This is achieved using the 21 existing trust relationship established by the shared first factor. 22 Third, make Kerberos pre-authentication more resilient against time 23 synchronization errors by removing the need to transfer an encrypted 24 timestamp from the client. 26 Status of This Memo 28 This Internet-Draft is submitted in full conformance with the 29 provisions of BCP 78 and BCP 79. 31 Internet-Drafts are working documents of the Internet Engineering 32 Task Force (IETF). Note that other groups may also distribute 33 working documents as Internet-Drafts. The list of current Internet- 34 Drafts is at https://datatracker.ietf.org/drafts/current/. 36 Internet-Drafts are draft documents valid for a maximum of six months 37 and may be updated, replaced, or obsoleted by other documents at any 38 time. It is inappropriate to use Internet-Drafts as reference 39 material or to cite them other than as "work in progress." 41 This Internet-Draft will expire on November 1, 2020. 43 Copyright Notice 45 Copyright (c) 2020 IETF Trust and the persons identified as the 46 document authors. All rights reserved. 48 This document is subject to BCP 78 and the IETF Trust's Legal 49 Provisions Relating to IETF Documents 50 (https://trustee.ietf.org/license-info) in effect on the date of 51 publication of this document. Please review these documents 52 carefully, as they describe your rights and restrictions with respect 53 to this document. Code Components extracted from this document must 54 include Simplified BSD License text as described in Section 4.e of 55 the Trust Legal Provisions and are provided without warranty as 56 described in the Simplified BSD License. 58 Table of Contents 60 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 61 1.1. Properties of PAKE . . . . . . . . . . . . . . . . . . . 3 62 1.2. PAKE Algorithm Selection . . . . . . . . . . . . . . . . 3 63 1.3. PAKE and Two-Factor Authentication . . . . . . . . . . . 4 64 1.4. SPAKE Overview . . . . . . . . . . . . . . . . . . . . . 5 65 2. Document Conventions . . . . . . . . . . . . . . . . . . . . 5 66 3. Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . 6 67 3.1. PA-ETYPE-INFO2 . . . . . . . . . . . . . . . . . . . . . 6 68 3.2. Cookie Support . . . . . . . . . . . . . . . . . . . . . 6 69 3.3. More Pre-Authentication Data Required . . . . . . . . . . 6 70 4. SPAKE Pre-Authentication Message Protocol . . . . . . . . . . 6 71 4.1. First Pass . . . . . . . . . . . . . . . . . . . . . . . 7 72 4.2. Second Pass . . . . . . . . . . . . . . . . . . . . . . . 7 73 4.3. Third Pass . . . . . . . . . . . . . . . . . . . . . . . 9 74 4.4. Subsequent Passes . . . . . . . . . . . . . . . . . . . . 10 75 4.5. Reply Key Strengthening . . . . . . . . . . . . . . . . . 11 76 4.6. Optimizations . . . . . . . . . . . . . . . . . . . . . . 11 77 5. SPAKE Parameters and Conversions . . . . . . . . . . . . . . 12 78 6. Transcript Hash . . . . . . . . . . . . . . . . . . . . . . . 12 79 7. Key Derivation . . . . . . . . . . . . . . . . . . . . . . . 13 80 8. Second Factor Types . . . . . . . . . . . . . . . . . . . . . 14 81 9. Hint for Authentication Sets . . . . . . . . . . . . . . . . 14 82 10. Security Considerations . . . . . . . . . . . . . . . . . . . 15 83 10.1. SPAKE Computations . . . . . . . . . . . . . . . . . . . 15 84 10.2. Unauthenticated Plaintext . . . . . . . . . . . . . . . 15 85 10.3. Side Channels . . . . . . . . . . . . . . . . . . . . . 16 86 10.4. KDC State . . . . . . . . . . . . . . . . . . . . . . . 17 87 10.5. Dictionary Attacks . . . . . . . . . . . . . . . . . . . 17 88 10.6. Brute Force Attacks . . . . . . . . . . . . . . . . . . 18 89 10.7. Denial of Service Attacks . . . . . . . . . . . . . . . 18 90 10.8. Reflection Attacks . . . . . . . . . . . . . . . . . . . 18 91 10.9. Reply-Key Encryption Type . . . . . . . . . . . . . . . 19 92 10.10. KDC Authentication . . . . . . . . . . . . . . . . . . . 19 93 11. Assigned Constants . . . . . . . . . . . . . . . . . . . . . 19 94 12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 19 95 12.1. Kerberos Second Factor Types . . . . . . . . . . . . . . 20 96 12.1.1. Registration Template . . . . . . . . . . . . . . . 20 97 12.1.2. Initial Registry Contents . . . . . . . . . . . . . 20 98 12.2. Kerberos SPAKE Groups . . . . . . . . . . . . . . . . . 20 99 12.2.1. Registration Template . . . . . . . . . . . . . . . 20 100 12.2.2. Initial Registry Contents . . . . . . . . . . . . . 21 101 13. References . . . . . . . . . . . . . . . . . . . . . . . . . 22 102 13.1. Normative References . . . . . . . . . . . . . . . . . . 22 103 13.2. Informative References . . . . . . . . . . . . . . . . . 24 104 Appendix A. ASN.1 Module . . . . . . . . . . . . . . . . . . . . 25 105 Appendix B. SPAKE M and N Value Selection . . . . . . . . . . . 26 106 Appendix C. Test Vectors . . . . . . . . . . . . . . . . . . . . 27 107 Appendix D. Acknowledgements . . . . . . . . . . . . . . . . . . 36 108 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 36 110 1. Introduction 112 When a client uses PA-ENC-TIMESTAMP (or similar schemes, or the KDC 113 does not require preauthentication), a passive attacker that observes 114 either the AS-REQ or AS-REP can perform an offline brute-force attack 115 against the transferred ciphertext. When the client principal's 116 long-term key is based on a password, offline dictionary attacks can 117 successfuly recover the key, with only modest effort needed if the 118 password is weak. 120 1.1. Properties of PAKE 122 Password authenticated key exchange (PAKE) algorithms provide several 123 properties which defend against offline dictionary attacks and make 124 them ideal for use as a Kerberos pre-authentication mechanism. 126 1. Each side of the exchange contributes entropy. 128 2. Passive attackers cannot determine the shared key. 130 3. Active attackers cannot perform a man-in-the-middle attack. 132 These properties of PAKE allow us to establish high-entropy 133 encryption keys resistant to offline brute force attack, even when 134 the passwords used are weak (low-entropy). 136 1.2. PAKE Algorithm Selection 138 The SPAKE algorithm works by encrypting the public keys of a Diffie- 139 Hellman key exchange with a shared secret. SPAKE was selected for 140 this pre-authentication mechanism for the following properties: 142 1. Because SPAKE's encryption method ensures that the result is a 143 member of the underlying group, it can be used with elliptic 144 curve cryptography, which is believed to provide equivalent 145 security levels to finite-field DH key exchange at much smaller 146 key sizes. 148 2. It can compute the shared key after just one message from each 149 party, minimizing the need for additional round trips and state. 151 3. It requires a small number of group operations, and can therefore 152 be implemented simply and efficiently. 154 1.3. PAKE and Two-Factor Authentication 156 Using PAKE in a pre-authentication mechanism also has another benefit 157 when used as a component of two-factor authentication (2FA). 2FA 158 methods often require the secure transfer of plaintext material to 159 the KDC for verification. This includes one-time passwords, 160 challenge/response signatures and biometric data. Encrypting this 161 data using the long-term secret results in packets that are 162 vulnerable to offline brute-force attack on the password, using 163 either an authentication tag or statistical properties of the 2FA 164 credentials to determine whether a password guess is correct. 166 In the OTP pre-authentication [RFC6560] specification, this problem 167 is mitigated by using FAST, which uses a secondary trust relationship 168 to create a secure encryption channel within which pre-authentication 169 data can be sent. However, the requirement for a secondary trust 170 relationship has proven to be cumbersome to deploy and often 171 introduces third parties into the trust chain (such as certification 172 authorities). These requirements make it difficult to enable FAST 173 without manual configuration of client hosts. SPAKE pre- 174 authentication, in contrast, can create a secure encryption channel 175 implicitly, using the key exchange to negotiate a high-entropy 176 encryption key. This key can then be used to securely encrypt 2FA 177 plaintext data without the need for a secondary trust relationship. 178 Further, if the second factor verifiers are sent at the same time as 179 the first factor verifier, and the KDC is careful to prevent timing 180 attacks, then an online brute-force attack cannot be used to attack 181 the factors separately. 183 For these reasons, this draft departs from the advice given in 184 Section 1 of RFC 6113 [RFC6113] which states that "Mechanism 185 designers should design FAST factors, instead of new pre- 186 authentication mechanisms outside of FAST." However, this pre- 187 authentication mechanism does not intend to replace FAST, and may be 188 used with it to further conceal the metadata of the Kerberos 189 messages. 