Content deleted Content added
Rescuing 1 sources and tagging 0 as dead.) #IABot (v2.0.9.5 |
|||
| (103 intermediate revisions by 40 users not shown) | |||
Line 1:
{{Short description|Concept in cryptography}}
'''Hash-based cryptography''' is the generic term for constructions of [[cryptographic primitive]]s based on the security of [[hash function]]s. It is of interest as a type of [[post-quantum cryptography]].
So far, hash-based cryptography is used to construct [[digital signature]]s schemes such as the [[Merkle signature scheme]], zero knowledge and computationally integrity proofs, such as the zk-STARK<ref name="bensasson2018">Ben-Sasson, Eli and Bentov, Iddo and Horesh, Yinon and Riabzev, Michael, 2018. [https://eprint.iacr.org/2018/046 Scalable, transparent, and post-quantum secure computational integrity].</ref> proof system and range proofs over issued credentials via the HashWires<ref name="kchalkias2021">{{Cite journal |last1=Chalkias |first1=Konstantinos |last2=Cohen |first2=Shir |last3=Lewi |first3=Kevin |last4=Moezinia |first4=Fredric |last5=Romailler |first5=Yolan |year=2021 |title=HashWires: Hyperefficient Credential-Based Range Proofs |url=https://eprint.iacr.org/2021/297 |journal=Privacy Enhancing Technologies Symposium (PETS) 2021}}</ref> protocol. Hash-based signature schemes combine a one-time signature scheme, such as a [[Lamport signature]], with a [[Merkle tree]] structure. Since a one-time signature scheme key can only sign a single message securely, it is practical to combine many such keys within a single, larger structure. A Merkle tree structure is used to this end. In this hierarchical data structure, a hash function and concatenation are used repeatedly to compute tree nodes.
==History==▼
[[Ralph Merkle]] invented hash-based signatures in 1979. The XMSS (eXtended Merkle Signature Scheme)<ref name="BuchmannDahmen2011">{{cite journal|last1=Buchmann|first1=Johannes|last2=Dahmen|first2=Erik|last3=Hülsing|first3=Andreas|title=XMSS - A Practical Forward Secure Signature Scheme Based on Minimal Security Assumptions|series=Lecture Notes in Computer Science|publisher=Springer Berlin Heidelberg|volume=7071|pages=117–129|year=2011|issn=0302-9743|doi=10.1007/978-3-642-25405-5_8}}</ref> and SPHINCS<ref>{{Cite book|url=http://link.springer.com/chapter/10.1007/978-3-662-46800-5_15|title=Advances in Cryptology -- EUROCRYPT 2015|last=Bernstein|first=Daniel J.|last2=Hopwood|first2=Daira|last3=Hülsing|first3=Andreas|last4=Lange|first4=Tanja|last5=Niederhagen|first5=Ruben|last6=Papachristodoulou|first6=Louiza|last7=Schneider|first7=Michael|last8=Schwabe|first8=Peter|last9=Wilcox-O’Hearn|first9=Zooko|year=2015|publisher=Springer Berlin Heidelberg|isbn=9783662467992|editor-last=Oswald|editor-first=Elisabeth|series=Lecture Notes in Computer Science|volume=9056|pages=368–397|language=en|doi=10.1007/978-3-662-46800-5_15|editor-last2=Fischlin|editor-first2=Marc}}</ref> hash-based signature schemes were introduced in 2011 and 2015, respectively. XMSS is based both on Merkle's seminal scheme and on the 2007 Generalized Merkle Signature Scheme (GMSS)<ref>{{cite journal|last1=Buchmann|first1=Johannes|last2=Dahmen|first2=Erik|last3=Klintsevich|first3=Elena|last4=Okeya|first4=Katsuyuki|last5=Vuillaume|first5=Camille|title=Merkle Signatures with Virtually Unlimited Signature Capacity|journal=Lecture Notes in Computer Science|date=2007|volume=4521|issue=Applied Cryptography and Network Security|pages=31–45|doi=10.1007/978-3-540-72738-5_3|url=https://link.springer.com/chapter/10.1007/978-3-540-72738-5_3|publisher=Springer, Berlin, Heidelberg|language=en}}</ref>. A multi-tree variant of XMSS, XMSS<sup>''MT''</sup>, was described in 2013.<ref>{{cite journal|last1=Hülsing|first1=Andreas|last2=Rausch|first2=Lea|last3=Buchmann|first3=Johannes|title=Optimal Parameters for XMSSMT|journal=Lecture Notes in Computer Science|date=2013|volume=8128|issue=Security Engineering and Intelligence Informatics|page=194-208|doi=10.1007/978-3-642-40588-4_14|url=https://link.springer.com/chapter/10.1007/978-3-642-40588-4_14|publisher=Springer, Berlin, Heidelberg|language=en}}</ref>▼
