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RFC 2119 keyword, line 179: '... is RECOMMENDED instead of step (2) in Section 5.1.6 of [RFC8032]:...' RFC 2119 keyword, line 188: '...ern, the following step is RECOMMENDED...' RFC 2119 keyword, line 203: '... steps are RECOMMENDED instead of st...' RFC 2119 keyword, line 230: '... Section 2 is RECOMMENDED....' RFC 2119 keyword, line 240: '... but SHALL be generated by a cryptog...' (1 more instance...) Miscellaneous warnings: ---------------------------------------------------------------------------- == The copyright year in the IETF Trust and authors Copyright Line does not match the current year -- The document date (March 11, 2020) is 1478 days in the past. Is this intentional? Checking references for intended status: Informational ---------------------------------------------------------------------------- == Outdated reference: A later version (-14) exists of draft-irtf-cfrg-randomness-improvements-10 -- Obsolete informational reference (is this intentional?): RFC 8152 (Obsoleted by RFC 9052, RFC 9053) -- Obsolete informational reference (is this intentional?): RFC 8208 (Obsoleted by RFC 8608) Summary: 2 errors (**), 0 flaws (~~), 2 warnings (==), 3 comments (--). Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 Network Working Group J. Preuss Mattsson 3 Internet-Draft E. Thormarker 4 Updates: 6979, 8032 (if approved) S. Ruohomaa 5 Intended status: Informational Ericsson 6 Expires: September 12, 2020 March 11, 2020 8 Deterministic ECDSA and EdDSA Signatures with Additional Randomness 9 draft-mattsson-cfrg-det-sigs-with-noise-02 11 Abstract 13 Deterministic elliptic-curve signatures such as deterministic ECDSA 14 and EdDSA have gained popularity over randomized ECDSA as their 15 security do not depend on a source of high-quality randomness. 16 Recent research has however found that implementations of these 17 signature algorithms may be vulnerable to certain side-channel and 18 fault injection attacks due to their determinism. One countermeasure 19 to such attacks is to re-add randomness to the otherwise 20 deterministic calculation of the per-message secret number. This 21 document updates RFC 6979 and RFC 8032 to recommend constructions 22 with additional randomness for deployments where side-channel attacks 23 and fault injection attacks are a concern. 25 Status of This Memo 27 This Internet-Draft is submitted in full conformance with the 28 provisions of BCP 78 and BCP 79. 30 Internet-Drafts are working documents of the Internet Engineering 31 Task Force (IETF). Note that other groups may also distribute 32 working documents as Internet-Drafts. The list of current Internet- 33 Drafts is at https://datatracker.ietf.org/drafts/current/. 35 Internet-Drafts are draft documents valid for a maximum of six months 36 and may be updated, replaced, or obsoleted by other documents at any 37 time. It is inappropriate to use Internet-Drafts as reference 38 material or to cite them other than as "work in progress." 40 This Internet-Draft will expire on September 12, 2020. 42 Copyright Notice 44 Copyright (c) 2020 IETF Trust and the persons identified as the 45 document authors. All rights reserved. 47 This document is subject to BCP 78 and the IETF Trust's Legal 48 Provisions Relating to IETF Documents 49 (https://trustee.ietf.org/license-info) in effect on the date of 50 publication of this document. Please review these documents 51 carefully, as they describe your rights and restrictions with respect 52 to this document. Code Components extracted from this document must 53 include Simplified BSD License text as described in Section 4.e of 54 the Trust Legal Provisions and are provided without warranty as 55 described in the Simplified BSD License. 