191 1.4. SPAKE Overview 193 The SPAKE algorithm can be broadly described in a series of four 194 steps: 196 1. Calculation and exchange of the public key 198 2. Calculation of the shared secret (K) 200 3. Derivation of an encryption key (K') 202 4. Verification of the derived encryption key (K') 204 In this mechanism, key verification happens implicitly by a 205 successful decryption of the 2FA data, or of a placeholder value when 206 no second factor is required. This mechanism uses a tailored method 207 of deriving encryption keys from the calculated shared secret K, for 208 several reasons: to fit within the framework of [RFC3961], to ensure 209 negotiation integrity using a transcript hash, to derive different 210 keys for each use, and to bind the KDC-REQ-BODY to the pre- 211 authentication exchange. 213 2. Document Conventions 215 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 216 "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and 217 "OPTIONAL" in this document are to be interpreted as described in BCP 218 14 [RFC2119] [RFC8174] when, and only when, they appear in all 219 capitals, as shown here. 221 This document refers to numerous terms and protocol messages defined 222 in [RFC4120]. 224 The terms "encryption type", "key generation seed length", and 225 "random-to-key" are defined in [RFC3961]. 227 The terms "FAST", "PA-FX-COOKIE", "KDC_ERR_PREAUTH_EXPIRED", 228 "KDC_ERR_MORE_PREAUTH_DATA_REQUIRED", "KDC_ERR_PREAUTH_FAILED", "pre- 229 authentication facility", and "authentication set" are defined in 230 [RFC6113]. 232 The [SPAKE] paper defines SPAKE as a family of two key exchange 233 algorithms differing only in derivation of the final key. This 234 mechanism uses a derivation similar to the second algorithm (SPAKE2) 235 with differences in detail. For simplicity, this document refers to 236 the algorithm as "SPAKE". 238 The terms "ASN.1" and "DER" are defined in [CCITT.X680.2002] and 239 [CCITT.X690.2002] respectively. 241 When discussing operations within algebraic groups, this document 242 uses additive notation (as described in Section 2.2 of [RFC6090]). 243 Group elements are denoted with uppercase letters, while scalar 244 multiplier values are denoted with lowercase letters. 246 3. Prerequisites 248 3.1. PA-ETYPE-INFO2 250 This mechanism requires the initial KDC pre-authentication state to 251 contain a singular reply key. Therefore, a KDC which offers SPAKE 252 pre-authentication as a stand-alone mechanism MUST supply a PA-ETYPE- 253 INFO2 value containing a single ETYPE-INFO2-ENTRY, following the 254 guidance in Section 2.1 of [RFC6113]. PA-ETYPE-INFO2 is specified in 255 Section 5.2.7.5 of [RFC4120]. 257 3.2. Cookie Support 259 KDCs which implement SPAKE pre-authentication MUST have some secure 260 mechanism for retaining state between AS-REQs. For stateless KDC 261 implementations, this method will most commonly be an encrypted PA- 262 FX-COOKIE. Clients which implement SPAKE pre-authentication MUST 263 support PA-FX-COOKIE, as described in Section 5.2 of [RFC6113]. 265 3.3. More Pre-Authentication Data Required 267 Both KDCs and clients which implement SPAKE pre-authentication MUST 268 support the use of KDC_ERR_MORE_PREAUTH_DATA_REQUIRED, as described 269 in Section 5.2 of [RFC6113]. 271 4. SPAKE Pre-Authentication Message Protocol 273 This mechanism uses the reply key and provides the Client 274 Authentication and Strengthening Reply Key pre-authentication 275 facilities (Section 3 of [RFC6113]). When the mechanism completes 276 successfully, the client will have proved knowledge of the original 277 reply key and possibly a second factor, and the reply key will be 278 strengthened to a more uniform distribution based on the PAKE 279 exchange. This mechanism also ensures the integrity of the KDC-REQ- 280 BODY contents. This mechanism can be used in an authentication set; 281 no pa-hint value is required or defined. 283 This mechanism negotiates a choice of group for the SPAKE algorithm. 284 Groups are defined in the IANA "Kerberos SPAKE Groups" registry 285 created by this document. Each group definition specifies an 286 associated hash function, which will be used for transcript 287 protection and key derivation. Clients and KDCs MUST implement the 288 edwards25519 group, but MAY choose not to offer or accept it by 289 default. 291 This section will describe the flow of messages when performing SPAKE 292 pre-authentication. We will begin by explaining the most verbose 293 version of the protocol which all implementations MUST support. Then 294 we will describe several optional optimizations to reduce round- 295 trips. 297 Mechanism messages are communicated using PA-DATA elements within the 298 padata field of KDC-REQ messages or within the METHOD-DATA in the 299 e-data field of KRB-ERROR messages. All PA-DATA elements for this 300 mechanism MUST use the following padata-type: 302 PA-SPAKE 151 304 The padata-value for all PA-SPAKE PA-DATA values MUST be empty or 305 contain a DER encoding for the ASN.1 type PA-SPAKE. 307 PA-SPAKE ::= CHOICE { 308 support [0] SPAKESupport, 309 challenge [1] SPAKEChallenge, 310 response [2] SPAKEResponse, 311 encdata [3] EncryptedData, 312 ... 313 } 315 4.1. First Pass 317 The SPAKE pre-authentication exchange begins when the client sends an 318 initial authentication service request (AS-REQ) without pre- 319 authentication data. Upon receipt of this AS-REQ, a KDC which 320 requires pre-authentication and supports SPAKE SHOULD reply with a 321 KDC_ERR_PREAUTH_REQUIRED error, with METHOD-DATA containing an empty 322 PA-SPAKE PA-DATA element (possibly in addition to other PA-DATA 323 elements). This message indicates to the client that the KDC 324 supports SPAKE pre-authentication. 326 4.2. Second Pass 328 Once the client knows that the KDC supports SPAKE pre-authentication 329 and the client desires to use it, the client will generate a new AS- 330 REQ message containing a PA-SPAKE PA-DATA element using the support 331 choice. This message indicates to the KDC which groups the client 332 prefers for the SPAKE operation. The group numbers are defined in 333 the IANA "Kerberos SPAKE Groups" registry created by this document. 335 The groups sequence is ordered from the most preferred group to the 336 least preferred group. 338 SPAKESupport ::= SEQUENCE { 339 groups [0] SEQUENCE (SIZE(1..MAX)) OF Int32, 340 ... 341 } 343 Upon receipt of the support message, the KDC will select a group. 344 The KDC SHOULD choose a group from the groups provided by the support 345 message. However, if the support message does not contain any group 346 that is supported by the KDC, the KDC MAY select another group in 347 hopes that the client might support it. Otherwise, the KDC MUST 348 respond with a KDC_ERR_PREAUTH_FAILED error. 350 The group selection determines the group order, which shall be a 351 large prime p multiplied by a small cofactor h (possibly 1), as well 352 as a generator P of a prime-order subgroup and two masking points M 353 and N. The KDC selects a random integer x in the range [0,h*p), 354 which MUST be divisible by h. The KDC computes a public key 355 T=x*P+w*M, where w is computed from the initial reply key according 356 to Section 5. 358 The KDC will reply to the client with a 359 KDC_ERR_MORE_PREAUTH_DATA_REQUIRED error containing a PA-SPAKE PA- 360 DATA element using the challenge choice. 362 SPAKEChallenge ::= SEQUENCE { 363 group [0] Int32, 364 pubkey [1] OCTET STRING, 365 factors [2] SEQUENCE (SIZE(1..MAX)) OF SPAKESecondFactor, 366 ... 367 } 369 The group field indicates the KDC-selected group used for all SPAKE 370 calculations as defined in the IANA "Kerberos SPAKE Groups" registry 371 created by this document. 373 The pubkey field indicates the KDC's public key T, serialized 374 according to Section 5. 376 The factors field contains an unordered list of second factors which 377 can be used to complete the authentication. Each second factor is 378 represented by a SPAKESecondFactor. 380 SPAKESecondFactor ::= SEQUENCE { 381 type [0] Int32, 382 data [1] OCTET STRING OPTIONAL 383 } 385 The type field is a unique integer which identifies the second factor 386 type. The factors field of SPAKEChallenge MUST NOT contain more than 387 one SPAKESecondFactor with the same type value. 389 The data field contains optional challenge data. The contents in 390 this field will depend upon the second factor type chosen. Note that 391 this challenge is initially transmitted as unauthenticated plaintext; 392 see Section 10.2. 394 The client and KDC will each initialize a transcript hash (Section 6) 395 using the hash function associated with the chosen group, and update 396 it with the concatenation of the DER-encoded PA-SPAKE messages sent 397 by the client and the KDC. 399 4.3. Third Pass 401 Upon receipt of the challenge message, the client observes which 402 group was selected by the KDC and deserializes the KDC's public key 403 T. The client selects a random integer y in the range [0,h*p), which 404 MUST be divisible by h. The client computes a public key S=y*P+w*N, 405 where w is computed from the initial reply key according to 406 Section 5. The client computes a shared group element K=y*(T-w*M). 408 The client will then choose one of the second factor types listed in 409 the factors field of the challenge message and gather whatever data 410 is required for the chosen second factor type, possibly using the 411 associated challenge data. Finally, the client will send an AS-REQ 412 containing a PA-SPAKE PA-DATA element using the response choice. 