]> Ericsson

john.mattsson@ericsson.com

Ericsson

erik.thormarker@ericsson.com

Ericsson

sini.ruohomaa@ericsson.com

IRTF Crypto Forum next generation unicorn sparkling distributed ledger 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 The latest revision of this draft can be found at . Status information for this document may be found at . Discussion of this document takes place on the Crypto Forum Research Group mailing list (), which is archived at . Subscribe at . Source for this draft and an issue tracker can be found at .

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., ). Repeated per-message secret numbers have caused several severe security accidents in practice. As stated in , the need for a cryptographically secure source of randomness is also a hindrance to deployment of randomized ECDSA in architectures where secure random number generation is challenging, in particular, embedded IoT systems and smartcards. 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) and Edwards-curve Digital Signature Algorithm (EdDSA) , 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 . 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 . It has been demonstrated how side-channel attacks such as power analysis and timing attacks allow for practical recovery of the private key in some existing implementations of randomized ECDSA. 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 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 , deterministic signatures like and might help an attacker to reduce the noise in the side-channel when the same message it signed multiple times. Recent research 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 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 . See also the discussions and references in . Fault attacks may also be possible without physical access to the device. RowHammer showed how an attacker to induce DRAM bit-flips in memory areas the attacker should not have access to. Plundervolt 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 . Government agencies are clearly concerned about these attacks. In and , 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 under standardization by NIST uses hedged signing by default. BSI has published and researchers from BSI have co-authored two research papers 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 . One countermeasure to entropy failures, side-channel attacks, and fault injection attacks recommended by and implemented in 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 . describes an alternative 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. 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 and 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 , and implementations can be tested against them.

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 when, and only when, they appear in all capitals, as shown here.

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 : 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 :

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 : When ECDSA is used with SHAKE the HMAC construction above MAY be used but it is RECOMMENDED to use the more efficient KMAC construction . 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 . 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). and 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 is RECOMMENDED.

Security Considerations The constructions in this document follow the high-level approach in 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 . 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 . 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. states that 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., ), by randomizing nonce generation. Fault injection attacks that achieve instruction skipping as in e.g., Section 3.4 of 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., ). The mitigation in this document agrees with one mentioned in and appears to be as effective against the referenced first order DPA attacks as the one in . 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 ). 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 . 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. 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 and LMS have now been standardized and deployed. 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 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 . 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 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.