One consideration with hash-based signature schemes is that they can only sign a limited number of messages securely, because of their use of one-time signature schemes. The US [[National Institute of Standards and Technology]] (NIST), specified that algorithms in its [[post-quantum cryptography]] competition support a minimum of 2{{Superscript|64}} signatures safely.<ref>{{Cite web |title=Submission Requirements and Evaluation Criteria for the Post-Quantum Cryptography Standardization Process |url=https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/call-for-proposals-final-dec-2016.pdf |website=NIST CSRC}}</ref>
==Properties of hash-based signature schemes==▼
NIST standardized stateful hash-based cryptography based on the [[eXtended Merkle Signature Scheme]] (XMSS) and [[Leighton–Micali Signatures]] (LMS),<ref name="rfc8554" /> which are applicable in different circumstances, in 2020, but noted that the requirement to maintain state when using them makes them more difficult to implement in a way that avoids misuse.<ref>{{Cite web |last=Computer Security Division |first=Information Technology Laboratory |date=2019-02-01 |title=Request for Public Comments on Stateful HBS {{!}} CSRC |url=https://csrc.nist.gov/news/2019/stateful-hbs-request-for-public-comments |access-date=2019-02-04 |website=CSRC {{!}} NIST |language=EN-US}}</ref><ref>{{Cite journal |last1=Alagic |first1=Gorjan |last2=Apon |first2=Daniel |last3=Cooper |first3=David |last4=Dang |first4=Quynh |last5=Dang |first5=Thinh |last6=Kelsey |first6=John |last7=Lichtinger |first7=Jacob |last8=Miller |first8=Carl |last9=Moody |first9=Dustin |last10=Peralta |first10=Rene |last11=Perlner |first11=Ray |date=2022-07-05 |title=Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process |url=https://csrc.nist.gov/publications/detail/nistir/8413/final |journal=NIST Ir 8413 |language=en |doi=10.6028/NIST.IR.8413-upd1|doi-access=free }}</ref><ref>{{Cite journal |last1=Cooper |first1=David |last2=Apon |first2=Daniel |last3=Dang |first3=Quynh |last4=Davidson |first4=Michael |last5=Dworkin |first5=Morris |last6=Miller |first6=Carl |date=2020-10-29 |title=Recommendation for Stateful Hash-Based Signature Schemes |url=https://csrc.nist.gov/publications/detail/sp/800-208/final |journal=NIST Special Publication 800-208 |language=en |doi=10.6028/NIST.SP.800-208}}</ref>
In 2022, NIST announced [[SPHINCS+]] as one of three algorithms to be standardized for digital signatures.<ref>{{Cite web |date=2022-07-05 |title=NIST announces four quantum-resistant algorithms |url=https://venturebeat.com/2022/07/05/nist-post-quantum-cryptography-standard/ |access-date=2022-07-10 |website=VentureBeat |language=en-US}}</ref> and in 2024 NIST announced the Stateless Hash-Based Digital Signature Standard (SLH-DSA)<ref>{{Cite journal |date=August 2024 |title=Stateless Hash-Based Digital Signature Standard |url=https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.205.pdf |website=[[NIST.gov]] |doi=10.6028/NIST.FIPS.205}}</ref> based on SPHINCS+.
▲== History ==
▲[[
Hash-based signature schemes use one-time signature schemes as their building block. A given one-time signing key can only be used to sign a single message securely. Indeed, signatures reveal part of the signing key. The security of (hash-based) one-time signature schemes relies exclusively on the security of an underlying hash function.