414 SPAKEResponse ::= SEQUENCE { 415 pubkey [0] OCTET STRING, 416 factor [1] EncryptedData, -- SPAKESecondFactor 417 ... 418 } 420 The client and KDC will update the transcript hash with the pubkey 421 value, and use the resulting hash for all encryption key derivations. 423 The pubkey field indicates the client's public key S, serialized 424 according to Section 5. 426 The factor field indicates the client's chosen second factor data. 427 The key for this field is K'[1] as specified in Section 7. The kvno 428 field of the EncryptedData sequence is omitted. The key usage number 429 for the encryption is KEY_USAGE_SPAKE. The plain text inside the 430 EncryptedData is an encoding of SPAKESecondFactor. Once decoded, the 431 SPAKESecondFactor contains the type of the second factor and any 432 optional data used. The contents of the data field will depend on 433 the second factor type chosen. The client MUST NOT send a response 434 containing a second factor type which was not listed in the factors 435 field of the challenge message. 437 When the KDC receives the response message from the client, it 438 deserializes the client's public key S, and computes the shared group 439 element K=x*(S-w*N). The KDC derives K'[1] and decrypts the factors 440 field. If decryption is successful, the first factor is successfully 441 validated. The KDC then validates the second factor. If either 442 factor fails to validate, the KDC SHOULD respond with a 443 KDC_ERR_PREAUTH_FAILED error. 445 If validation of the second factor requires further round-trips, the 446 KDC MUST reply to the client with KDC_ERR_MORE_PREAUTH_DATA_REQUIRED 447 containing a PA-SPAKE PA-DATA element using the encdata choice. The 448 kvno field of the EncryptedData sequence is omitted. The key for the 449 EncryptedData value is K'[2] as specified in Section 7, and the key 450 usage number is KEY_USAGE_SPAKE. The plain text of this message 451 contains a DER-encoded SPAKESecondFactor message. As before, the 452 type field of this message will contain the second factor type, and 453 the data field will optionally contain second factor type specific 454 data. 456 KEY_USAGE_SPAKE 65 458 4.4. Subsequent Passes 460 Any number of additional round trips may occur using the encdata 461 choice. The contents of the plaintexts are specific to the second 462 factor type. If a client receives a PA-SPAKE PA-DATA element using 463 the encdata choice from the KDC, it MUST reply with a subsequent AS- 464 REQ with a PA-SPAKE PA-DATA using the encdata choice, or abort the AS 465 exchange. 467 The key for client-originated encdata messages in subsequent passes 468 is K'[3] as specified in Section 7 for the first subsequent pass, 469 K'[5] for the second, and so on. The key for KDC-originated encdata 470 messages is K'[4] for the first subsequent pass, K'[6] for the 471 second, and so on. 473 4.5. Reply Key Strengthening 475 When the KDC has successfully validated both factors, the reply key 476 is strengthened and the mechanism is complete. To strengthen the 477 reply key, the client and KDC replace it with K'[0] as specified in 478 Section 7. The KDC then replies with a KDC-REP message, or continues 479 on to the next mechanism in the authentication set. There is no 480 final PA-SPAKE PA-DATA message from the KDC to the client. 482 Reply key strengthening occurs only once at the end of the exchange. 483 The client and KDC MUST use the initial reply key as the base key for 484 all K'[n] derivations. 486 4.6. Optimizations 488 The full protocol has two possible optimizations. 490 First, the KDC MAY reply to the initial AS-REQ (containing no pre- 491 authentication data) with a PA-SPAKE PA-DATA element using the 492 challenge choice, instead of an empty padata-value. In this case, 493 the KDC optimistically selects a group which the client may not 494 support. If the group chosen by the challenge message is supported 495 by the client, the client MUST skip to the third pass by issuing an 496 AS-REQ with a PA-SPAKE message using the response choice. In this 497 case no SPAKESupport message is sent by the client, so the first 498 update to the transcript hash contains only the KDC's optimistic 499 challenge. If the KDC's chosen group is not supported by the client, 500 the client MUST continue to the second pass. In this case both the 501 client and KDC MUST reinitialize the transcript hash for the client's 502 support message. Clients MUST support this optimization. 504 Second, clients MAY skip the first pass and send an AS-REQ with a PA- 505 SPAKE PA-DATA element using the support choice. If the KDC accepts 506 the support message and generates a challenge, it MUST include a PA- 507 ETYPE-INFO2 value within the METHOD-DATA of the 508 KDC_ERR_MORE_PREAUTH_DATA_REQUIRED error response, as the client may 509 not otherwise be able to compute the initial reply key. If the KDC 510 cannot continue with SPAKE (either because initial reply key type is 511 incompatible with SPAKE or because it does not support any of the 512 client's groups) but can offer other pre-authentication mechanisms, 513 it MUST respond with a KDC_ERR_PREAUTH_FAILED error containing 514 METHOD-DATA for the available mechanisms. A client supporting this 515 optimization MUST continue after a KDC_ERR_PREAUTH_FAILED error as 516 described in Section 2 of [RFC6113]. KDCs MUST support this 517 optimization. 519 5. SPAKE Parameters and Conversions 521 Group elements are converted to and from octet strings using the 522 serialization method defined in the IANA "Kerberos SPAKE Groups" 523 registry created by this document. 525 The SPAKE algorithm requires constants M and N for each group. These 526 constants are defined in the IANA "Kerberos SPAKE Groups" registry 527 created by this document. 529 The SPAKE algorithm requires a shared secret input w to be used as a 530 scalar multiplier. This value MUST be produced from the initial 531 reply key as follows: 533 1. Determine the length of the multiplier octet string as defined in 534 the IANA "Kerberos SPAKE Groups" registry created by this 535 document. 537 2. Compose a pepper string by concatenating the string "SPAKEsecret" 538 and the group number as a big-endian four-byte two's complement 539 binary number. 541 3. Produce an octet string of the required length using PRF+(K, 542 pepper), where K is the initial reply key and PRF+ is defined in 543 Section 5.1 of [RFC6113]. 545 4. Convert the octet string to a multiplier scalar using the 546 multiplier conversion method defined in the IANA "Kerberos SPAKE 547 Groups" registry created by this document. 549 The KDC chooses a secret scalar value x and the client chooses a 550 secret scalar value y. As required by the SPAKE algorithm, these 551 values are chosen randomly and uniformly. The KDC and client MUST 552 NOT reuse x or y values for authentications involving different 553 initial reply keys (see Section 10.4). 555 6. Transcript Hash 557 The transcript hash is an octet string of length equal to the output 558 length of the hash function associated with the selected group. The 559 initial value consists of all bits set to zero. 561 When the transcript hash is updated with an octet string input, the 562 new value is the hash function computed over the concatenation of the 563 old value and the input. 565 In the normal message flow or with the second optimization described 566 in Section 4.6, the transcript hash is first updated with the 567 concatenation of the client's support message and the KDC's 568 challenge, and then updated a second time with the client's pubkey 569 value. It therefore incorporates the client's supported groups, the 570 KDC's chosen group, the KDC's initial second-factor messages, and the 571 client and KDC public values. Once the transcript hash is finalized, 572 it is used without change for all key derivations (Section 7). In 573 particular, encrypted second-factor messages are not included in the 574 transcript hash. 576 If the first optimization described in Section 4.6 is used 577 successfully, the transcript hash is updated first with the KDC's 578 challenge message, and second with the client's pubkey value. 580 If first optimization is used unsuccessfully (i.e. the client does 581 not accept the KDC's selected group), the transcript hash is computed 582 as in the normal message flow, without including the KDC's optimistic 583 challenge. 585 7. Key Derivation 587 Implementations MUST NOT use the shared group element (denoted by K) 588 directly for any cryptographic operation. Instead, the SPAKE result 589 is used to derive keys K'[n] as defined in this section. 591 First, the hash function associated with the selected group is 592 computed over the concatenation of the following values: 594 o The fixed string "SPAKEkey". 596 o The group number as a big-endian four-byte two's complement binary 597 number. 599 o The encryption type of the initial reply key as a big-endian four- 600 byte two's complement binary number. 602 o The PRF+ output used to compute the initial secret input w as 603 specified in Section 5. 605 o The SPAKE result K, converted to an octet string as specified in 606 Section 5. 608 o The transcript hash. 610 o The KDC-REQ-BODY encoding for the request being sent or responded 611 to. Within a FAST channel, the inner KDC-REQ-BODY encoding MUST 612 be used. 614 o The value n as a big-endian four-byte unsigned binary number. 