57 Table of Contents 59 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 60 2. Updates to RFC 8032 (EdDSA) . . . . . . . . . . . . . . . . . 4 61 3. Updates to RFC 6979 (Deterministic ECDSA) . . . . . . . . . . 5 62 4. Security Considerations . . . . . . . . . . . . . . . . . . . 5 63 5. For discussion (to be removed in the future) . . . . . . . . 7 64 6. References . . . . . . . . . . . . . . . . . . . . . . . . . 7 65 6.1. Normative References . . . . . . . . . . . . . . . . . . 7 66 6.2. Informative References . . . . . . . . . . . . . . . . . 8 67 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 12 68 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 12 70 1. Introduction 72 In Elliptic-Curve Cryptography (ECC) signature algorithms, the per- 73 message secret number has traditionally been generated from a random 74 number generator (RNG). The security of such algorithms depends on 75 the cryptographic quality of the random number generation and biases 76 in the randomness may have catastrophic effects such as compromising 77 private keys. Repeated per-message secret numbers have caused 78 several severe security accidents in practice. As stated in 79 [RFC6979], the need for a cryptographically secure source of 80 randomness is also a hindrance to deployment of randomized ECDSA 81 [FIPS-186-4] in architectures where secure random number generation 82 is challenging, in particular, embedded IoT systems and smartcards. 83 [ABFJLM17] does however state that smartcards typically has a high- 84 quality RNG on board, which makes it significantly easier and faster 85 to use the RNG instead of doing a hash computation. 87 In deterministic ECC signatures schemes such as Deterministic 88 Elliptic Curve Digital Signature Algorithm (ECDSA) [RFC6979] and 89 Edwards-curve Digital Signature Algorithm (EdDSA) [RFC8032], the per- 90 message secret number is instead generated in a fully-deterministic 91 way as a function of the message and the private key. Except for key 92 generation, the security of such deterministic signatures does not 93 depend on a source of high-quality randomness. As they are presumed 94 to be safer, deterministic signatures have gained popularity and are 95 referenced and recommended by a large number of recent RFCs [RFC8037] 96 [RFC8080] [RFC8152] [RFC8225] [RFC8387] [RFC8410] [RFC8411] [RFC8419] 98 [RFC8420] [RFC8422] [RFC8446] [RFC8463] [RFC8550] [RFC8591] [RFC8624] 99 [RFC8208] [RFC8608]. 101 Side-channel attacks are potential attack vectors for implementations 102 of cryptographic algorithms. Side-Channel attacks can in general be 103 classified along three orthogonal axes: passive vs. active, physical 104 vs. logical, and local vs. remote [SideChannel]. It has been 105 demonstrated how side-channel attacks such as power analysis 106 [BCPST14] and timing attacks [Minerva19] [TPM-Fail19] allow for 107 practical recovery of the private key in some existing 108 implementations of randomized ECDSA. [BSI] summarizes minimum 109 requirements for evaluating side-channel attacks of elliptic curve 110 implementations and writes that deterministic ECDSA and EdDSA 111 requires extra care. The deterministic ECDSA specification [RFC6979] 112 notes that the deterministic generation of per-message secret numbers 113 may be useful to an attacker in some forms of side-channel attacks 114 and as stated in [Minerva19], deterministic signatures like [RFC6979] 115 and [RFC8032] might help an attacker to reduce the noise in the side- 116 channel when the same message it signed multiple times. Recent 117 research [SH16] [BP16] [RP17] [ABFJLM17] [SBBDS17] [PSSLR17] [SB18] 118 [WPB19] [AOTZ19] [FG19] have theoretically and experimentally 119 analyzed the resistance of deterministic ECC signature algorithms 120 against side-channel and fault injection attacks. The conclusions 121 are that deterministic signature algorithms have theoretical 122 weaknesses against certain instances of these types of attacks and 123 that the attacks are practically feasibly in some environments. 