Hedged ECDSA and EdDSA Signatures
draft-irtf-cfrg-det-sigs-with-noise-03
| Document | Type | Active Internet-Draft (cfrg RG) | |
|---|---|---|---|
| Authors | John Preuß Mattsson , Erik Thormarker , Sini Ruohomaa | ||
| Last updated | 2024-03-16 | ||
| Replaces | draft-mattsson-cfrg-det-sigs-with-noise | ||
| RFC stream | Internet Research Task Force (IRTF) | ||
| Intended RFC status | Informational | ||
| Formats | |||
| Additional resources | Mailing list discussion | ||
| Stream | IRTF state | Active RG Document | |
| Consensus boilerplate | Unknown | ||
| Document shepherd | (None) | ||
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draft-irtf-cfrg-det-sigs-with-noise-03
Crypto Forum J. Preuß Mattsson
Internet-Draft E. Thormarker
Updates: 6979, 8032 (if approved) S. Ruohomaa
Intended status: Informational Ericsson
Expires: 17 September 2024 16 March 2024
Hedged ECDSA and EdDSA Signatures
draft-irtf-cfrg-det-sigs-with-noise-03
Abstract
Deterministic elliptic-curve signatures such as deterministic ECDSA
and EdDSA have gained popularity over randomized ECDSA as their
security does not depend on a source of high-quality randomness.
Recent research, however, has found that implementations of these
signature algorithms may be vulnerable to certain side-channel and
fault injection attacks due to their deterministic nature. One
countermeasure to such attacks is hedged signatures where the
calculation of the per-message secret number includes both fresh
randomness and the message. This document updates RFC 6979 and RFC
8032 to recommend hedged constructions in deployments where side-
channel attacks and fault injection attacks are a concern. The
updates are invisible to the validator of the signature and
compatible with existing ECDSA and EdDSA validators.
About This Document
This note is to be removed before publishing as an RFC.
The latest revision of this draft can be found at
https://cfrg.github.io/draft-irtf-cfrg-det-sigs-with-noise/draft-
irtf-cfrg-det-sigs-with-noise.html. Status information for this
document may be found at https://datatracker.ietf.org/doc/draft-irtf-
cfrg-det-sigs-with-noise/.
Discussion of this document takes place on the Crypto Forum Research
Group mailing list (mailto:cfrg@ietf.org), which is archived at
https://mailarchive.ietf.org/arch/search/?email_list=cfrg. Subscribe
at https://www.ietf.org/mailman/listinfo/cfrg/.
Source for this draft and an issue tracker can be found at
https://github.com/cfrg/draft-irtf-cfrg-det-sigs-with-noise.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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Copyright Notice
Copyright (c) 2024 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
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Please review these documents carefully, as they describe your rights
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Conventions Used in This Document . . . . . . . . . . . . . . 5
3. Hedged EdDSA . . . . . . . . . . . . . . . . . . . . . . . . 5
4. Hedged ECDSA . . . . . . . . . . . . . . . . . . . . . . . . 6
5. Security Considerations . . . . . . . . . . . . . . . . . . . 7
6. Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . 9
6.1. Hedged Ed25519 . . . . . . . . . . . . . . . . . . . . . 9
6.2. Hedged ECDSA with P-256 and SHA-256 . . . . . . . . . . . 9
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 9
7.1. Normative References . . . . . . . . . . . . . . . . . . 9
7.2. Informative References . . . . . . . . . . . . . . . . . 10
Change log . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 17
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 17
1. Introduction
In Elliptic-Curve Cryptography (ECC) signature algorithms, the per-
message secret number has traditionally been generated from a random
number generator (RNG). The security of such algorithms depends on
the cryptographic quality of the random number generation and biases
in the randomness may have catastrophic effects such as compromising
private keys (see e.g., [Bernstein19]). Repeated per-message secret
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numbers have caused several severe security accidents in practice.
As stated in [RFC6979], the need for a cryptographically secure
source of randomness is also a hindrance to deployment of randomized
ECDSA [FIPS-186-5] in architectures where secure random number
generation is challenging, in particular, embedded IoT systems and
smartcards. [ABFJLM17] does however state that smartcards typically
have a high-quality RNG on board, which makes it significantly easier
and faster to use the RNG instead of doing a hash computation.