616 o A single-byte block counter, with the initial value 0x01. 618 If the hash output is too small for the encryption type's key 619 generation seed length, the block counter value is incremented and 620 the hash function re-computed to produce as many blocks as are 621 required. The result is truncated to the key generation seed length, 622 and the random-to-key function is used to produce an intermediate key 623 with the same encryption type as the initial reply key. 625 The key K'[n] has the same encryption type as the initial reply key, 626 and has the value KRB-FX-CF2(initial-reply-key, intermediate-key, 627 "SPAKE", "keyderiv"), where KRB-FX-CF2 is defined in Section 5.1 of 628 [RFC6113]. 630 8. Second Factor Types 632 This document defines one second factor type: 634 SF-NONE 1 636 This second factor type indicates that no second factor is used. 637 Whenever a SPAKESecondFactor is used with SF-NONE, the data field 638 MUST be omitted. The SF-NONE second factor always successfully 639 validates. 641 9. Hint for Authentication Sets 643 If a KDC offers SPAKE pre-authentication as part of an authentication 644 set (Section 5.3 of [RFC6113]), it MAY provide a pa-hint value 645 containing the DER encoding of the ASN.1 type PA-SPAKE-HINT, to help 646 the client determine whether SPAKE pre-authentication is likely to 647 succeed if the authentication set is chosen. 649 PA-SPAKE-HINT ::= SEQUENCE { 650 groups [0] SEQUENCE (SIZE(1..MAX)) OF Int32, 651 factors [1] SEQUENCE (SIZE(1..MAX)) OF SPAKESecondFactor 652 } 654 The groups field indicates the KDC's supported groups. The factors 655 field indicates the KDC's supported second factors. The KDC MAY omit 656 the data field of values in the factors list. 658 A KDC MUST NOT include a PA-SPAKE-HINT message directly in a pa-value 659 field; hints must only be provided within authentication sets. A KDC 660 SHOULD include a hint if SPAKE pre-authentication is offered as the 661 second or later element of an authentication set. 663 The PA-SPAKE-HINT message is not part of the transcript, and does not 664 replace any part of the SPAKE message flow. 666 10. Security Considerations 668 10.1. SPAKE Computations 670 The deserialized public keys S and T MUST be verified to be elements 671 of the group, to prevent invalid curve attacks. It is not necessary 672 to verify that they are members of the prime-order subgroup, as the 673 computation of K by both parties involves a multiplication by the 674 cofactor h. 676 The aforementioned cofactor multiplication is accomplished by 677 choosing private scalars x and y which are divisible by the cofactor. 678 If the client or KDC chooses a scalar which might not be divisible by 679 the cofactor, an attacker might be able to coerce values of K which 680 are not members of the prime-order subgroup, and deduce a limited 681 amount of information about w from the order of K. 683 The scalars x and y MUST be chosen uniformly, and must not be reused 684 for different initial reply keys. If an x or y value is reused for 685 pre-authentications involving two different initial reply keys, an 686 attacker who observes both authentications and knows one of the 687 initial reply keys can conduct an offline dictionary attack to 688 recover the other one. 690 The M and N values for a group MUST NOT have known discrete logs. An 691 attacker who knows the discrete log of M or N can perform an offline 692 dictionary attack on passwords. It is therefore important to 693 demonstrate that the M and N values for each group were computed 694 without multiplying a known value by the generator P. 696 10.2. Unauthenticated Plaintext 698 This mechanism includes unauthenticated plaintext in the support and 699 challenge messages. Beginning with the third pass, the integrity of 700 this plaintext is ensured by incorporating the transcript hash into 701 the derivation of the final reply key and second factor encryption 702 keys. Downgrade attacks on support and challenge messages will 703 result in the client and KDC deriving different reply keys and 704 EncryptedData keys. The KDC-REQ-BODY contents are also incorporated 705 into key derivation, ensuring their integrity. The unauthenticated 706 plaintext in the KDC-REP message is not protected by this mechanism. 708 Unless FAST is used, the factors field of a challenge message is not 709 integrity-protected until the response is verified. Second factor 710 types MUST account for this when specifying the semantics of the data 711 field. Second factor data in the challenge should not be included in 712 user prompts, as it could be modified by an attacker to contain 713 misleading or offensive information. 715 Unless FAST is used, the factors field of a challenge message is 716 visible to an attacker, who can use it to determine whether a second 717 factor is required for the client. 719 Subsequent factor data, including the data in the response, are 720 encrypted in a derivative of the shared secret K. Therefore, it is 721 not possible to exploit the untrustworthiness of the challenge to 722 turn the client into an encryption or signing oracle for the second 723 factor credentials, unless the attacker knows the client's long-term 724 key. 726 Unless FAST is used, any PA-SPAKE-HINT messages included when SPAKE 727 is advertised in authentication sets are unauthenticated, and are not 728 protected by the transcript hash. Since hints do not replace any 729 part of the message flow, manipulation of hint messages can only 730 affect the client's decision to use or not use an authentication set, 731 which could more easily be accomplished by removing authentication 732 sets entirely. 734 10.3. Side Channels 736 An implementation of this pre-authentication mechanism can have the 737 property of indistinguishability, meaning that an attacker who 738 guesses a long-term key and a second factor value cannot determine 739 whether one of the factors was correct unless both are correct. 740 Indistinguishability is only maintained if the second factor can be 741 validated solely based on the data in the response; the use of 742 additional round trips will reveal to the attacker whether the long- 743 term key is correct. Indistinguishability also requires that there 744 are no side channels. When processing a response message, whether or 745 not the KDC successfully decrypts the factor field, it must reply 746 with the same error fields, take the same amount of time, and make 747 the same observable communications to other servers. 749 Both the size of the EncryptedData and the number of EncryptedData 750 messages used for second-factor data (including the factor field of 751 the SPAKEResponse message and messages using the encdata PA-SPAKE 752 choice) may reveal information about the second factor used in an 753 authentication. Care should be taken to keep second factor messages 754 as small and as few as possible. 756 Any side channels in the creation of the shared secret input w, or in 757 the multiplications wM and wN, could allow an attacker to recover the 758 client long-term key. Implementations MUST take care to avoid side 759 channels, particularly timing channels. Generation of the secret 760 scalar values x and y need not take constant time, but the amount of 761 time taken MUST NOT provide information about the resulting value. 763 The conversion of the scalar multiplier for the SPAKE w parameter may 764 produce a multiplier that is larger than the order of the group. 765 Some group implementations may be unable to handle such a multiplier. 766 Others may silently accept such a multiplier, but proceed to perform 767 multiplication that is not constant time. This is only a minor risk 768 in most commonly-used groups, but is a more serious risk for P-521 769 due to the extra seven high bits in the input octet string. A common 770 solution to this problem is achieved by reducing the multiplier 771 modulo the group order, taking care to ensure constant time 772 operation. 774 10.4. KDC State 776 A stateless KDC implementation generally must use a PA-FX-COOKIE 777 value to remember its private scalar value x and the transcript hash. 778 The KDC MUST maintain confidentiality and integrity of the cookie 779 value, perhaps by encrypting it in a key known only to the realm's 780 KDCs. Cookie values may be replayed by attackers, perhaps splicing 781 them into different SPAKE exchanges. The KDC SHOULD limit the time 782 window of replays using a timestamp, and SHOULD prevent cookie values 783 from being applied to other pre-authentication mechanisms or other 784 client principals. Within the validity period of a cookie, an 785 attacker can replay the final message of a pre-authentication 786 exchange to any of the realm's KDCs and make it appear that the 787 client has authenticated. 