124 These types of attacks may be of particular concern for hardware 125 implementations such as embedded IoT devices and smartcards where the 126 adversary can be assumed to have access to the device to induce 127 faults and measure its side-channels such as timing information with 128 low signal-to-noise ratio, power consumption, electromagnetic leaks, 129 or sound. Fault attacks may also be possible without physical access 130 to the device. RowHammer [RowHammer14] showed how an attacker to 131 induce DRAM bit-flips in memory areas the attacker should not have 132 access to and Plundervolt [Plundervolt19] showed how an attacker with 133 root access can use frequency and voltage scaling interfaces to 134 induce faults that bypasses even secure execution technologies. 135 RowHammer can e.g. be used in operating systems with several 136 processes or cloud scenarios with virtualized servers. Protocols 137 like TLS, SSH, and IKEv2 that adds a random number to the message to 138 be signed mitigate some types of attacks [PSSLR17]. 140 Government agencies are clearly concerned about these attacks. In 141 [Notice-186-5] and [Draft-186-5], NIST warns about side-channel and 142 fault injection attacks, but states that deterministic ECDSA may be 143 desirable for devices that lack good randomness. BSI has published 144 [BSI] and researchers from BSI have co-authored two research papers 145 [ABFJLM17] [PSSLR17] on attacks on deterministic signatures. For 146 many industries it is important to be compliant with both RFCs and 147 government publications, alignment between IETF, NIST, and BSI 148 recommendations would be preferable. 150 One countermeasure to side-channel and fault injection attacks 151 recommended by [RP17] [ABFJLM17] [SBBDS17] [PSSLR17] [SB18] [AOTZ19] 152 [FG19] and implemented in [XEdDSA] [libSodium] [libHydrogen] is to 153 re-introduce some additional randomness to the otherwise 154 deterministic generation of the per-message secret number. This 155 combines the security benefits of fully-randomized per-message secret 156 numbers with the security benefits of fully-deterministic secret 157 numbers. Such a construction protects against key compromise due to 158 weak random number generation, but still effectively prevents many 159 side-channel and fault injection attacks that exploit determinism. 160 Such a constuction require minor changes to the implementation and 161 does not increase the number of elliptic curve point multiplications 162 and is therefore suitable for constained IoT. Deterministic ECDSA 163 with additional randomness can be made compliant with [FIPS-186-4] 164 but would not be compliant with the recommendations in many RFCs. 165 Adding randomness to EdDSA is not compliant with [RFC8032]. 167 This document updates [RFC6979] and [RFC8032] to recommend 168 constructions with additional randomness for deployments where side- 169 channel and fault injection attacks are a concern. Produced 170 signatures remain fully compatible with unmodified ECDSA and EdDSA 171 verifiers and existing key pairs can continue to be used. As the 172 precise use of the noise is specified, test vectors can still be 173 produced and implementations can be tested against them. 175 2. Updates to RFC 8032 (EdDSA) 177 For Ed25519ph, Ed25519ctx, and Ed25519: In deployments where side- 178 channel and fault injection attacks are a concern, the following step 179 is RECOMMENDED instead of step (2) in Section 5.1.6 of [RFC8032]: 181 2. Compute SHA-512(dom2(F, C) || Z || prefix || 000... || PH(M)), 182 where M is the message to be signed, Z is 32 octets of random 183 data, the number of zeroes 000... is chosen so that the length 184 of (dom2(F, C) || Z || prefix || 000...) is 1024 bytes. 