In deterministic ECC signatures schemes such as Deterministic
Elliptic Curve Digital Signature Algorithm (ECDSA)
[RFC6979][FIPS-186-5] and Edwards-curve Digital Signature Algorithm
(EdDSA) [RFC8032], the per-message secret number is instead generated
in a fully deterministic way as a function of the message and the
private key. Except for key generation, the security of such
deterministic signatures does not rely on a source of high-quality
randomness. This makes verification of implementations easier. As
they are presumed to be safer, deterministic signatures have gained
popularity and are referenced and recommended by a large number of
recent RFCs [RFC8037] [RFC8080] [RFC8225] [RFC8387] [RFC8410]
[RFC8411] [RFC8419] [RFC8420] [RFC8422] [RFC8446] [RFC8463] [RFC8550]
[RFC8591] [RFC8608] [RFC8624] [RFC9053].
Side-channel attacks are potential attack vectors for implementations
of cryptographic algorithms. Side-Channel attacks can in general be
classified along three orthogonal axes: passive vs. active, physical
vs. logical, and local vs. remote [SideChannel]. It has been
demonstrated how side-channel attacks such as power analysis
[BCPST14] and timing attacks [Minerva19] [TPM-Fail19] allow for
practical recovery of the private key in some existing
implementations of randomized ECDSA. [BSI] summarizes minimum
requirements for evaluating side-channel attacks of elliptic curve
implementations and writes that deterministic ECDSA and EdDSA
requires extra care. The deterministic ECDSA specification [RFC6979]
notes that the deterministic generation of per-message secret numbers
may be useful to an attacker in some forms of side-channel attacks
and as stated in [Minerva19], deterministic signatures like [RFC6979]
and [RFC8032] might help an attacker to reduce the noise in the side-
channel when the same message it signed multiple times. Recent
research [SH16] [BP16] [RP17] [ABFJLM17] [SBBDS17] [PSSLR17] [SB18]
[WPB19] [AOTZ19] [FG19] have theoretically and experimentally
analyzed the resistance of deterministic ECC signature algorithms
against side-channel and fault injection attacks. The conclusions
are that deterministic signature algorithms have theoretical
weaknesses against certain instances of these types of attacks and
that the attacks are practically feasibly in some environments.
These types of attacks may be of particular concern for hardware
implementations such as embedded IoT devices and smartcards where the
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adversary can be assumed to have access to the device to induce
faults and measure its side-channels such as timing information,
power consumption, electromagnetic leaks, or sound with low signal-
to-noise ratio. A good summary of fault attacks in given by [Cao20].
See also the discussions and references in [Comments-186-5].
Fault attacks may also be possible without physical access to the
device. RowHammer [RowHammer14] showed how an attacker to induce
DRAM bit-flips in memory areas the attacker should not have access
to. Plundervolt [Plundervolt19] showed how an attacker with root
access can use frequency and voltage scaling interfaces to induce
faults that bypass even secure execution technologies. RowHammer can
e.g., be used in operating systems with several processes or cloud
scenarios with virtualized servers. Protocols like TLS, SSH, and
IKEv2 that add a random number to the message to be signed mitigate
some types of attacks [PSSLR17].
Government agencies are clearly concerned about these attacks. In
[Notice-186-5] and [FIPS-186-5], NIST warns about side-channel and
fault injection attacks, but states that deterministic ECDSA may be
desirable for devices that lack good randomness. The quantum-
resistant ML-DSA [Draft-204] under standardization by NIST uses
hedged signing by default. BSI has published [BSI] and researchers
from BSI have co-authored two research papers [ABFJLM17] [PSSLR17] on
attacks on deterministic signatures. For many industries it is
important to be compliant with both RFCs and government publications,
alignment between IETF, NIST, and BSI recommendations would be
preferable.
Note that deriving per-message secret number deterministically, is
also insecure in a multi-party signature setting
[I-D.irtf-cfrg-frost].