789 This pre-authentication mechanism is not designed to provide forward 790 secrecy. Nevertheless, some measure of forward secrecy may result 791 depending on implementation choices. A passive attacker who 792 determines the client long-term key after the exchange generally will 793 not be able to recover the ticket session key; however, an attacker 794 who also determines the PA-FX-COOKIE encryption key (if the KDC uses 795 an encrypted cookie) will be able to recover the ticket session key. 796 The KDC can mitigate this risk by periodically rotating the cookie 797 encryption key. If the KDC or client retains the x or y value for 798 reuse with the same client long-term key, an attacker who recovers 799 the x or y value and the long-term key will be able to recover the 800 ticket session key. 802 10.5. Dictionary Attacks 804 Although this pre-authentication mechanism is designed to prevent an 805 offline dictionary attack by an active attacker posing as the KDC, 806 such an attacker can attempt to downgrade the client to encrypted 807 timestamp. Client implementations SHOULD provide a configuration 808 option to disable encrypted timestamp on a per-realm basis to 809 mitigate this attack. 811 If the user enters the wrong password, the client might fall back to 812 encrypted timestamp after receiving a KDC_ERR_PREAUTH_FAILED error 813 from the KDC, if encrypted timestamp is offered by the KDC and not 814 disabled by client configuration. This fallback will enable a 815 passive attacker to mount an offline dictionary attack against the 816 incorrect password, which may be similar to the correct password. 817 Client implementations SHOULD assume that encrypted timestamp and 818 encrypted challenge are unlikely to succeed if SPAKE pre- 819 authentication fails in the second pass and SF-NONE was used. 821 Like any other pre-authentication mechanism using the client long- 822 term key, this pre-authentication mechanism does not prevent online 823 password guessing attacks. The KDC is made aware of unsuccessful 824 guesses, and can apply facilities such as rate limiting to mitigate 825 the risk of online attacks. 827 10.6. Brute Force Attacks 829 The selected group's resistance to offline brute-force attacks may 830 not correspond to the size of the reply key. For performance 831 reasons, a KDC MAY select a group whose brute-force work factor is 832 less than the reply key length. A passive attacker who solves the 833 group discrete logarithm problem after the exchange will be able to 834 conduct an offline attack against the client long-term key. Although 835 the use of password policies and costly, salted string-to-key 836 functions may increase the cost of such an attack, the resulting cost 837 will likely not be higher than the cost of solving the group discrete 838 logarithm. 840 10.7. Denial of Service Attacks 842 Elliptic curve group operations are more computationally expensive 843 than secret-key operations. As a result, the use of this mechanism 844 may affect the KDC's performance under normal load and its resistance 845 to denial of service attacks. 847 10.8. Reflection Attacks 849 The encdata choice of PA-SPAKE can be used in either direction, and 850 the factor-specific plaintext does not necessarily indicate a 851 direction. However, each encdata message is encrypted using a 852 derived key K'[n], with client-originated messages using only odd 853 values of n and KDC-originated messages using only even values. An 854 attempted reflection attack would therefore result in a failed 855 decryption. 857 10.9. Reply-Key Encryption Type 859 This mechanism does not upgrade the encryption type of the initial 860 reply key, and relies on that encryption type for confidentiality, 861 integrity, and pseudo-random functions. If the client long-term key 862 uses a weak encryption type, an attacker might be able to subvert the 863 exchange, and the replaced reply key will also be of the same weak 864 encryption type. 866 10.10. KDC Authentication 868 This mechanism does not directly provide the KDC Authentication pre- 869 authentication facility, because it does not send a key confirmation 870 from the KDC to the client. When used as a stand-alone mechanism, 871 the traditional KDC authentication provided by the KDC-REP enc-part 872 still applies. 874 11. Assigned Constants 876 The following key usage values are assigned for this mechanism: 878 KEY_USAGE_SPAKE 65 880 12. IANA Considerations 882 IANA has assigned the following number for PA-SPAKE in the "Pre- 883 authentication and Typed Data" registry: 885 +----------+-------+-----------------+ 886 | Type | Value | Reference | 887 +----------+-------+-----------------+ 888 | PA-SPAKE | 151 | [this document] | 889 +----------+-------+-----------------+ 891 This document establishes two registries with the following 892 procedure, in accordance with [RFC8126]: 894 Registry entries are to be evaluated using the Specification Required 895 method. All specifications must be be published prior to entry 896 inclusion in the registry. Once published, they can be submitted 897 directly to the krb5-spake-review@ietf.org mailing list, where there 898 will be a three-week long review period by Designated Experts. 900 Prior to the end of the review period, the Designated Experts must 901 approve or deny the request. This decision is conveyed to both IANA 902 and the submitter. Since the mailing list archives are not public, 903 it should include both a reasonably detailed explanation in the case 904 of a denial as well as whether the request can be resubmitted. 906 12.1. Kerberos Second Factor Types 908 This section species the IANA "Kerberos Second Factor Types" 909 registry. This registry records the number, name, and reference for 910 each second factor protocol. 912 12.1.1. Registration Template 914 ID Number: This is a value that uniquely identifies this entry. It 915 is a signed integer in range -2147483648 to 2147483647, inclusive. 916 Positive values must be assigned only for algorithms specified in 917 accordance with these rules for use with Kerberos and related 918 protocols. Negative values should be used for private and 919 experimental algorithms only. Zero is reserved and must not be 920 assigned. 922 Name: Brief, unique, human-readable name for this algorithm. 924 Reference: URI or otherwise unique identifier for where the details 925 of this algorithm can be found. It should be as specific as 926 reasonably possible. 928 12.1.2. Initial Registry Contents 930 o ID Number: 1 931 o Name: SF-NONE 932 o Reference: this draft. 934 12.2. Kerberos SPAKE Groups 936 This section specifies the IANA "Kerberos SPAKE Groups" registry. 937 This registry records the number, name, specification, serialization, 938 multiplier length, multiplier conversion, SPAKE M and N constants, 939 and associated hash function. 941 12.2.1. Registration Template 943 ID Number: This is a value that uniquely identifies this entry. It 944 is a signed integer in range -2147483648 to 2147483647, inclusive. 945 Positive values must be assigned only for algorithms specified in 946 accordance with these rules for use with Kerberos and related 947 protocols. Negative values should be used for private and 948 experimental use only. Zero is reserved and must not be assigned. 949 Values should be assigned in increasing order. 951 Name: Brief, unique, human readable name for this entry. 953 Specification: Reference to the definition of the group parameters 954 and operations. 956 Serialization: Reference to the definition of the method used to 957 serialize and deserialize group elements. 959 Multiplier Length: The length of the input octet string to 960 multiplication operations. 962 Multiplier Conversion: Reference to the definition of the method 963 used to convert an octet string to a multiplier scalar. 965 SPAKE M Constant: The serialized value of the SPAKE M constant in 966 hexadecimal notation. 968 SPAKE N Constant: The serialized value of the SPAKE N constant in 969 hexadecimal notation. 971 Hash Function: The group's associated hash function. 973 12.2.2. Initial Registry Contents 975 o ID Number: 1 976 o Name: edwards25519 977 o Specification: Section 4.1 of [RFC7748] (edwards25519) 978 o Serialization: Section 3.1 of [RFC8032] 979 o Multiplier Length: 32 980 o Multiplier Conversion: Section 3.1 of [RFC8032] 981 o SPAKE M Constant: 982 d048032c6ea0b6d697ddc2e86bda85a33adac920f1bf18e1b0c6d166a5cecdaf 983 o SPAKE N Constant: 984 d3bfb518f44f3430f29d0c92af503865a1ed3281dc69b35dd868ba85f886c4ab 985 o Hash function: SHA-256 ([RFC6234]) 987 o ID Number: 2 988 o Name: P-256 989 o Specification: Section 2.4.2 of [SEC2] 990 o Serialization: Section 2.3.3 of [SEC1] (compressed format) 991 o Multiplier Length: 32 992 o Multiplier Conversion: Section 2.3.8 of [SEC1] 993 o SPAKE M Constant: 994 02886e2f97ace46e55ba9dd7242579f2993b64e16ef3dcab95afd497333d8fa12f 995 o SPAKE N Constant: 996 03d8bbd6c639c62937b04d997f38c3770719c629d7014d49a24b4f98baa1292b49 997 o Hash function: SHA-256 ([RFC6234]) 998 o ID Number: 3 999 o Name: P-384 1000 o Specification: Section 2.5.1 of [SEC2] 1001 o Serialization: Section 2.3.3 of [SEC1] (compressed format) 1002 o Multiplier Length: 48 1003 o Multiplier Conversion: Section 2.3.8 of [SEC1] 1004 o SPAKE M Constant: 1005 030ff0895ae5ebf6187080a82d82b42e2765e3b2f8749c7e05eba3664 1006 34b363d3dc36f15314739074d2eb8613fceec2853 1007 o SPAKE N Constant: 1008 02c72cf2e390853a1c1c4ad816a62fd15824f56078918f43f922ca215 1009 18f9c543bb252c5490214cf9aa3f0baab4b665c10 1010 o Hash function: SHA-384 ([RFC6234]) 1012 o ID Number: 4 1013 o Name: P-521 1014 o Specification: Section 2.6.1 of [SEC2] 1015 o Serialization: Section 2.3.3 of [SEC1] (compressed format) 1016 o Multiplier Length: 66 1017 o Multiplier Conversion: Section 2.3.8 of [SEC1] 1018 o SPAKE M Constant: 1019 02003f06f38131b2ba2600791e82488e8d20ab889af753a41806c5db1 1020 8d37d85608cfae06b82e4a72cd744c719193562a653ea1f119eef9356907edc9b5 1021 6979962d7aa 1022 o SPAKE N Constant: 1023 0200c7924b9ec017f3094562894336a53c50167ba8c5963876880542b 1024 c669e494b2532d76c5b53dfb349fdf69154b9e0048c58a42e8ed04cef052a3bc34 1025 9d95575cd25 1026 o Hash function: SHA-512 ([RFC6234]) 1028 13. References 1030 13.1. Normative References 1032 [CCITT.X680.2002] 1033 International Telephone and Telegraph Consultative 1034 Committee, "Abstract Syntax Notation One (ASN.1): 1035 Specification of basic notation", CCITT Recommendation 1036 X.680, July 2002. 