Commonly used one-time signature schemes include the [[Lamport signatures|Lamport–Diffie scheme]], the Winternitz scheme<ref>{{Cite book |last1=Dods |first1=C. |title=Cryptography and Coding |last2=Smart |first2=N. P. |last3=Stam |first3=M. |date=2005 |isbn=978-3-540-30276-6 |series=Lecture Notes in Computer Science |volume=3796 |pages=96–115 |language=en |chapter=Hash Based Digital Signature Schemes |doi=10.1007/11586821_8}}</ref> and its improvements, such as the W-OTS<sup>+</sup> scheme.<ref name="wotsplus">{{Cite book |last=Hülsing |first=Andreas |title=Progress in Cryptology – AFRICACRYPT 2013 |date=2013 |isbn=978-3-642-38552-0 |series=Lecture Notes in Computer Science |volume=7918 |pages=173–188 |chapter=W-OTS+ – Shorter Signatures for Hash-Based Signature Schemes |doi=10.1007/978-3-642-38553-7_10}}</ref> Unlike the seminal Lamport–Diffie scheme, the Winternitz scheme and variants can sign many bits at once. The number of bits to be signed at once is determined by a value: the Winternitz parameter. The existence of this parameter provides a trade-off between size and speed. Large values of the Winternitz parameter yield short signatures and keys, at the price of slower signing and verifying. In practice, a typical value for this parameter is 16.
In the case of stateless hash-based signatures, few-time signature schemes are used. Such schemes allow security to decrease gradually in case a few-time key is used more than once. HORST is an example of a few-time signature scheme.
== Combining many one-time key pairs into a hash-based signature scheme ==
The central idea of hash-based signature schemes is to combine a larger number of one-time key pairs into a single structure to obtain a practical way of signing more than once (yet a limited number of times). This is done using a Merkle tree structure, with possible variations. One public and one private key are constructed from the numerous public and private keys of the underlying one-time scheme. The global public key is the single node at the very top of the Merkle tree. Its value is an output of the selected hash function, so a typical public key size is 32 bytes. The validity of this global public key is related to the validity of a given one-time public key using a sequence of tree nodes. This sequence is called the authentication path. It is stored as part of the signature, and allows a verifier to reconstruct the node path between those two public keys.
The global private key is generally handled using a pseudo-random number generator. It is then sufficient to store a seed value. One-time secret keys are derived successively from the seed value using the generator. With this approach, the global private key is also very small, e.g. typically 32 bytes.
The problem of tree traversal is critical to signing performance. Increasingly efficient approaches have been introduced, dramatically speeding up signing time.
Some hash-based signature schemes use multiple layers of tree, offering faster signing at the price of larger signatures. In such schemes, only the lowest layer of trees is used to sign messages, while all other trees sign root values of lower trees.
▲== Properties of hash-based signature schemes ==
Hash-based signature schemes rely on security assumptions about the underlying hash function, but any hash function fulfilling these assumptions can be used. As a consequence, each adequate hash function yields a different corresponding hash-based signature scheme. Even if a given hash function becomes insecure, it is sufficient to replace it by a different, secure one to obtain a secure instantiation of the hash-based signature scheme under consideration. Some hash-based signature schemes (such as XMSS with pseudorandom key generation) are forward secure, meaning that previous signatures remain valid if a secret key is compromised.
The minimality of security assumptions is another characteristic of hash-based signature schemes. Generally, these schemes only require a secure (for instance in the sense of [[Preimage attack|second preimage resistance]]) cryptographic hash function to guarantee the overall security of the scheme. This kind of assumption is necessary for any digital signature scheme; however, other signature schemes require additional [[Computational hardness assumption|security assumptions]], which is not the case here.