Test Vectors TODO

Hedged Ed25519

Hedged ECDSA with P-256 and SHA-256

References Normative References In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. This document defines a deterministic digital signature generation procedure. Such signatures are compatible with standard Digital Signature Algorithm (DSA) and Elliptic Curve Digital Signature Algorithm (ECDSA) digital signatures and can be processed with unmodified verifiers, which need not be aware of the procedure described therein. Deterministic signatures retain the cryptographic security features associated with digital signatures but can be more easily implemented in various environments, since they do not need access to a source of high-quality randomness. This document describes elliptic curve signature scheme Edwards-curve Digital Signature Algorithm (EdDSA). The algorithm is instantiated with recommended parameters for the edwards25519 and edwards448 curves. An example implementation and test vectors are provided. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. Digital signatures are used to sign messages, X.509 certificates, and Certificate Revocation Lists (CRLs). This document updates the "Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile" (RFC 3279) and describes the conventions for using the SHAKE function family in Internet X.509 certificates and revocation lists as one-way hash functions with the RSA Probabilistic signature and Elliptic Curve Digital Signature Algorithm (ECDSA) signature algorithms. The conventions for the associated subject public keys are also described. Informative References Randomness is a crucial ingredient for Transport Layer Security (TLS) and related security protocols. Weak or predictable "cryptographically secure" pseudorandom number generators (CSPRNGs) can be abused or exploited for malicious purposes. An initial entropy source that seeds a CSPRNG might be weak or broken as well, which can also lead to critical and systemic security problems. This document describes a way for security protocol implementations to augment their CSPRNGs using long-term private keys. This improves randomness from broken or otherwise subverted CSPRNGs. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. Zcash Foundation University of Waterloo, Zcash Foundation University of Waterloo Cloudflare This document specifies the Flexible Round-Optimized Schnorr Threshold (FROST) signing protocol. FROST signatures can be issued after a threshold number of entities cooperate to compute a signature, allowing for improved distribution of trust and redundancy with respect to a secret key. FROST depends only on a prime-order group and cryptographic hash function. This document specifies a number of ciphersuites to instantiate FROST using different prime- order groups and hash functions. One such ciphersuite can be used to produce signatures that can be verified with an Edwards-Curve Digital Signature Algorithm (EdDSA, as defined in RFC8032) compliant verifier. However, unlike EdDSA, the signatures produced by FROST are not deterministic. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. n.d. n.d. n.d. n.d. This document defines how to use the Diffie-Hellman algorithms "X25519" and "X448" as well as the signature algorithms "Ed25519" and "Ed448" from the IRTF CFRG elliptic curves work in JSON Object Signing and Encryption (JOSE). This document describes how to specify Edwards-curve Digital Security Algorithm (EdDSA) keys and signatures in DNS Security (DNSSEC). It uses EdDSA with the choice of two curves: Ed25519 and Ed448. This document defines a method for creating and validating a token that cryptographically verifies an originating identity or, more generally, a URI or telephone number representing the originator of personal communications. The Personal Assertion Token, PASSporT, is cryptographically signed to protect the integrity of the identity of the originator and to verify the assertion of the identity information at the destination. The cryptographic signature is defined with the intention that it can confidently verify the originating persona even when the signature is sent to the destination party over an insecure channel. PASSporT is particularly useful for many personal-communications applications over IP networks and other multi-hop interconnection scenarios where the originating and destination parties may not have a direct trusted relationship. This memo describes challenges associated with securing resource- constrained smart object devices. The memo describes a possible deployment model where resource-constrained devices sign message objects, discusses the availability of cryptographic libraries for resource-constrained devices, and presents some preliminary experiences with those libraries for message signing on resource- constrained devices. Lastly, the memo discusses trade-offs involving different types of security approaches. This note describes the eXtended Merkle Signature Scheme (XMSS), a hash-based digital signature system that is based on existing descriptions in scientific literature. This note specifies Winternitz One-Time Signature Plus (WOTS+), a one-time signature scheme; XMSS, a single-tree scheme; and XMSS^MT, a multi-tree variant of XMSS. Both XMSS and XMSS^MT use WOTS+ as a main building block. XMSS provides cryptographic digital signatures without relying on the conjectured hardness of mathematical problems. Instead, it is proven that it only relies on the properties of cryptographic hash functions. XMSS provides strong security guarantees and is even secure when the collision resistance of the underlying hash function is broken. It is suitable for compact implementations, is relatively simple to implement, and naturally resists side-channel attacks. Unlike most other signature systems, hash-based signatures can so far withstand known attacks using quantum computers. This document specifies algorithm identifiers and ASN.1 encoding formats for elliptic curve constructs using the curve25519 and curve448 curves. The signature algorithms covered are Ed25519 and