1038 [CCITT.X690.2002] 1039 International Telephone and Telegraph Consultative 1040 Committee, "ASN.1 encoding rules: Specification of basic 1041 encoding Rules (BER), Canonical encoding rules (CER) and 1042 Distinguished encoding rules (DER)", CCITT Recommendation 1043 X.690, July 2002. 1045 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate 1046 Requirement Levels", BCP 14, RFC 2119, 1047 DOI 10.17487/RFC2119, March 1997, 1048 . 1050 [RFC3961] Raeburn, K., "Encryption and Checksum Specifications for 1051 Kerberos 5", RFC 3961, DOI 10.17487/RFC3961, February 1052 2005, . 1054 [RFC4120] Neuman, C., Yu, T., Hartman, S., and K. Raeburn, "The 1055 Kerberos Network Authentication Service (V5)", RFC 4120, 1056 DOI 10.17487/RFC4120, July 2005, 1057 . 1059 [RFC6113] Hartman, S. and L. Zhu, "A Generalized Framework for 1060 Kerberos Pre-Authentication", RFC 6113, 1061 DOI 10.17487/RFC6113, April 2011, 1062 . 1064 [RFC6234] Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms 1065 (SHA and SHA-based HMAC and HKDF)", RFC 6234, 1066 DOI 10.17487/RFC6234, May 2011, 1067 . 1069 [RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves 1070 for Security", RFC 7748, DOI 10.17487/RFC7748, January 1071 2016, . 1073 [RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital 1074 Signature Algorithm (EdDSA)", RFC 8032, 1075 DOI 10.17487/RFC8032, January 2017, 1076 . 1078 [RFC8126] Cotton, M., Leiba, B., and T. Narten, "Guidelines for 1079 Writing an IANA Considerations Section in RFCs", BCP 26, 1080 RFC 8126, DOI 10.17487/RFC8126, June 2017, 1081 . 1083 [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 1084 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, 1085 May 2017, . 1087 [SEC1] Standards for Efficient Cryptography Group, "SEC 1: 1088 Elliptic Curve Cryptography", May 2009. 1090 [SEC2] Standards for Efficient Cryptography Group, "SEC 2: 1091 Recommended Elliptic Curve Domain Parameters", January 1092 2010. 1094 13.2. Informative References 1096 [RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic 1097 Curve Cryptography Algorithms", RFC 6090, 1098 DOI 10.17487/RFC6090, February 2011, 1099 . 1101 [RFC6560] Richards, G., "One-Time Password (OTP) Pre- 1102 Authentication", RFC 6560, DOI 10.17487/RFC6560, April 1103 2012, . 1105 [SPAKE] Abdalla, M. and D. Pointcheval, "Simple Password-Based 1106 Encrypted Key Exchange Protocols", February 2005. 1108 Appendix A. ASN.1 Module 1110 KerberosV5SPAKE { 1111 iso(1) identified-organization(3) dod(6) internet(1) 1112 security(5) kerberosV5(2) modules(4) spake(8) 1113 } DEFINITIONS EXPLICIT TAGS ::= BEGIN 1115 IMPORTS 1116 EncryptedData, Int32 1117 FROM KerberosV5Spec2 { iso(1) identified-organization(3) 1118 dod(6) internet(1) security(5) kerberosV5(2) modules(4) 1119 krb5spec2(2) }; 1120 -- as defined in RFC 4120. 1122 SPAKESupport ::= SEQUENCE { 1123 groups [0] SEQUENCE (SIZE(1..MAX)) OF Int32, 1124 ... 1125 } 1127 SPAKEChallenge ::= SEQUENCE { 1128 group [0] Int32, 1129 pubkey [1] OCTET STRING, 1130 factors [2] SEQUENCE (SIZE(1..MAX)) OF SPAKESecondFactor, 1131 ... 1132 } 1134 SPAKESecondFactor ::= SEQUENCE { 1135 type [0] Int32, 1136 data [1] OCTET STRING OPTIONAL 1137 } 1139 SPAKEResponse ::= SEQUENCE { 1140 pubkey [0] OCTET STRING, 1141 factor [1] EncryptedData, -- SPAKESecondFactor 1142 ... 1143 } 1145 PA-SPAKE ::= CHOICE { 1146 support [0] SPAKESupport, 1147 challenge [1] SPAKEChallenge, 1148 response [2] SPAKEResponse, 1149 encdata [3] EncryptedData, 1150 ... 1151 } 1153 PA-SPAKE-HINT ::= SEQUENCE { 1154 groups [0] SEQUENCE (SIZE(1..MAX)) OF Int32, 1155 factors [1] SEQUENCE (SIZE(1..MAX)) OF SPAKESecondFactor 1157 } 1159 END 1161 Appendix B. SPAKE M and N Value Selection 1163 The M and N values for the initial contents of the SPAKE group 1164 registry were generated using the following Python snippet, which 1165 assumes an elliptic curve implementation following the interface of 1166 Edwards25519Point.stdbase() and Edwards448Point.stdbase() in 1167 Appendix A of [RFC8032]: 1169 def iterhash(seed, n): 1170 h = seed 1171 for i in range(n): 1172 h = hashlib.sha256(h).digest() 1173 return h 1175 def bighash(seed, start, sz): 1176 n = -(-sz // 32) 1177 hashes = [iterhash(seed, i) for i in range(start, start + n)] 1178 return b''.join(hashes)[:sz] 1180 def canon_pointstr(ecname, s): 1181 if ecname == 'edwards25519': 1182 return s 1183 elif ecname == 'edwards448': 1184 return s[:-1] + bytes([s[-1] & 0x80]) 1185 else: 1186 return bytes([(s[0] & 1) | 2]) + s[1:] 1188 def gen_point(seed, ecname, ec): 1189 for i in range(1, 1000): 1190 hval = bighash(seed, i, len(ec.encode())) 1191 pointstr = canon_pointstr(ecname, hval) 1192 try: 1193 p = ec.decode(pointstr) 1194 if p != ec.zero_elem() and p * p.l() == ec.zero_elem(): 1195 return pointstr, i 1196 except Exception: 1197 pass 1199 The seed initial seed strings are: 1201 o For group 1 M: edwards25519 point generation seed (M) 1203 o For group 1 N: edwards25519 point generation seed (N) 1204 o For group 2 M: 1.2.840.10045.3.1.7 point generation seed (M) 1206 o For group 2 N: 1.2.840.10045.3.1.7 point generation seed (N) 1208 o For group 3 M: 1.3.132.0.34 point generation seed (M) 1210 o For group 3 N: 1.3.132.0.34 point generation seed (N) 1212 o For group 4 M: 1.3.132.0.35 point generation seed (M) 1214 o For group 4 N: 1.3.132.0.35 point generation seed (N) 1216 Appendix C. Test Vectors 1218 For the following text vectors: 1220 o The key is the string-to-key of "password" with the salt 1221 "ATHENA.MIT.EDUraeburn" for the designated initial reply key 1222 encryption type. 1224 o x and y were chosen randomly within the order of the designated 1225 group, then multiplied by the cofactor.. 1227 o The SPAKESupport message contains only the designated group's 1228 number. 1230 o The SPAKEChallenge message offers only the SF-NONE second factor 1231 type. 1233 o The KDC-REQ-BODY message contains no KDC options, the client 1234 principal name "raeburn@ATHENA.MIT.EDU", the server principal name 1235 "krbtgt/ATHENA.MIT.EDU", the realm "ATHENA.MIT.EDU", the till 1236 field "19700101000000Z", the nonce zero, and an etype list 1237 containing only the designated encryption type. 1239 des3-cbc-sha1 edwards25519 1240 key: 850bb51358548cd05e86768c313e3bfef7511937dcf72c3e 1241 w (PRF+ output): 686d84730cb8679ae95416c6567c6a63 1242 f2c9cef124f7a3371ae81e11cad42a37 1243 w (reduced multiplier): a1f1a25cbd8e3092667e2fddba8ecd24 1244 f2c9cef124f7a3371ae81e11cad42a07 1245 x: 201012d07bfd48ddfa33c4aac4fb1e229fb0d043cfe65ebfb14399091c71a723 1246 y: 500b294797b8b042aca1bedc0f5931a4f52c537b3608b2d05cc8a2372f439f25 1247 X: ec274df1920dc0f690c8741b794127233745444161016ef950ad75c51db58c3e 1248 Y: d90974f1c42dac1cd4454561ac2d49af762f2ac87bf02436d461e7b661b43028 1249 T: 18f511e750c97b592acd30db7d9e5fca660389102e6bf610c1bfbed4616c8362 1250 S: 5d10705e0d1e43d5dbf30240ccfbde4a0230c70d4c79147ab0b317edad2f8ae7 1251 K: 25bde0d875f0feb5755f45ba5e857889d916ecf7476f116aa31dc3e037ec4292 1252 SPAKESupport: a0093007a0053003020101 1253 SPAKEChallenge: a1363034a003020101a122042018f511e750c97b592acd30 1254 db7d9e5fca660389102e6bf610c1bfbed4616c8362a20930 1255 073005a003020101 1256 Transcript hash after challenge: 22bb2271e34d329d52073c70b1d11879 1257 73181f0bc7614266bb79ee80d3335175 1258 Final transcript hash after pubkey: eaaa08807d0616026ff51c849efbf35b 1259 a0ce3c5300e7d486da46351b13d4605b 1260 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1261 1b077261656275726ea2101b0e415448454e412e4d49542e 1262 454455a3233021a003020102a11a30181b066b7262746774 1263 1b0e415448454e412e4d49542e454455a511180f31393730 1264 303130313030303030305aa703020100a8053003020110 1265 K'[0]: baf12fae7cd958cbf1a29bfbc71f89ce49e03e295d89dafd 1266 K'[1]: 64f73dd9c41908206bcec1f719026b574f9d13463d7a2520 1267 K'[2]: 0454520b086b152c455829e6baeff78a61dfe9e3d04a895d 1268 K'[3]: 4a92260b25e3ef94c125d5c24c3e5bced5b37976e67f25c4 1270 rc4-hmac edwards25519 1271 key: 8846f7eaee8fb117ad06bdd830b7586c 1272 w (PRF+ output): 7c86659d29cf2b2ea93bfe79c3cefb88 1273 50e82215b3ea6fcd896561d48048f49c 1274 w (reduced multiplier): 2713c1583c53861520b849bfef0525cd 1275 4fe82215b3ea6fcd896561d48048f40c 1276 x: c8a62e7b626f44cad807b2d695450697e020d230a738c5cd5691cc781dce8754 1277 y: 18fe7c1512708c7fd06db270361f04593775bc634ceaf45347e5c11c38aae017 1278 X: b0bcbbdd25aa031f4608d0442dd4924be7731d49c089a8301859d77343ffb567 1279 Y: 7d1ab8aeda1a2b1f9eab8d11c0fda60b616005d0f37d1224c5f12b8649f579a5 1280 T: 7db465f1c08c64983a19f560bce966fe5306c4b447f70a5bca14612a92da1d63 1281 S: 