185 Interpret the 64-octet digest as a little-endian integer r. 187 For Ed448ph and Ed448: In deployments where side-channel and fault 188 injection attacks are a concern, the following step is RECOMMENDED 189 instead of step (2) in Section 5.3.6 of [RFC8032]: 191 2. Compute SHAKE256(dom4(F, C) || Z || prefix || 000... || PH(M), 192 114), where M is the message to be signed, and Z is 57 octets 193 of random data, the number of zeroes 000... is chosen so that 194 the length of (dom4(F, C) || Z || prefix || 000...) is 1088 195 bytes. F is 1 for Ed448ph, 0 for Ed448, and C is the context 196 to use. Interpret the 114-octet digest as a little-endian 197 integer r. 199 3. Updates to RFC 6979 (Deterministic ECDSA) 201 For Deterministic ECDSA: In existing ECDSA deployments where side- 202 channel and fault injection attacks are a concern, the following 203 steps are RECOMMENDED instead of steps (d) and (f) in Section 3.2 of 204 [RFC6979]: 206 d. Set: 208 K = HMAC_K(V || 0x00 || Z || int2octets(x) || 000... || 209 bits2octets(h1)) where '||' denotes concatenation. In other 210 words, we compute HMAC with key K, over the concatenation of 211 the following, in order: the current value of V, a sequence of 212 eight bits of value 0, random data Z (of the same length as 213 int2octets(x)), the encoding of the (EC)DSA private key x, a 214 sequence of zero bits 000... chosen so that the length of 215 (V || 0x00 || Z || int2octets(x) || 000...) is equal to the 216 block size of the hash function, and the hashed message 217 (possibly truncated and extended as specified by the 218 bits2octets transform). The HMAC result is the new value of K. 219 Note that the private key x is in the [1, q-1] range, hence a 220 proper input for int2octets, yielding rlen bits of output, 221 i.e., an integral number of octets (rlen is a multiple of 8). 223 f. Set: 225 K = HMAC_K(V || 0x01 || Z || int2octets(x) || 000... || 226 bits2octets(h1)) 228 In new deployments, where side-channel and fault injection attacks 229 are a concern, EdDSA with additional randomness as specified in 230 Section 2 is RECOMMENDED. 232 4. Security Considerations 234 The constructions in this document follows the high-level approach in 235 [XEdDSA] to calculate the per-message secret number from the hash of 236 the private key and the message, but add additional randomness into 237 the calculation for greater resilience. This does not re-introduce 238 the strong security requirement of randomness needed by randomized 239 ECDSA [FIPS-186-4]. The randomness of Z does not need to be perfect, 240 but SHALL be generated by a cryptographically secure pseudo random 241 number generator (PRNG) and SHALL be secret. Even if the same random 242 number Z is used to sign two different messages, the security will be 243 the same as deterministic ECDSA and EdDSA and an attacker will not be 244 able to compromise the private key with algebraic means as in fully- 245 randomized ECDSA [FIPS-186-4]. With the construction specified in 246 this document, two signatures over two equal messages are different 247 which prevents information leakage in use cases where signatures but 248 not messages are public. The construction in this document place the 249 additional randomness before the message to align with randomized 250 hashing methods. 