Ed448. The key agreement algorithms covered are X25519 and X448. The encoding for public key, private key, and Edwards-curve Digital Signature Algorithm (EdDSA) structures is provided. When the Curdle Security Working Group was chartered, a range of object identifiers was donated by DigiCert, Inc. for the purpose of registering the Edwards Elliptic Curve key agreement and signature algorithms. This donated set of OIDs allowed for shorter values than would be possible using the existing S/MIME or PKIX arcs. This document describes the donated range and the identifiers that were assigned from that range, transfers control of that range to IANA, and establishes IANA allocation policies for any future assignments within that range. This document specifies the conventions for using the Edwards-curve Digital Signature Algorithm (EdDSA) for curve25519 and curve448 in the Cryptographic Message Syntax (CMS). For each curve, EdDSA defines the PureEdDSA and HashEdDSA modes. However, the HashEdDSA mode is not used with the CMS. In addition, no context string is used with the CMS. This document describes the use of the Edwards-curve Digital Signature Algorithm (EdDSA) in the Internet Key Exchange Protocol Version 2 (IKEv2). This document describes key exchange algorithms based on Elliptic Curve Cryptography (ECC) for the Transport Layer Security (TLS) protocol. In particular, it specifies the use of Ephemeral Elliptic Curve Diffie-Hellman (ECDHE) key agreement in a TLS handshake and the use of the Elliptic Curve Digital Signature Algorithm (ECDSA) and Edwards-curve Digital Signature Algorithm (EdDSA) as authentication mechanisms. This document obsoletes RFC 4492. This document specifies version 1.3 of the Transport Layer Security (TLS) protocol. TLS allows client/server applications to communicate over the Internet in a way that is designed to prevent eavesdropping, tampering, and message forgery. This document updates RFCs 5705 and 6066, and obsoletes RFCs 5077, 5246, and 6961. This document also specifies new requirements for TLS 1.2 implementations. This document adds a new signing algorithm, Ed25519-SHA256, to "DomainKeys Identified Mail (DKIM) Signatures" (RFC 6376). DKIM verifiers are required to implement this algorithm. This document specifies conventions for X.509 certificate usage by Secure/Multipurpose Internet Mail Extensions (S/MIME) v4.0 agents. S/MIME provides a method to send and receive secure MIME messages, and certificates are an integral part of S/MIME agent processing. S/MIME agents validate certificates as described in RFC 5280 ("Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile"). S/MIME agents must meet the certificate-processing requirements in this document as well as those in RFC 5280. This document obsoletes RFC 5750. Mobile messaging applications used with the Session Initiation Protocol (SIP) commonly use some combination of the SIP MESSAGE method and the Message Session Relay Protocol (MSRP). While these provide mechanisms for hop-by-hop security, neither natively provides end-to-end protection. This document offers guidance on how to provide end-to-end authentication, integrity protection, and confidentiality using the Secure/Multipurpose Internet Mail Extensions (S/MIME). It updates and provides clarifications for RFCs 3261, 3428, and 4975. This document specifies the algorithms, algorithm parameters, asymmetric key formats, asymmetric key sizes, and signature formats used in BGPsec (Border Gateway Protocol Security). This document updates RFC 7935 ("The Profile for Algorithms and Key Sizes for Use in the Resource Public Key Infrastructure") and obsoletes RFC 8208 ("BGPsec Algorithms, Key Formats, and Signature Formats") by adding Documentation and Experimentation Algorithm IDs, correcting the range of unassigned algorithms IDs to fill the complete range, and restructuring the document for better reading. This document also includes example BGPsec UPDATE messages as well as the private keys used to generate the messages and the certificates necessary to validate those signatures. The DNSSEC protocol makes use of various cryptographic algorithms in order to provide authentication of DNS data and proof of nonexistence. To ensure interoperability between DNS resolvers and DNS authoritative servers, it is necessary to specify a set of algorithm implementation requirements and usage guidelines to ensure that there is at least one algorithm that all implementations support. This document defines the current algorithm implementation requirements and usage guidance for DNSSEC. This document obsoletes RFC 6944. This note describes a digital-signature system based on cryptographic hash functions, following the seminal work in this area of Lamport, Diffie, Winternitz, and Merkle, as adapted by Leighton and Micali in 1995. It specifies a one-time signature scheme and a general signature scheme. These systems provide asymmetric authentication without using large integer mathematics and can achieve a high security level. They are suitable for compact implementations, are relatively simple to implement, and are naturally resistant to side-channel attacks. Unlike many other signature systems, hash-based signatures would still be secure even if it proves feasible for an attacker to build a quantum computer. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. This has been reviewed by many researchers, both in the research group and outside of it. The Acknowledgements section lists many of them. Concise Binary Object Representation (CBOR) is a data format designed for small code size and small message size. There is a need to be able to define basic security services for this data format. This document defines a set of algorithms that can be used with the CBOR Object Signing and Encryption (COSE) protocol (RFC 9052). This document, along with RFC 9052, obsoletes RFC 8152.

Change log 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.
• Editorial changes.

Acknowledgments The authors would like to thank , , , , , , , , , , , , , and for their valuable comments and feedback.