Because of their reliance on an underlying one-time signature scheme, hash-based signature schemes can only sign a fixed amount of messages securely. In the case of the Merkle and XMSS schemes, a maximum of <math>2^h</math> messages can be signed securely, with <math>h</math> the total Merkle tree height.▼
▲Because of their reliance on an underlying one-time signature scheme, hash-based signature schemes can only sign a fixed
▲==Examples of hash-based signature schemes==
In addition to Merkle's seminal scheme, more recent hash-based signature schemes include the XMSS scheme, the Leighton-Micali (LMS) and the SPHINCS scheme. Most hash-based signature schemes are [[State (computer science)|stateful]], meaning that signing requires updating the secret key, unlike conventional digital signature schemes. For stateful hash-based signature schemes, signing requires keeping state of the used one-time keys and making sure they are never reused. The XMSS and LMS schemes are stateful, while the SPHINCS scheme is stateless. SPHINCS signatures are larger than XMSS and LMS signatures. Additionally to the WOTS+ one-time signature scheme, SPHINCS also uses a few-time (hash-based) signature scheme called HORST. HORST is an improvement of an older few-time signature scheme, HORS (Hash to Obtain Random Subset).<ref>{{cite journal|last1=Reyzin|first1=Leonid|last2=Reyzin|first2=Natan|title=Better than BiBa: Short One-Time Signatures with Fast Signing and Verifying|journal=Lecture Notes in Computer Science|date=2002|volume=2384|issue=Information Security and Privacy|page=144-153|doi=10.1007/3-540-45450-0_11|url=https://link.springer.com/chapter/10.1007/3-540-45450-0_11|publisher=Springer, Berlin, Heidelberg|language=en}}</ref> ▼
== Examples of hash-based signature schemes ==
Two [[Internet Research Task Force|IRTF]] [[Internet Draft]]s on stateful hash-based schemes (XMSS/XMSS<sup>''MT''</sup> and LMS) are currently active.<ref>{{cite web|last1=Hülsing|first1=Andreas|last2=Butin|first2=Denis|last3=Gazdag|first3=Stefan|last4=Mohaisen|first4=Aziz|title=draft-irtf-cfrg-xmss-hash-based-signatures-09 - XMSS: Extended Hash-Based Signatures|url=https://datatracker.ietf.org/doc/draft-irtf-cfrg-xmss-hash-based-signatures/|website=datatracker.ietf.org|publisher=IETF|language=en}}</ref><ref>{{cite web|last1=McGrew|first1=David|last2=Curcio|first2=Michael|last3=Fluhrer|first3=Scott|title=draft-mcgrew-hash-sigs-06 - Hash-Based Signatures|url=https://datatracker.ietf.org/doc/draft-mcgrew-hash-sigs/|website=datatracker.ietf.org|publisher=IETF|language=en}}</ref> Practical improvement have been proposed in the literature that alleviate the concerns introduced by stateful schemes.<ref>{{cite journal|last1=McGrew|first1=David|last2=Kampanakis|first2=Panos|last3=Fluhrer|first3=Scott|last4=Gazdag|first4=Stefan-Lukas|last5=Butin|first5=Denis|last6=Buchmann|first6=Johannes|title=State Management for Hash-Based Signatures|journal=Security Standardisation Research|date=2016|volume=10074|pages=244–260|doi=10.1007/978-3-319-49100-4_11|url=http://link.springer.com/chapter/10.1007/978-3-319-49100-4_11|publisher=Springer, Cham|language=en}}</ref> Hash functions appropriate for these schemes include [[SHA-2]], [[SHA-3]] and [[BLAKE (hash function)|BLAKE]]▼
▲
▲
==References==▼
The stateless hash-based scheme SLH-DSA is specified in [https://doi.org/10.6028/NIST.FIPS.205 FIPS-205].
== Implementations ==
The XMSS, GMSS and SPHINCS schemes are available in the Java [[Bouncy Castle (cryptography)|Bouncy Castle]] cryptographic APIs.<ref>{{Cite web |date=2018-12-18 |title=bcgit/bc-java |url=https://github.com/bcgit/bc-java/tree/master/core/src/main/java/org/bouncycastle/pqc/crypto |website=GitHub |language=en}}</ref> LMS<ref>{{Cite web |date=2024-06-18 |title=wolfCrypt implementations of LMS/HSS and XMSS/XMSS^MT signatures: build options and benchmarks (Intel x86) |url=https://www.wolfssl.com/wolfcrypt-implementations-of-lms-hss-and-xmss-xmssmt-signatures-build-options-and-benchmarks-intel-x86/ |website=wolfSSL |language=en}}</ref> and XMSS schemes are available in the [[wolfSSL]] cryptographic APIs.<ref>{{Cite web |date=2023-11-22 |title=wolfSSL/wolfssl |url=https://github.com/wolfSSL/wolfssl/blob/master/wolfssl/wolfcrypt/lms.h |website=GitHub |language=en}}</ref> SPHINCS is implemented in the SUPERCOP benchmarking toolkit.<ref>{{Cite web |title=SUPERCOP |url=http://bench.cr.yp.to/supercop.html |url-status=dead |archive-url=https://web.archive.org/web/20150215055126/http://bench.cr.yp.to/supercop.html |archive-date=2015-02-15 |access-date=2017-05-31}}</ref> Optimised<ref>{{Cite web |title=Code |url=https://huelsing.wordpress.com/code/ |url-status=dead |archive-url=https://web.archive.org/web/20170822224019/https://huelsing.wordpress.com/code/ |archive-date=2017-08-22 |access-date=2017-05-31 |website=Andreas Hülsing}}</ref> and unoptimised<ref>{{Cite web |title=squareUP > Publications |url=http://www.pqsignatures.org/index/publications.html#code |website=www.pqsignatures.org |language=en-gb}}</ref> reference implementations of the XMSS RFC exist. The LMS scheme has been implemented in Python<ref>{{Cite web |last=David |first=McGrew |date=2018-05-29 |title=The hash-sigs package: an implementation of the Leighton–Micali Hierarchical Signature System (HSS). |url=https://github.com/davidmcgrew/hash-sigs/ |website=GitHub |language=en}}</ref> and in C<ref>{{Cite web |last=David |first=McGrew |date=2018-11-22 |title=A full-featured implementation of the LMS and HSS Hash Based Signature Schemes from draft-mcgrew-hash-sigs-07. |url=https://github.com/cisco/hash-sigs |website=GitHub |language=en}}</ref> following its Internet-Draft.