252 [SBBDS17] states that [XEdDSA] would not prevent their attack due to 253 insufficient mixing of the hashed private key with the additional 254 randomness. [SBBDS17] suggest a construction where the randomness is 255 padded with zeroes so that the first 1024-bit SHA-512 block is 256 composed only of the hashed private key and the random value, but not 257 the message. The construction in this document follows this 258 recommendation and pads with zeroes so that the first block is 259 composed only of the hashed private key and the random value, but not 260 the message. 262 Another countermeasure to fault attacks is to force the signer to 263 verify the signature in the last step of the signature generation or 264 to calculate the signature twice and compare the results. These 265 countermeasure would catch a single fault but would not protect 266 against attackers that are able to precisely inject faults several 267 times [RP17] [PSSLR17] [SB18]. Adding an additional sign or 268 verification operation would also significantly affect performance, 269 especially verification which is a heavier operation than signing in 270 ECDSA and EdDSA. 272 [ABFJLM17] suggests using both additional randomness and a counter, 273 which makes the signature generation stateful. While most used 274 signatures have traditionally been stateless, stateful signatures 275 like XMSS [RFC8391] and LMS [RFC8554] have now been standardized and 276 deployed. [I-D.irtf-cfrg-randomness-improvements] specifies a PRNG 277 construction with a random seed, a secret key, a context string, and 278 a nonce, which makes the random number generation stateful. The 279 generation of the per-message secret number in this document is not 280 stateful, but it can be used with a stateful PRNG. The exact 281 construction in [I-D.irtf-cfrg-randomness-improvements] is however 282 not recommended in deployments where side-channel and fault injection 283 attacks are a concern as it relies on deterministic signatures. 285 With the construction in this document, the repetition of the same 286 per-message secret number for two different messages is highly 287 unlikely even with an imperfect random number generator, but not 288 impossible. As an extreme countermeasure, previously used secret 289 numbers can be tracked to ensure their uniqueness for a given key, 290 and a different random number can be used if a collision is detected. 291 This document does not mandate nor stop an implementation from taking 292 such a precaution. 294 Implementations need to follow best practices on how to protect 295 against all side-channel attacks, not just attacks that exploits 296 determinism, see for example [BSI]. 298 5. For discussion (to be removed in the future) 300 o Amount of randomness - The current construction uses random data 301 of the same length as 'prefix' or 'int2octets(x)' which means 32 302 bytes of randomness for Ed25519. XEdDSA uses 64 bytes of 303 randomness which might be overkill. As discussed in [SBBDS17], 304 the amount of randomness needed depends on the targeted security 305 level. 32 bytes of randomness should be enough for Ed448 and 16 306 bytes of randomness should be enough for Ed25519. Even less than 307 that is likely sufficient to prevent practical attacks. 309 o Deterministic ECDSA with SHAKE - NIST is planning to approve 310 SHAKE128(M,128) and SHAKE256(M,256) for use in ECDSA 311 [Draft-186-5]. Deterministic ECDSA as specified in [RFC6979] 312 would then use HMAC-SHAKE instead of a more optimal KMAC, which 313 would be the prefered keyed hash function for use with SHAKE. It 314 should be discussed if IETF (or NIST) should specify that the 315 resulting HMAC-SHAKE128(K, M) and HMAC-SHAKE256(K, M) in 316 deterministic ECDSA should be replaced with KMAC128(K,M,128) and 317 KMAC256(K,M,128). 319 6. References 321 6.1. Normative References 323 [FIPS-186-4] 324 Department of Commerce, National., "Digital Signature 325 Standard (DSS)", NIST FIPS PUB 186-4 , July 2013, 326 . 