One countermeasure to entropy failures, side-channel attacks, and
fault injection attacks recommended by [Langley13] [RP17] [ABFJLM17]
[SBBDS17] [PSSLR17] [SB18] [AOTZ19] [FG19] and implemented in
[OpenSSL13a] [OpenSSL13b] [XEdDSA] [libSodium] [libHydrogen] is to
generate the per-message secret number from a random string, a secret
key, and the message. This combines the security benefits of fully
randomized per-message secret numbers with the security benefits of
fully deterministic secret numbers. Such a hedged construction
protects against key compromise due to weak random number generation,
but still effectively prevents many side-channel and fault injection
attacks that exploit determinism. Hedged constructions require minor
changes to the implementation and does not increase the number of
elliptic curve point multiplications and is therefore suitable for
constrained IoT. Adding randomness to EdDSA is not compliant with
[RFC8032]. [Kampanakis16] describes an alternative [FIPS-186-5]
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compliant approach where message specific pseudo-random information
is used as an additional input to the random number generation to
create per-message secret number. [Bernstein14] states that
generation of the per-message secret number from a subset of a random
string, a secret key, the message, and a message counter is common in
DSA/ECDSA implementations.
This document updates [RFC6979] and [RFC8032] to recommend hedged
constructions in deployments where side-channel and fault injection
attacks are a concern. The updates are invisible to the validator of
the signature. Produced signatures remain fully compatible with
unmodified ECDSA and EdDSA verifiers and existing key pairs can
continue to be used. As the precise use of the noise is specified,
test vectors can still be produced, see Section 6, and
implementations can be tested against them.
2. Conventions Used in This Document
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in BCP
14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
3. Hedged EdDSA
This document updates RFC 8032 (EdDSA) to recommend hedged variants
of EdDSA for deployments where side-channel attacks and fault
injection attacks are a concern, the variants are called hedged
EdDSA. The updates are invisible to the validator of the signature
and compatible with existing EdDSA validators.
Update to RFC 8032:
For Ed25519ph, Ed25519ctx, and Ed25519: In deployments where side-
channel and fault injection attacks are a concern, the following step
is RECOMMENDED instead of step (2) in Section 5.1.6 of [RFC8032]:
2. Compute SHA-512(0x00 || Z || dom2(F, C) || 000... || prefix ||
000... || PH(M)), where M is the message to be signed, Z is 32
octets of random data, the number of zeroes 000... is chosen so
that the lengths of (0x00 || Z || dom2(F, C) || 000...) and
(prefix || 000...) are multiples of 128 octets. Interpret the
64-octet digest as a little-endian integer r.
For Ed448ph and Ed448: In deployments where side-channel and fault
injection attacks are a concern, the following step is RECOMMENDED
instead of step (2) in Section 5.2.6 of [RFC8032]:
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2. Compute SHAKE256(0x00 || Z || dom4(F, C) || 000... || prefix ||
000... || PH(M), 114), where M is the message to be signed, and Z
is 57 octets of random data, the number of zeroes 000... is
chosen so that the length of (0x00 || Z || dom4(F, C) || 000...)
and (prefix || 000...) are multiples of 136 octets. F is 1 for
Ed448ph, 0 for Ed448, and C is the context to use. Interpret the
114-octet digest as a little-endian integer r.
4. Hedged ECDSA
This document updates RFC 6979 (deterministic ECDSA) to recommend a
hedged variant of ECDSA for deployments where side-channel attacks
and fault injection attacks are a concern, the variant is called
hedged ECDSA. The updates are invisible to the validator of the
signature and compatible with existing ECDSA validators.
Update to RFC 6979: In ECDSA deployments where side-channel and fault
injection attacks are a concern, the following steps are RECOMMENDED
instead of steps (d) and (f) in Section 3.2 of [RFC6979]:
d. Set:
K = HMAC_K(V || 0x00 || Z || 000... || int2octets(x) || 000...
|| bits2octets(h1))
where '||' denotes concatenation. In other words, we compute
HMAC with key K, over the concatenation of the following, in
order: the current value of V, a sequence of eight bits of value
0, random data Z (of the same length as int2octets(x)), a
sequence of zero bits 000..., the encoding of the (EC)DSA private
key x, a sequence of zero bits 000..., and the hashed message
(possibly truncated and extended as specified by the bits2octets
transform). The number of zeroes 000... is chosen so that the
length of (V || 0x00 || Z || 000...) and (int2octets(x) ||
000...) are multiples of the block size of the hash function.
The HMAC result is the new value of K. Note that the private key
x is in the [1, q-1] range, hence a proper input for int2octets,
yielding rlen bits of output, i.e., an integral number of octets
(rlen is a multiple of 8).
f. Set:
K = HMAC_K(V || 0x01 || Z || 000... || int2octets(x) || 000...
|| bits2octets(h1))
Note that the "internal octet" is 0x01 this time. The string
(Z || 000... || int2octets(x) || 000.. || bits2octets(h1)),
called provided_data in HMAC_DRBG, is the same as in step (d).