38f8d4568090148ebc9fd17c241b4cc2769505a7ca6f3f7104417b72b5b5cf54 1282 K: 03e75edd2cd7e7677642dd68736e91700953ac55dc650e3c2a1b3b4acdb800f8 1283 SPAKESupport: a0093007a0053003020101 1284 SPAKEChallenge: a1363034a003020101a12204207db465f1c08c64983a19f5 1285 60bce966fe5306c4b447f70a5bca14612a92da1d63a20930 1286 073005a003020101 1287 Transcript hash after challenge: 3cde9ed9b562a09d816885b6c225f733 1288 6d9e2674bb4df903dfc894d963a2af42 1289 Final transcript hash after pubkey: f4b208458017de6ef7f6a307d47d87db 1290 6c2af1d291b726860f68bc08bfef440a 1291 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1292 1b077261656275726ea2101b0e415448454e412e4d49542e 1293 454455a3233021a003020102a11a30181b066b7262746774 1294 1b0e415448454e412e4d49542e454455a511180f31393730 1295 303130313030303030305aa703020100a8053003020117 1296 K'[0]: 770b720c82384cbb693e85411eedecba 1297 K'[1]: 621deec88e2865837c4d3462bb50a1d5 1298 K'[2]: 1cc8f6333b9fa3b42662fd9914fbd5bb 1299 K'[3]: edb4032b7fc3806d5211a534dcbc390c 1300 aes128-cts-hmac-sha1-96 edwards25519 1301 key: fca822951813fb252154c883f5ee1cf4 1302 w (PRF+ output): 0d591b197b667e083c2f5f98ac891d3c 1303 9f99e710e464e62f1fb7c9b67936f3eb 1304 w (reduced multiplier): 17c2a9030afb7c37839bd4ae7fdfeb17 1305 9e99e710e464e62f1fb7c9b67936f30b 1306 x: 50be049a5a570fa1459fb9f666e6fd80602e4e87790a0e567f12438a2c96c138 1307 y: b877afe8612b406d96be85bd9f19d423e95be96c0e1e0b5824127195c3ed5917 1308 X: e73a443c678913eb4a0cad5cbd3086cf82f65a5a91b611e01e949f5c52efd6dd 1309 Y: 473c5b44ed2be9cb50afe1762b535b3930530489816ea6bd962622cccf39f6e8 1310 T: 9e9311d985c1355e022d7c3c694ad8d6f7ad6d647b68a90b0fe46992818002da 1311 S: fbe08f7f96cd5d4139e7c9eccb95e79b8ace41e270a60198c007df18525b628e 1312 K: c2f7f99997c585e6b686ceb62db42f17cc70932def3bb4cf009e36f22ea5473d 1313 SPAKESupport: a0093007a0053003020101 1314 SPAKEChallenge: a1363034a003020101a12204209e9311d985c1355e022d7c 1315 3c694ad8d6f7ad6d647b68a90b0fe46992818002daa20930 1316 073005a003020101 1317 Transcript hash after challenge: 4512310282c01b39dd9aebd0cc2a5e53 1318 2ed077a6c11d4c973c4593d525078797 1319 Final transcript hash after pubkey: 951285f107c87f0169b9c918a1f51f60 1320 cb1a75b9f8bb799a99f53d03add94b5f 1321 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1322 1b077261656275726ea2101b0e415448454e412e4d49542e 1323 454455a3233021a003020102a11a30181b066b7262746774 1324 1b0e415448454e412e4d49542e454455a511180f31393730 1325 303130313030303030305aa703020100a8053003020111 1326 K'[0]: 548022d58a7c47eae8c49dccf6baa407 1327 K'[1]: b2c9ba0e13fc8ab3a9d96b51b601cf4a 1328 K'[2]: 69f0ee5fdb6c237e7fcd38d9f87df1bd 1329 K'[3]: 78f91e2240b5ee528a5cc8d7cbebfba5 1331 aes256-cts-hmac-sha1-96 edwards25519 1332 key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1 1333 w (PRF+ output): e902341590a1b4bb4d606a1c643cccb3 1334 f2108f1b6aa97b381012b9400c9e3f4e 1335 w (reduced multiplier): 35b35ca126156b5bf4ec8b90e9545060 1336 f2108f1b6aa97b381012b9400c9e3f0e 1337 x: 88c6c0a4f0241ef217c9788f02c32d00b72e4310748cd8fb5f94717607e6417d 1338 y: 88b859df58ef5c69bacdfe681c582754eaab09a74dc29cff50b328613c232f55 1339 X: 23c48eaff2721051946313840723b38f563c59b92043d6ffd752f95781af0327 1340 Y: 3d51486ec1d9be69bc45386bb675c013db87fd0488f6a9cacf6b43e8c81a0641 1341 T: 6f301aacae1220e91be42868c163c5009aeea1e9d9e28afcfc339cda5e7105b5 1342 S: 9e2cc32908fc46273279ec75354b4aeafa70c3d99a4d507175ed70d80b255dda 1343 K: cf57f58f6e60169d2ecc8f20bb923a8e4c16e5bc95b9e64b5dc870da7026321b 1344 SPAKESupport: a0093007a0053003020101 1345 SPAKEChallenge: a1363034a003020101a12204206f301aacae1220e91be428 1346 68c163c5009aeea1e9d9e28afcfc339cda5e7105b5a20930 1347 073005a003020101 1349 Transcript hash after challenge: 23a5e72eb4dedd1ca860f43736c458f0 1350 775c3bb1370a26af8a9374d521d70ec9 1351 Final transcript hash after pubkey: 1c605649d4658b58cbe79a5faf227acc 1352 16c355c58b7dade022f90c158fe5ed8e 1353 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1354 1b077261656275726ea2101b0e415448454e412e4d49542e 1355 454455a3233021a003020102a11a30181b066b7262746774 1356 1b0e415448454e412e4d49542e454455a511180f31393730 1357 303130313030303030305aa703020100a8053003020112 1358 K'[0]: a9bfa71c95c575756f922871524b6528 1359 8b3f695573ccc0633e87449568210c23 1360 K'[1]: 1865a9ee1ef0640ec28ac007391cac62 1361 4c42639c714767a974e99aa10003015f 1362 K'[2]: e57781513fefdb978e374e156b0da0c1 1363 a08148f5eb26b8e157ac3c077e28bf49 1364 K'[3]: 008e6487293c3cc9fabbbcdd8b392d6d 1365 cb88222317fd7fe52d12fbc44fa047f1 1367 aes256-cts-hmac-sha1-96 P-256 1368 key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1 1369 w (PRF+ output): eb2984af18703f94dd5288b8596cd369 1370 88d0d4e83bfb2b44de14d0e95e2090bd 1371 w (reduced multiplier): eb2984af18703f94dd5288b8596cd369 1372 88d0d4e83bfb2b44de14d0e95e2090bd 1373 x: 935ddd725129fb7c6288e1a5cc45782198a6416d1775336d71eacd0549a3e80e 1374 y: e07405eb215663abc1f254b8adc0da7a16febaa011af923d79fdef7c42930b33 1375 X: 03bc802165aea7dbd98cc155056249fe0a37a9c203a7c0f7e872d5bf687bd105e2 1376 Y: 0340b8d91ce3852d0a12ae1f3e82c791fc86df6b346006431e968a1b869af7c735 1377 T: 024f62078ceb53840d02612195494d0d0d88de21feeb81187c71cbf3d01e71788d 1378 S: 021d07dc31266fc7cfd904ce2632111a169b7ec730e5f74a7e79700f86638e13c8 1379 K: 0268489d7a9983f2fde69c6e6a1307e9d252259264f5f2dfc32f58cca19671e79b 1380 SPAKESupport: a0093007a0053003020102 1381 SPAKEChallenge: a1373035a003020102a1230421024f62078ceb53840d0261 1382 2195494d0d0d88de21feeb81187c71cbf3d01e71788da209 1383 30073005a003020101 1384 Transcript hash after challenge: 0a142afca77c2e92b066572a90389eac 1385 40a6b1f1ed8b534d342591c0e7727e00 1386 Final transcript hash after pubkey: 20ad3c1a9a90fc037d1963a1c4bfb15a 1387 b4484d7b6cf07b12d24984f14652de60 1388 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1389 1b077261656275726ea2101b0e415448454e412e4d49542e 1390 454455a3233021a003020102a11a30181b066b7262746774 1391 1b0e415448454e412e4d49542e454455a511180f31393730 1392 303130313030303030305aa703020100a8053003020112 1393 K'[0]: 7d3b906f7be49932db22cd3463f032d0 1394 6c9c078be4b1d076d201fc6e61ef531e 1395 K'[1]: 17d74e36f8993841fbb7feb12fa4f011 1396 243d3ae4d2ace55b39379294bbc4db2c 1398 K'[2]: d192c9044081a2aa6a97a6c69e2724e8 1399 e5671c2c9ce073dd439cdbaf96d7dab0 1400 K'[3]: 41e5bad6b67f12c53ce0e2720dd6a988 1401 7f877bf9463c2d5209c74c36f8d776b7 1403 aes256-cts-hmac-sha1-96 P-384 1404 key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1 1405 w (PRF+ output): 0304cfc55151c6bbe889653db96dbfe0ba4acafc024c1e88 1406 40cb3a486f6d80c16e1b8974016aa4b7fa43042a9b3825b1 1407 w (reduced multiplier): 0304cfc55151c6bbe889653db96dbfe0 1408 ba4acafc024c1e8840cb3a486f6d80c1 1409 6e1b8974016aa4b7fa43042a9b3825b1 1410 x: f323ca74d344749096fd35d0adf20806e521460637176e84d977e9933c49d76f 1411 cfc6e62585940927468ff53d864a7a50 1412 y: 5b7c709acb175a5afb82860deabca8d0b341facdff0ac0f1a425799aa905d750 1413 7e1ea9c573581a81467437419466e472 1414 X: 0211e3334f117b76635dd802d4022f601680a1fd066a56606b7f246493a10351 1415 7797b81789b225bd5bb1d9ae1da2962250 1416 Y: 0383dfa413496e5e7599fc8c6430f8d6910d37cf326d81421bc92c0939b555c4 1417 ca2ef6a993f6d3db8cb7407655ef60866e 1418 T: 02a1524603ef14f184696f854229d3397507a66c63f841ba748451056be07879 1419 ac298912387b1c5cdff6381c264701be57 1420 S: 020d5adfdb92bc377041cf5837412574c5d13e0f4739208a4f0c859a0a302bc6 1421 a533440a245b9d97a0d34af5016a20053d 1422 K: 0264aa8c61da9600dfb0beb5e46550d63740e4ef29e73f1a30d543eb43c25499 1423 037ad16538586552761b093cf0e37c703a 1424 SPAKESupport: a0093007a0053003020103 1425 SPAKEChallenge: a1473045a003020103a133043102a1524603ef14f184696f 1426 854229d3397507a66c63f841ba748451056be07879ac2989 1427 12387b1c5cdff6381c264701be57a20930073005a0030201 1428 01 1429 Transcript hash after challenge: 4d4095d9f94552e15015881a3f2cf458 1430 1be83217cf7ad830d2f051dba3ec8caa 1431 6e354eaa85738d7035317ac557f8c294 1432 Final transcript hash after pubkey: 5ac0d99ef9e5a73998797fe64f074673 1433 e3952dec4c7d1aacce8b75f64d2b0276 1434 a901cb8539b4e8ed69e4db0ce805b47b 1435 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1436 1b077261656275726ea2101b0e415448454e412e4d49542e 1437 454455a3233021a003020102a11a30181b066b7262746774 1438 1b0e415448454e412e4d49542e454455a511180f31393730 1439 303130313030303030305aa703020100a8053003020112 1440 K'[0]: b917d37c16dd1d8567fbe379f64e1ee3 1441 6ca3fd127aa4e60f97e4afa3d9e56d91 1442 K'[1]: 93d40079dab229b9c79366829f4e7e72 1443 82e6a4b943ac7bac69922d516673f49a 1444 K'[2]: bfc4f16f12f683e71589f9a888e23287 1445 5ef293ac9793db6c919567cd7b94bcd4 1447 K'[3]: 3630e2b5b99938e7506733141e8ec344 1448 166f6407e5fc2ef107c156e764d1bc20 1450 aes256-cts-hmac-sha1-96 P-521 1451 key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1 1452 w (PRF+ output): de3a095a2b2386eff3eb15b735398da1caf95bc8425665d8 1453 2370aff58b0471f34a57bccddf1ebf0a2965b58a93ee5b45 1454 e85d1a5435d1c8c83662999722d542831f9a 1455 w (reduced multiplier): 003a095a2b2386eff3eb15b735398da1 1456 caf95bc8425665d82370aff58b0471f3 1457 4cce63791cfed967f0c94c16054b3e17 1458 03133681bece1e05219f5426bc944b0f 1459 bfb3 1460 x: 017c38701a14b490b6081dfc83524562be7fbb42e0b20426465e3e37952d30bc 1461 ab0ed857010255d44936a1515607964a870c7c879b741d878f9f9cdf5a865306 1462 f3f5 1463 y: 003e2e2950656fa231e959acdd984d125e7fa59cec98126cbc8f3888447911eb 1464 cd49428a1c22d5fdb76a19fbeb1d9edfa3da6cf55b158b53031d05d51433ade9 1465 b2b4 1466 X: 