329 [I-D.irtf-cfrg-randomness-improvements] 330 Cremers, C., Garratt, L., Smyshlyaev, S., Sullivan, N., 331 and C. Wood, "Randomness Improvements for Security 332 Protocols", draft-irtf-cfrg-randomness-improvements-10 333 (work in progress), February 2020. 335 [RFC6979] Pornin, T., "Deterministic Usage of the Digital Signature 336 Algorithm (DSA) and Elliptic Curve Digital Signature 337 Algorithm (ECDSA)", RFC 6979, DOI 10.17487/RFC6979, August 338 2013, . 340 [RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital 341 Signature Algorithm (EdDSA)", RFC 8032, 342 DOI 10.17487/RFC8032, January 2017, 343 . 345 6.2. Informative References 347 [ABFJLM17] 348 Ambrose, C., Bos, J., Fay, B., Joye, M., Lochter, M., and 349 B. Murray, "Differential Attacks on Deterministic 350 Signatures", October 2017, 351 . 353 [AOTZ19] Aranha, D., Orlandi, C., Takahashi, A., and G. Zaverucha, 354 "Security of Hedged Fiat-Shamir Signatures under Fault 355 Attacks", September 2019, 356 . 358 [BCPST14] Batina, L., Chmielewski, L., Papachristodoulou, L., 359 Schwabe, P., and M. Tunstall, "Online Template Attacks", 360 December 2014, . 363 [BP16] Barenghi, A. and G. Pelosi, "A Note on Fault Attacks 364 Against Deterministic Signature Schemes (Short Paper)", 365 September 2016, . 368 [BSI] Bundesamt fuer Sicherheit in der Informationstechnik, ., 369 "Minimum Requirements for Evaluating Side-Channel Attack 370 Resistance of Elliptic Curve Implementations", November 371 2016, 372 . 376 [Draft-186-5] 377 National Institute of Standards and Technology (NIST), ., 378 "FIPS PUB 186-5 (Draft)", October 2019, 379 . 382 [FG19] Fischlin, M. and F. Guenther, "Modeling Memory Faults in 383 Signature and Encryption Schemes", September 2019, 384 . 386 [libHydrogen] 387 "The Hydrogen library", n.d., 388 . 390 [libSodium] 391 "The Sodium library", n.d., 392 . 394 [Minerva19] 395 Centre for Research on Cryptography and Security (CRoCS), 396 ., "Minerva", October 2019, 397 . 399 [Notice-186-5] 400 National Institute of Standards and Technology (NIST), ., 401 "Request for Comments on FIPS 186-5 and SP 800-186", 402 October 2019, . 406 [Plundervolt19] 407 Murdock, K., Oswald, D., Garcia, F., Van Bulck, J., Gruss, 408 D., and F. Piessens, "How a little bit of undervolting can 409 cause a lot of problems", December 2019, 410 . 412 [PSSLR17] Poddebniak, D., Somorovsky, J., Schinzel, S., Lochter, M., 413 and P. Roesler, "Attacking Deterministic Signature Schemes 414 using Fault Attacks", October 2017, 415 . 417 [RFC8037] Liusvaara, I., "CFRG Elliptic Curve Diffie-Hellman (ECDH) 418 and Signatures in JSON Object Signing and Encryption 419 (JOSE)", RFC 8037, DOI 10.17487/RFC8037, January 2017, 420 . 422 [RFC8080] Sury, O. and R. Edmonds, "Edwards-Curve Digital Security 423 Algorithm (EdDSA) for DNSSEC", RFC 8080, 424 DOI 10.17487/RFC8080, February 2017, 425 . 427 [RFC8152] Schaad, J., "CBOR Object Signing and Encryption (COSE)", 428 RFC 8152, DOI 10.17487/RFC8152, July 2017, 429 . 431 [RFC8208] Turner, S. and O. Borchert, "BGPsec Algorithms, Key 432 Formats, and Signature Formats", RFC 8208, 433 DOI 10.17487/RFC8208, September 2017, 434 . 436 [RFC8225] Wendt, C. and J. Peterson, "PASSporT: Personal Assertion 437 Token", RFC 8225, DOI 10.17487/RFC8225, February 2018, 438 . 440 [RFC8387] Sethi, M., Arkko, J., Keranen, A., and H. Back, "Practical 441 Considerations and Implementation Experiences in Securing 442 Smart Object Networks", RFC 8387, DOI 10.17487/RFC8387, 443 May 2018, . 445 [RFC8391] Huelsing, A., Butin, D., Gazdag, S., Rijneveld, J., and A. 446 Mohaisen, "XMSS: eXtended Merkle Signature Scheme", 447 RFC 8391, DOI 10.17487/RFC8391, May 2018, 448 . 450 [RFC8410] Josefsson, S. and J. Schaad, "Algorithm Identifiers for 451 Ed25519, Ed448, X25519, and X448 for Use in the Internet 452 X.509 Public Key Infrastructure", RFC 8410, 453 DOI 10.17487/RFC8410, August 2018, 454 . 