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When ECDSA is used with SHAKE [SHA3] the HMAC construction above MAY
be used but it is RECOMMENDED to use the more efficient KMAC
construction [KMAC]. SHAKE is a variable-length hash function
defined as SHAKE(M, d) where the output is a d-bits-long digest of
message M. When ECDSA is used with SHAKE128(M, d), it is RECOMMENDED
to replace HMAC(K, M) with KMAC128(K, M, d2, ""), where d2 = max(d,
qlen) and qlen is the binary length of the order of the base point of
the elliptic curve [RFC6979]. When ECDSA is used with SHAKE256(M,
d), it is RECOMMENDED to replace HMAC(K, M) with KMAC256(K, M, d2,
""), where d2 = max(d, qlen). [RFC8692] and [FIPS-186-5] define the
use of SHAKE128 with an output length of 256 bits and SHAKE256 with
an output length or 512 bits.
In new deployments, where side-channel and fault injection attacks
are a concern, EdDSA with additional randomness as specified in
Section 3 is RECOMMENDED.
5. Security Considerations
The constructions in this document follow the high-level approach in
[XEdDSA] to calculate the per-message secret number from the hash of
the private key and the message, but add additional randomness into
the calculation for greater resilience. This does not re-introduce
the strong security requirement of randomness needed by randomized
ECDSA [FIPS-186-5]. The randomness of Z need not be perfect but
SHALL be generated by a cryptographically secure pseudo random number
generator (CSPRNG) and SHALL be secret. Even if the same random
number Z is used to sign two different messages, the security will be
the same as deterministic ECDSA and EdDSA and an attacker will not be
able to compromise the private key with algebraic means as in fully
randomized ECDSA [FIPS-186-5]. With the construction specified in
this document, two signatures over two equal messages are different
which prevents information leakage in use cases where signatures but
not messages are public. The construction in this document place the
additional randomness before the message to align with randomized
hashing methods.
[SBBDS17] states that [XEdDSA] would not prevent their attack due to
insufficient mixing of the hashed private key with the additional
randomness. The construction in this document aims to mitigate fault
injection attacks that leverage determinism in deterministic ECDSA
and EdDSA signatures (see e.g., [ABFJLM17]), by randomizing nonce
generation. Fault injection attacks that achieve instruction
skipping as in e.g., Section 3.4 of [ABFJLM17] are not necessarily
stopped. It seems to be possible to, at the same time, also mitigate
attacks that use first order differential power analysis (DPA)
against the hash computation of deterministic nonces in EdDSA and
ECDSA (see e.g., [ABFJLM17][SBBDS17]). The mitigation in this
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document agrees with one mentioned in [ABFJLM17] and appears to be as
effective against the referenced first order DPA attacks as the one
in [SBBDS17]. The random bytes Z are re-used in step d and f of
Hedged ECDSA to align with HMAC_DRBG (see Section 3.3 of [RFC6979]).
This may make certain DPA attacks easier than if randomness had been
sampled fresh for each respective step. Note however that V is
updated between the steps and that the secret key x is processed in a
new input block of the hash function after processing V and Z in each
respective step.
Another countermeasure to fault attacks is to force the signer to
verify the signature in the last step of the signature generation or
to calculate the signature twice and compare the results. These
countermeasure would catch a single fault but would not protect
against attackers that are able to precisely inject faults several
times [RP17] [PSSLR17] [SB18]. Adding an additional sign or
verification operation would also significantly affect performance,
especially verification which is a heavier operation than signing in
ECDSA and EdDSA.
[ABFJLM17] suggests using both additional randomness and a counter,
which makes the signature generation stateful. While most used
signatures have traditionally been stateless, stateful signatures
like XMSS [RFC8391] and LMS [RFC8554] have now been standardized and
deployed. [RFC8937] specifies a PRNG construction with a random
seed, a secret key, a context string, and a nonce, which makes the
random number generation stateful. The generation of the per-message
secret number in this document is not stateful, but it can be used
with a stateful PRNG. The exact construction in [RFC8937] is however
not recommended in deployments where side-channel and fault injection
attacks are a concern as it relies on deterministic signatures.