▲== References ==
{{Reflist}}
* T. Lange. "Hash-Based Signatures". Encyclopedia of Cryptography and Security, Springer U.S., 2011. [https://link.springer.com/referenceworkentry/10.1007%2F978-1-4419-5906-5_413]
* F. T. Leighton, S. Micali. "Large provably fast and secure digital signature schemes based one secure hash functions". US Patent 5,432,852, [https://patents.google.com/patent/US5432852] 1995.
* E. Dahmen, M. Dring, E. Klintsevich, J. Buchmann, L.C. Coronado Garcia. "CMSS — an improved merkle signature scheme". Progress in Cryptology - Indocrypt 2006. [https://eprint.iacr.org/2006/320.pdf]▼
* G. Becker. "Merkle Signature Schemes, Merkle Trees and Their Cryptanalysis", seminar 'Post Quantum Cryptology' at the Ruhr-University Bochum, Germany, 2008. [https://www.emsec.rub.de/media/crypto/attachments/files/2011/04/becker_1.pdf] {{Webarchive|url=https://web.archive.org/web/20170830030943/http://www.emsec.rub.de/media/crypto/attachments/files/2011/04/becker_1.pdf |date=2017-08-30 }}
* R. Merkle. "Secrecy, authentication and public key systems / A certified digital signature". Ph.D. dissertation, Dept. of Electrical Engineering, Stanford University, 1979. [http://www.merkle.com/papers/Thesis1979.pdf]▼
▲* E. Dahmen, M. Dring, E. Klintsevich, J. Buchmann, L. C. Coronado Garcia. "CMSS —
▲* M. Naor, M. Yung. "Universal One-Way Hash Functions and their Cryptographic Applications". STOC 1989. [http://www.wisdom.weizmann.ac.il/~naor/PAPERS/uowhf.pdf]
▲* R. Merkle. "Secrecy, authentication and public key systems / A certified digital signature". Ph.D. dissertation, Dept. of Electrical Engineering, Stanford University, 1979. [http://www.merkle.com/papers/Thesis1979.pdf] {{Webarchive|url=https://web.archive.org/web/20180814211110/http://www.merkle.com/papers/Thesis1979.pdf |date=2018-08-14 }}
* S. Micali, M. Jakobsson, T. Leighton, M. Szydlo. "Fractal Merkle Tree Representation and Traversal". RSA-CT 03. [
* P. Kampanakis, S. Fluhrer. "LMS vs XMSS: A comparison of the Stateful Hash-Based Signature Proposed Standards". Cryptology ePrint Archive, Report 2017/349. [http://eprint.iacr.org/2017/349.pdf]
* D. Naor, A. Shenhav, A. Wool. "One-Time Signatures Revisited: Practical Fast Signatures Using Fractal Merkle Tree Traversal". IEEE 24th Convention of Electrical and Electronics Engineers in Israel, 2006. [https://www.eng.tau.ac.il/~yash/Naor_Shenhav_Wool.pdf] {{Webarchive|url=https://web.archive.org/web/20180205043107/http://www.eng.tau.ac.il/~yash/Naor_Shenhav_Wool.pdf |date=2018-02-05 }}
== External links ==
* [https://huelsing.net/wordpress
* [http://pqcrypto.org/hash.html] Another list of references (uncommented).
▲* [https://huelsing.wordpress.com/hash-based-signature-schemes/literature/] A commented list of literature about hash-based signature schemes.
{{Cryptography navbox}}
[[Category:Hash-based cryptography| ]]
[[Category:Post-quantum cryptography]]
[[Category:Public-key cryptography]]
| |||