456 [RFC8411] Schaad, J. and R. Andrews, "IANA Registration for the 457 Cryptographic Algorithm Object Identifier Range", 458 RFC 8411, DOI 10.17487/RFC8411, August 2018, 459 . 461 [RFC8419] Housley, R., "Use of Edwards-Curve Digital Signature 462 Algorithm (EdDSA) Signatures in the Cryptographic Message 463 Syntax (CMS)", RFC 8419, DOI 10.17487/RFC8419, August 464 2018, . 466 [RFC8420] Nir, Y., "Using the Edwards-Curve Digital Signature 467 Algorithm (EdDSA) in the Internet Key Exchange Protocol 468 Version 2 (IKEv2)", RFC 8420, DOI 10.17487/RFC8420, August 469 2018, . 471 [RFC8422] Nir, Y., Josefsson, S., and M. Pegourie-Gonnard, "Elliptic 472 Curve Cryptography (ECC) Cipher Suites for Transport Layer 473 Security (TLS) Versions 1.2 and Earlier", RFC 8422, 474 DOI 10.17487/RFC8422, August 2018, 475 . 477 [RFC8446] Rescorla, E., "The Transport Layer Security (TLS) Protocol 478 Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018, 479 . 481 [RFC8463] Levine, J., "A New Cryptographic Signature Method for 482 DomainKeys Identified Mail (DKIM)", RFC 8463, 483 DOI 10.17487/RFC8463, September 2018, 484 . 486 [RFC8550] Schaad, J., Ramsdell, B., and S. Turner, "Secure/ 487 Multipurpose Internet Mail Extensions (S/MIME) Version 4.0 488 Certificate Handling", RFC 8550, DOI 10.17487/RFC8550, 489 April 2019, . 491 [RFC8554] McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali 492 Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554, 493 April 2019, . 495 [RFC8591] Campbell, B. and R. Housley, "SIP-Based Messaging with 496 S/MIME", RFC 8591, DOI 10.17487/RFC8591, April 2019, 497 . 499 [RFC8608] Turner, S. and O. Borchert, "BGPsec Algorithms, Key 500 Formats, and Signature Formats", RFC 8608, 501 DOI 10.17487/RFC8608, June 2019, 502 . 504 [RFC8624] Wouters, P. and O. Sury, "Algorithm Implementation 505 Requirements and Usage Guidance for DNSSEC", RFC 8624, 506 DOI 10.17487/RFC8624, June 2019, 507 . 509 [RowHammer14] 510 Kim, Y., Daly, R., Kim, J., Fallin, C., Lee, J., Lee, D., 511 Wilkerson, C., and K. Mutlu, "Flipping Bits in Memory 512 Without Accessing Them: An Experimental Study of DRAM 513 Disturbance Errors", June 2014, 514 . 517 [RP17] Romailler, Y. and S. Pelissier, "Practical fault attack 518 against the Ed25519 and EdDSA signature schemes", 519 September 2017, 520 . 522 [SB18] Samwel, N. and L. Batina, "Practical Fault Injection on 523 Deterministic Signatures: The Case of EdDSA", April 2018, 524 . 526 [SBBDS17] Samwel, N., Batina, L., Bertoni, G., Daemen, J., and R. 527 Susella, "Breaking Ed25519 in WolfSSL", October 2017, 528 . 530 [SH16] Seuschek, H., Heyszl, J., and F. De Santis, "A Cautionary 531 Note: Side-Channel Leakage Implications of Deterministic 532 Signature Schemes", January 2016, 533 . 536 [SideChannel] 537 Spreitzer, R., Moonsamy, V., Korak, T., and S. Mangard, 538 "Systematic Classification of Side-Channel Attacks: A Case 539 Study for Mobile Devices", December 2017, 540 . 542 [TPM-Fail19] 543 Moghimi, D., Sunar, B., Eisenbarth, T., and N. Heninge, 544 "TPM-FAIL: TPM meets Timing and Lattice Attacks", October 545 2019, . 547 [WPB19] Weissbart, L., Picek, S., and L. Batina, "One trace is all 548 it takes: Machine Learning-based Side-channel Attack on 549 EdDSA", July 2019, . 551 [XEdDSA] Signal, ., "The XEdDSA and VXEdDSA Signature Schemes", 552 October 2016, 553 . 555 Acknowledgments 557 The authors want to thank Tony Arcieri, Uri Blumenthal, and Quynh 558 Dang for their valuable comments and feedback. 560 Authors' Addresses 562 John Preuss Mattsson 563 Ericsson 565 Email: john.mattsson@ericsson.com 567 Erik Thormarker 568 Ericsson 570 Email: erik.thormarker@ericsson.com 571 Sini Ruohomaa 572 Ericsson 574 Email: sini.ruohomaa@ericsson.com