With the construction in this document, the repetition of the same
per-message secret number for two different messages is highly
unlikely even with an imperfect random number generator, but not
impossible. As an extreme countermeasure, previously used secret
numbers can be tracked to ensure their uniqueness for a given key,
and a different random number can be used if a collision is detected.
This document neither mandates nor prohibits implementations from
taking such precautions.
Implementations need to follow best practices on how to protect
against all side-channel attacks, not just attacks that exploit
determinism, see for example [BSI].
The leading 0x00 octet in Hedged EdDSA provides domain separation
with RFC 8032 since the first octets of dom2 and dom4 are distinct
from 0x00. In the case of Ed25519, for which dom2 is the empty
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string, note that Ed25519 in RFC 8032 would have to contain the
prefix also in PH(M) to collide with any of the inputs to the hash
computations in the hedged variants in this document.
6. Test Vectors
TODO
6.1. Hedged Ed25519
MESSAGE = { }
SECRET KEY = { }
RANDOM DATA = { }
SIGNATURE = { }
6.2. Hedged ECDSA with P-256 and SHA-256
MESSAGE = { }
SECRET KEY = { }
RANDOM DATA = { }
SIGNATURE = { }
7. References
7.1. Normative References
[FIPS-186-5]
Department of Commerce, N. S., "Digital Signature Standard
(DSS)", NIST FIPS PUB 186-5 , February 2023,
<https://doi.org/10.6028/NIST.FIPS.186-5>.
[KMAC] National Institute of Standards and Technology (NIST),
"SHA-3 Derived Functions: cSHAKE, KMAC, TupleHash and
ParallelHash", NIST SP 800-185 , December 2016,
<http://nvlpubs.nist.gov/nistpubs/SpecialPublications/
NIST.SP.800-185.pdf>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/rfc/rfc2119>.
[RFC6979] Pornin, T., "Deterministic Usage of the Digital Signature
Algorithm (DSA) and Elliptic Curve Digital Signature
Algorithm (ECDSA)", RFC 6979, DOI 10.17487/RFC6979, August
2013, <https://www.rfc-editor.org/rfc/rfc6979>.
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[RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", RFC 8032,
DOI 10.17487/RFC8032, January 2017,
<https://www.rfc-editor.org/rfc/rfc8032>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/rfc/rfc8174>.
[RFC8692] Kampanakis, P. and Q. Dang, "Internet X.509 Public Key
Infrastructure: Additional Algorithm Identifiers for
RSASSA-PSS and ECDSA Using SHAKEs", RFC 8692,
DOI 10.17487/RFC8692, December 2019,
<https://www.rfc-editor.org/rfc/rfc8692>.
[SHA3] National Institute of Standards and Technology (NIST),
"SHA-3 Standard: Permutation-Based Hash and Extendable-
Output Functions", NIST FIPS PUB 202 , August 2015,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.202.pdf>.
7.2. Informative References
[ABFJLM17] Ambrose, C., Bos, J., Fay, B., Joye, M., Lochter, M., and
B. Murray, "Differential Attacks on Deterministic
Signatures", October 2017,
<https://eprint.iacr.org/2017/975>.
[AOTZ19] Aranha, D., Orlandi, C., Takahashi, A., and G. Zaverucha,
"Security of Hedged Fiat-Shamir Signatures under Fault
Attacks", September 2019,
<https://eprint.iacr.org/2019/956>.
[BCPST14] Batina, L., Chmielewski, L., Papachristodoulou, L.,
Schwabe, P., and M. Tunstall, "Online Template Attacks",
December 2014, <http://citeseerx.ist.psu.edu/viewdoc/
download?doi=10.1.1.854.7836&rep=rep1&type=pdf>.
[Bernstein14]
Bernstein, D., "How to design an elliptic-curve signature
system", March 2014,
<https://blog.cr.yp.to/20140323-ecdsa.html>.
[Bernstein19]
Bernstein, D., "Why EdDSA held up better than ECDSA
against Minerva", October 2019,
<https://blog.cr.yp.to/20191024-eddsa.html>.
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[BP16] Barenghi, A. and G. Pelosi, "A Note on Fault Attacks
Against Deterministic Signature Schemes (Short Paper)",
September 2016, <https://link.springer.com/
chapter/10.1007/978-3-319-44524-3_11>.