03003e95272223b210b48cfd908b956a36add04a7ff443511432f94ddd87e064 1467 1d680ba3b3d532c21fa6046192f6bfae7af81c4b803aa154e12459d1428f8f2f 1468 56e9f2 1469 Y: 030064916687960df496557ecab08298bf075429eca268c6dabbae24e258d568 1470 c62841664dc8ecf545369f573ea84548faa22f118128c0a87e1d47315afabb77 1471 3bb082 1472 T: 02017d3de19a3ec53d0174905665ef37947d142535102cd9809c0dfbd0dfe007 1473 353d54cf406ce2a59950f2bb540df6fbe75f8bbbef811c9ba06cc275adbd9675 1474 6696ec 1475 S: 02004d142d87477841f6ba053c8f651f3395ad264b7405ca5911fb9a55abd454 1476 fef658a5f9ed97d1efac68764e9092fa15b9e0050880d78e95fd03abf5931791 1477 6822b5 1478 K: 03007c303f62f09282cc849490805bd4457a6793a832cbeb55df427db6a31e99 1479 b055d5dc99756d24d47b70ad8b6015b0fb8742a718462ed423b90fa3fe631ac1 1480 3fa916 1481 SPAKESupport: a0093007a0053003020104 1482 SPAKEChallenge: a1593057a003020104a145044302017d3de19a3ec53d0174 1483 905665ef37947d142535102cd9809c0dfbd0dfe007353d54 1484 cf406ce2a59950f2bb540df6fbe75f8bbbef811c9ba06cc2 1485 75adbd96756696eca20930073005a003020101 1486 Transcript hash after challenge: 554405860f8a80944228f1fa2466411d 1487 cf236162aa385e1289131b39e1fd59f2 1488 5e58b4c281ff059c28dc20f5803b87c6 1489 7571ce64cea01b39a21819d1ef1cdc7f 1490 Final transcript hash after pubkey: 8d6a89ae4d80cc4e47b6f4e48ea3e579 1491 19cc69598d0d3dc7c8bd49b6f1db1409 1492 ca0312944cd964e213aba98537041102 1493 237cff5b331e5347a0673869b412302e 1494 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1495 1b077261656275726ea2101b0e415448454e412e4d49542e 1496 454455a3233021a003020102a11a30181b066b7262746774 1497 1b0e415448454e412e4d49542e454455a511180f31393730 1498 303130313030303030305aa703020100a8053003020112 1499 K'[0]: 1eb3d10bee8fab483adcd3eb38f3ebf1 1500 f4feb8db96ecc035f563cf2e1115d276 1501 K'[1]: 482b92781ce57f49176e4c94153cc622 1502 fe247a7dbe931d1478315f856f085890 1503 K'[2]: a2c215126dd3df280aab5a27e1e0fb7e 1504 594192cbff8d6d8e1b6f1818d9bb8fac 1505 K'[3]: cc06603de984324013a01f888de6d43b 1506 410a4da2dea53509f30e433c352fb668 1508 aes256-cts-hmac-sha1-96 edwards25519, accepted optimistic challenge 1509 key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1 1510 w (PRF+ output): e902341590a1b4bb4d606a1c643cccb3 1511 f2108f1b6aa97b381012b9400c9e3f4e 1512 w (reduced multiplier): 35b35ca126156b5bf4ec8b90e9545060 1513 f2108f1b6aa97b381012b9400c9e3f0e 1514 x: 70937207344cafbc53c8a55070e399c584cbafce00b836980dd4e7e74fad2a64 1515 y: 785d6801a2490df028903ac6449b105f2ff0db895b252953cdc2076649526103 1516 X: 13841224ea50438c1d9457159d05f2b7cd9d05daf154888eeed223e79008b47c 1517 Y: d01fc81d5ce20d6ea0939a6bb3e40ccd049f821baaf95e323a3657309ef75d61 1518 T: 83523b35f1565006cbfc4f159885467c2fb9bc6fe23d36cb1da43d199f1a3118 1519 S: 2a8f70f46cee9030700037b77f22cec7970dcc238e3e066d9d726baf183992c6 1520 K: d3c5e4266aa6d1b2873a97ce8af91c7e4d7a7ac456acced7908d34c561ad8fa6 1521 SPAKEChallenge: a1363034a003020101a122042083523b35f1565006cbfc4f 1522 159885467c2fb9bc6fe23d36cb1da43d199f1a3118a20930 1523 073005a003020101 1524 Transcript hash after challenge: 0332da8ba3095ccd127c51740cb905ba 1525 c76e90725e769570b9d8338e6d62a7f2 1526 Final transcript hash after pubkey: 26f07f9f8965307434d11ea855461d41 1527 e0cbabcc0a1bab48ecee0c6c1a4292b7 1528 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1529 1b077261656275726ea2101b0e415448454e412e4d49542e 1530 454455a3233021a003020102a11a30181b066b7262746774 1531 1b0e415448454e412e4d49542e454455a511180f31393730 1532 303130313030303030305aa703020100a8053003020112 1533 K'[0]: 4569ec08b5de5c3cc19d941725913ace 1534 8d74524b521a341dc746acd5c3784d92 1535 K'[1]: 0d96ce1a4ac0f2e280a0cfc31742b064 1536 61d83d04ae45433db2d80478dd882a4c 1537 K'[2]: 58018c19315a1ba5d5bb9813b58029f0 1538 aec18a6f9ca59e0847de1c60bc25945c 1539 K'[3]: ed7e9bffd68c54d86fb19cd3c03f317f 1540 88a71ad9a5e94c28581d93fc4ec72b6a 1542 aes256-cts-hmac-sha1-96 P-521, rejected edwards25519 challenge 1543 key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1 1544 w (PRF+ output): de3a095a2b2386eff3eb15b735398da1caf95bc8425665d8 1545 2370aff58b0471f34a57bccddf1ebf0a2965b58a93ee5b45 1546 e85d1a5435d1c8c83662999722d542831f9a 1547 w (reduced multiplier): 003a095a2b2386eff3eb15b735398da1 1548 caf95bc8425665d82370aff58b0471f3 1549 4cce63791cfed967f0c94c16054b3e17 1550 03133681bece1e05219f5426bc944b0f 1551 bfb3 1552 x: 01687b59051bf40048d7c31d5a973d792fa12284b7a447e7f5938b5885ca0bb2 1553 c3f0bd30291a55fea08e143e2e04bdd7d19b753c7c99032f06cab0d9c2aa8f83 1554 7ef7 1555 y: 01ded675ebf74fe30c9a53710f577e9cf84f09f6048fe245a4600004884cc167 1556 733f9a9e43108fb83babe8754cd37cbd7025e28bc9ff870f084c7244f536285e 1557 25b4 1558 X: 03001bed88af987101ef52db5b8876f6287eb49a72163876c2cf99deb94f4c74 1559 9bfd118f0f400833cc8daad81971fe40498e6075d8ba0a2acfac35eb9ec8530e 1560 e0edd5 1561 Y: 02007bd3bf214200795ea449852976f241c9f50f445f78ff2714fffe42983f25 1562 cd9c9094ba3f9d7adadd6c251e9dc0991fc8210547e7769336a0ac406878fb94 1563 be2f1f 1564 T: 02014cb2e5b592ece5990f0ef30d308c061de1598bc4272b4a6599bed466fd15 1565 21693642abcf4dbe36ce1a2d13967de45f6c4f8d0fa8e14428bf03fb96ef5f1e 1566 d3e645 1567 S: 02016c64995e804416f748fd5fa3aa678cbc7cbb596a4f523132dc8af7ce84e5 1568 41f484a2c74808c6b21dcf7775baefa6753398425becc7b838b210ac5daa0cb0 1569 b710e2 1570 K: 0200997f4848ae2e7a98c23d14ac662030743ab37fccc2a45f1c721114f40bcc 1571 80fe6ec6aba49868f8aea1aa994d50e81b86d3e4d3c1130c8695b68907c673d9 1572 e5886a 1573 Optimistic SPAKEChallenge: a1363034a003020102a122042047ca8c 1574 24c3a4a70b6eca228322529dadcfa85c 1575 f58faceecf5d5c02907b9e2deba20930 1576 073005a003020101 1577 SPAKESupport: a0093007a0053003020104 1578 SPAKEChallenge: a1593057a003020104a145044302014cb2e5b592ece5990f 1579 0ef30d308c061de1598bc4272b4a6599bed466fd15216936 1580 42abcf4dbe36ce1a2d13967de45f6c4f8d0fa8e14428bf03 1581 fb96ef5f1ed3e645a20930073005a003020101 1582 Transcript hash after challenge: cb925b8baeae5e2867ab5b10ae1c941c 1583 4ff4b58a4812c1f7bd1c862ad480a8e1 1584 c6fcd5e88d846a2045e385841c91a75a 1585 d2035f0ff692717608e2a5a90842eff2 1586 Final transcript hash after pubkey: d0efed5e3e2c39c26034756d92a66fec 1587 3082ad793d0197f3f89ad36026f146a3 1588 996e548aa3fc49e2e82f8cac5d132c50 1589 5aa475b39e7be79cded22c26c41aa777 1590 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1591 1b077261656275726ea2101b0e415448454e412e4d49542e 1592 454455a3233021a003020102a11a30181b066b7262746774 1593 1b0e415448454e412e4d49542e454455a511180f31393730 1594 303130313030303030305aa703020100a8053003020112 1595 K'[0]: 631fcc8596e7f40e59045950d72aa0b7 1596 bac2810a07b767050e983841cf3a2d4c 1597 K'[1]: 881464920117074dbc67155a8f3341d1 1598 121ef65f78ea0380bfa81a134c1c47b1 1599 K'[2]: 377b72ac3af2caad582d73ae4682fd56 1600 b531ee56706200dd6c38c42b8219837a 1601 K'[3]: 35ad8e4d580ed3f0d15ad928329773c0 1602 81bd19f9a56363f3a5f77c7e66108c26 1604 There are currently no encryption types with a seed size large enough 1605 to require multiple hash blocks during key derivation with any of the 1606 assigned hash functions. To exercise this possibility, the following 1607 test vector illustrates what keys would be derived if there were a 1608 copy of the edwards25519 group with group number -1 and associated 1609 hash function SHA-1: 1611 AES256 edwards25519 SHA-1 group number -1 1612 key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1 1613 w (PRF+ output): 26da6b118cee6fa5ea795ed32d61490d 1614 82b2f11102312f3f2fc04fb01c93df91 1615 w (reduced multiplier): d166c7cc9e72ca8c61f6a9185a987251 1616 81b2f11102312f3f2fc04fb01c93df01 1617 x: 606c1b668008ed78fe2eee942e8f08007f3f1dcbef66d37fd69033525bda2030 1618 y: 10fc4e0bb1a902e58f632a1ea0bceb366360ac985f46996d956a02572bfcf050 1619 X: 389621509665abad35eaab26eab3a0f593c7b4380562aa5513c1140fd78ce048 1620 Y: de3ed05986eeac518958b566f9bad065b321402025cd188f3d198dc55c6d6b8d 1621 T: 2289a4f3c613e6e1df95e94aaa3c127dc062b9fceec3f9b62378dc729d61d0e3 1622 S: f9a7fa352930dedb422d567700bfcd39ba221e7f9ac3e6b36f2b63b68b88642c 1623 K: 6f61d6b18323b6c3ddaac7c56712845335384f095d3e116f69feb926a04f1340 1624 SPAKESupport: a0093007a00530030201ff 1625 SPAKEChallenge: a1363034a0030201ffa12204202289a4f3c613e6e1df95e9 1626 4aaa3c127dc062b9fceec3f9b62378dc729d61d0e3a20930 1627 073005a003020101 1628 Transcript hash after challenge: f5c051eb75290f92142c 1629 bbe80557ec2c85902c94 1630 Final transcript hash after pubkey: 9e26a3b148400c8f9cb8 1631 545331e4e7dcab399cc0 1632 KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009 1633 1b077261656275726ea2101b0e415448454e412e4d49542e 1634 454455a3233021a003020102a11a30181b066b7262746774 1635 1b0e415448454e412e4d49542e454455a511180f31393730 1636 303130313030303030305aa703020100a8053003020112 1637 K'[0]: 40bceb51bba474fd29ae65950022b704 1638 17b80d973fa8d8d6cd39833ff89964ad 1639 K'[1]: c29a7315453dc1cce938fa12a9e5c0db 1640 2894b2194da14c9cd4f7bc3a6a37223d 1641 K'[2]: f261984dba3c230fad99d324f871514e 1642 5aad670e44f00daef3264870b0851c25 1643 K'[3]: d24b2b46bab7c4d1790017d9116a7eeb 1644 ca88b0562a5ad8989c826cb7dab715c7 1646 Appendix D. Acknowledgements 1648 Nico Williams (Cryptonector) 1649 Taylor Yu (MIT) 1651 Authors' Addresses 1653 Nathaniel McCallum 1654 Red Hat, Inc. 1656 EMail: npmccallum@redhat.com 1657 Simo Sorce 1658 Red Hat, Inc. 1660 EMail: ssorce@redhat.com 1662 Robbie Harwood 1663 Red Hat, Inc. 1665 EMail: rharwood@redhat.com 1667 Greg Hudson 1668 MIT 1670 EMail: ghudson@mit.edu