[BSI] Bundesamt für Sicherheit in der Informationstechnik,
"Minimum Requirements for Evaluating Side-Channel Attack
Resistance of Elliptic Curve Implementations", November
2016,
<https://www.bsi.bund.de/SharedDocs/Downloads/DE/BSI/
Zertifizierung/Interpretationen/
AIS_46_ECCGuide_e_pdf.pdf?__blob=publicationFile>.
[Cao20] Weiqiong Cao, Hongsong Shi, Hua Chen, Jiazhe Chen, Limin
Fan, and Wenling Wu, "Lattice-based Fault Attacks on
Deterministic Signature Schemes of ECDSA and EdDSA", June
2020, <https://eprint.iacr.org/2020/803>.
[Comments-186-5]
"Public Comments Received on Draft FIPS 186-5: Digital
Signature Standards (DSS)", March 2021,
<https://csrc.nist.gov/CSRC/media/Publications/fips/186/5/
draft/documents/fips-186-5-draft-comments-received.pdf>.
[Draft-204]
National Institute of Standards and Technology (NIST),
"FIPS PUB 204 (Draft)", August 2023,
<https://csrc.nist.gov/pubs/fips/204/ipd>.
[FG19] Fischlin, M. and F. Günther, "Modeling Memory Faults in
Signature and Encryption Schemes", September 2019,
<https://eprint.iacr.org/2019/1053>.
[I-D.irtf-cfrg-frost]
Connolly, D., Komlo, C., Goldberg, I., and C. A. Wood,
"Two-Round Threshold Schnorr Signatures with FROST", Work
in Progress, Internet-Draft, draft-irtf-cfrg-frost-15, 18
September 2023, <https://datatracker.ietf.org/doc/html/
draft-irtf-cfrg-frost-15>.
[Kampanakis16]
Kampanakis, P., "FIPS and Deterministic ECDSA: Achieving
robust security and conformance", December 2016,
<https://blogs.cisco.com/security/fips-and-deterministic-
ecdsa-achieving-robust-security-and-conformance>.
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[Langley13]
Langley, A., "Sudden Death Entropy Failures", June 2013,
<https://www.imperialviolet.org/2013/06/15/
suddendeathentropy.html>.
[libHydrogen]
"The Hydrogen library", n.d.,
<https://github.com/jedisct1/libhydrogen>.
[libSodium]
"The Sodium library", n.d.,
<https://github.com/jedisct1/libsodium>.
[Minerva19]
Centre for Research on Cryptography and Security (CRoCS),
"Minerva", October 2019,
<https://minerva.crocs.fi.muni.cz/>.
[Notice-186-5]
National Institute of Standards and Technology (NIST),
"Request for Comments on FIPS 186-5 and SP 800-186",
October 2019, <https://www.federalregister.gov/
documents/2019/10/31/2019-23742/request-for-comments-on-
fips-186-5-and-sp-800-186>.
[OpenSSL13a]
"Add secure DSA nonce flag", n.d.,
<https://github.com/openssl/openssl/
commit/8a99cb29d1f0013243a532bccc1dc70ed678eebe>.
[OpenSSL13b]
"Make `safe' (EC)DSA nonces the default", n.d.,
<https://github.com/openssl/openssl/
commit/190c615d4398cc6c8b61eb7881d7409314529a75>.
[Plundervolt19]
Murdock, K., Oswald, D., Garcia, F., Van Bulck, J., Gruss,
D., and F. Piessens, "How a little bit of undervolting can
cause a lot of problems", December 2019,
<https://plundervolt.com/>.
[PSSLR17] Poddebniak, D., Somorovsky, J., Schinzel, S., Lochter, M.,
and P. Rösler, "Attacking Deterministic Signature Schemes
using Fault Attacks", October 2017,
<https://eprint.iacr.org/2017/1014>.
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[RFC8037] Liusvaara, I., "CFRG Elliptic Curve Diffie-Hellman (ECDH)
and Signatures in JSON Object Signing and Encryption
(JOSE)", RFC 8037, DOI 10.17487/RFC8037, January 2017,
<https://www.rfc-editor.org/rfc/rfc8037>.
[RFC8080] Sury, O. and R. Edmonds, "Edwards-Curve Digital Security
Algorithm (EdDSA) for DNSSEC", RFC 8080,
DOI 10.17487/RFC8080, February 2017,
<https://www.rfc-editor.org/rfc/rfc8080>.
[RFC8225] Wendt, C. and J. Peterson, "PASSporT: Personal Assertion
Token", RFC 8225, DOI 10.17487/RFC8225, February 2018,
<https://www.rfc-editor.org/rfc/rfc8225>.
[RFC8387] Sethi, M., Arkko, J., Keranen, A., and H. Back, "Practical
Considerations and Implementation Experiences in Securing
Smart Object Networks", RFC 8387, DOI 10.17487/RFC8387,
May 2018, <https://www.rfc-editor.org/rfc/rfc8387>.
[RFC8391] Huelsing, A., Butin, D., Gazdag, S., Rijneveld, J., and A.
Mohaisen, "XMSS: eXtended Merkle Signature Scheme",
RFC 8391, DOI 10.17487/RFC8391, May 2018,
<https://www.rfc-editor.org/rfc/rfc8391>.
[RFC8410] Josefsson, S. and J. Schaad, "Algorithm Identifiers for
Ed25519, Ed448, X25519, and X448 for Use in the Internet
X.509 Public Key Infrastructure", RFC 8410,
DOI 10.17487/RFC8410, August 2018,
<https://www.rfc-editor.org/rfc/rfc8410>.
[RFC8411] Schaad, J. and R. Andrews, "IANA Registration for the
Cryptographic Algorithm Object Identifier Range",
RFC 8411, DOI 10.17487/RFC8411, August 2018,
<https://www.rfc-editor.org/rfc/rfc8411>.
[RFC8419] Housley, R., "Use of Edwards-Curve Digital Signature
Algorithm (EdDSA) Signatures in the Cryptographic Message
Syntax (CMS)", RFC 8419, DOI 10.17487/RFC8419, August
2018, <https://www.rfc-editor.org/rfc/rfc8419>.
[RFC8420] Nir, Y., "Using the Edwards-Curve Digital Signature
Algorithm (EdDSA) in the Internet Key Exchange Protocol
Version 2 (IKEv2)", RFC 8420, DOI 10.17487/RFC8420, August
2018, <https://www.rfc-editor.org/rfc/rfc8420>.
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[RFC8422] Nir, Y., Josefsson, S., and M. Pegourie-Gonnard, "Elliptic
Curve Cryptography (ECC) Cipher Suites for Transport Layer
Security (TLS) Versions 1.2 and Earlier", RFC 8422,
DOI 10.17487/RFC8422, August 2018,
<https://www.rfc-editor.org/rfc/rfc8422>.
[RFC8446] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
<https://www.rfc-editor.org/rfc/rfc8446>.
[RFC8463] Levine, J., "A New Cryptographic Signature Method for
DomainKeys Identified Mail (DKIM)", RFC 8463,
DOI 10.17487/RFC8463, September 2018,
<https://www.rfc-editor.org/rfc/rfc8463>.
[RFC8550] Schaad, J., Ramsdell, B., and S. Turner, "Secure/
Multipurpose Internet Mail Extensions (S/MIME) Version 4.0
Certificate Handling", RFC 8550, DOI 10.17487/RFC8550,
April 2019, <https://www.rfc-editor.org/rfc/rfc8550>.
[RFC8554] McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali
Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554,
April 2019, <https://www.rfc-editor.org/rfc/rfc8554>.
[RFC8591] Campbell, B. and R. Housley, "SIP-Based Messaging with S/
MIME", RFC 8591, DOI 10.17487/RFC8591, April 2019,
<https://www.rfc-editor.org/rfc/rfc8591>.
[RFC8608] Turner, S. and O. Borchert, "BGPsec Algorithms, Key
Formats, and Signature Formats", RFC 8608,
DOI 10.17487/RFC8608, June 2019,
<https://www.rfc-editor.org/rfc/rfc8608>.
[RFC8624] Wouters, P. and O. Sury, "Algorithm Implementation
Requirements and Usage Guidance for DNSSEC", RFC 8624,
DOI 10.17487/RFC8624, June 2019,
<https://www.rfc-editor.org/rfc/rfc8624>.
[RFC8937] Cremers, C., Garratt, L., Smyshlyaev, S., Sullivan, N.,
and C. Wood, "Randomness Improvements for Security
Protocols", RFC 8937, DOI 10.17487/RFC8937, October 2020,
<https://www.rfc-editor.org/rfc/rfc8937>.
[RFC9053] Schaad, J., "CBOR Object Signing and Encryption (COSE):
Initial Algorithms", RFC 9053, DOI 10.17487/RFC9053,
August 2022, <https://www.rfc-editor.org/rfc/rfc9053>.
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[RowHammer14]
Kim, Y., Daly, R., Kim, J., Fallin, C., Lee, J., Lee, D.,
Wilkerson, C., and K. Mutlu, "Flipping Bits in Memory
Without Accessing Them: An Experimental Study of DRAM
Disturbance Errors", June 2014,
<https://users.ece.cmu.edu/~yoonguk/papers/kim-
isca14.pdf>.
[RP17] Romailler, Y. and S. Pelissier, "Practical fault attack
against the Ed25519 and EdDSA signature schemes",
September 2017,
<https://romailler.ch/ddl/10.1109_FDTC.2017.12_eddsa.pdf>.
[SB18] Samwel, N. and L. Batina, "Practical Fault Injection on
Deterministic Signatures: The Case of EdDSA", April 2018,
<https://nielssamwel.nl/papers/africacrypt2018_fault.pdf>.
[SBBDS17] Samwel, N., Batina, L., Bertoni, G., Daemen, J., and R.
Susella, "Breaking Ed25519 in WolfSSL", October 2017,
<https://eprint.iacr.org/2017/985.pdf>.
[SH16] Seuschek, H., Heyszl, J., and F. De Santis, "A Cautionary
Note: Side-Channel Leakage Implications of Deterministic
Signature Schemes", January 2016,
<http://www.cs2.deib.polimi.it/
slides_16/01_Seuschek_Deterministic_Signatures.pdf>.
[SideChannel]
Spreitzer, R., Moonsamy, V., Korak, T., and S. Mangard,
"Systematic Classification of Side-Channel Attacks: A Case
Study for Mobile Devices", December 2017,
<https://arxiv.org/pdf/1611.03748.pdf>.
[TPM-Fail19]
Moghimi, D., Sunar, B., Eisenbarth, T., and N. Heninge,
"TPM-FAIL: TPM meets Timing and Lattice Attacks", October
2019, <https://tpm.fail/>.
[WPB19] Weissbart, L., Picek, S., and L. Batina, "One trace is all
it takes: Machine Learning-based Side-channel Attack on
EdDSA", July 2019, <https://eprint.iacr.org/2019/358.pdf>.
[XEdDSA] Signal, "The XEdDSA and VXEdDSA Signature Schemes",
October 2016,
<https://signal.org/docs/specifications/xeddsa/>.
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Change log
This section is to be removed before publishing as an RFC.
Changes from -02 to -03:
* Same randomness Z in step d and f to align with HMAC_DRBG.
* Changed Hedged EdDSA order to 0x00 || Z || dom2(F, C) instead of
dom2(F, C) || Z. This avoids collisions with RFC 8032 and aligns
with Bernstein's recommendation to put Z before the context.
* Changed KMAC output length recommendations to avoid multiple
invocations.
* Updates some text to align with the hedged signatures/signing
terminology.
* Added more description about the construction.
* Editorial changes.
Changes from -01 to -02:
* Different names Zd and Zf for the randomness in ECDSA.
* Added empty test vector section as TODO.
Changes from -00 to -01:
* Changed terminology to hedged signatures/signing.
* Added reference to the FIPS 204 (ML-DSA) where hedged signatures
are the default.
* Added a second 000... padding that separates the context from the
prefix, aligning with BSI recommendations.
* Added note that Z in step f is not reused from step d.
* Added note on "internal octet" is 0x01 from RFC 6979.
* Removed incorrect statement that context fit in first block.
* Added more description about the construction.
* Moved "For discussion" section to GitHub issue.
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* Editorial changes.
Acknowledgments
The authors would like to thank Tony Arcieri, Uri Blumenthal, Carsten
Bormann, Taylor R Campbell, Quynh Dang, Håkan Englund, Janos Follath,
Phillip Hallam-Baker, Chelsea Komlo, Niklas Lindskog, Ilari
Liusvaara, Danny Niu, Jim Schaad, and Ruggero Susella for their
valuable comments and feedback.
Authors' Addresses
John Preuß Mattsson
Ericsson
Email: john.mattsson@ericsson.com
Erik Thormarker
Ericsson
Email: erik.thormarker@ericsson.com
Sini Ruohomaa
Ericsson
Email: sini.ruohomaa@ericsson.com
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