Hash-based cryptography: Difference between revisions

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'''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"> [https://eprint.iacr.org/2018/046 Scalable, transparent, and post-quantum secure computational integrity], Ben-Sasson, Eli and Bentov, Iddo and Horesh, Yinon and Riabzev, Michael, 2018

</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.

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== History ==

[[Leslie Lamport]] 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|journal=Lecture Notes in Computer Science|volume=7071|pages=117–129|issue=Post-Quantum Cryptography. PQCrypto 2011|year=2011|issn=0302-9743|doi=10.1007/978-3-642-25405-5_8|citeseerx=10.1.1.400.6086}}</ref> and SPHINCS<ref>{{Cite book|issue=Advances in Cryptology --– EUROCRYPT 2015|last1=Bernstein|first1=Daniel J.|last2=Hopwood|first2=Daira|last3=Hülsing|first3=Andreas|last4=Lange|first4=Tanja|author4-link=Tanja Lange|last5=Niederhagen|first5=Ruben|last6=Papachristodoulou|first6=Louiza|last7=Schneider|first7=Michael|last8=Schwabe|first8=Peter|last9=Wilcox-O’Hearn|first9=Zooko|title=SPHINCS: practical stateless hash-based signatures|year=2015|publisher=Springer Berlin Heidelberg|isbn=9783662467992|editor-last=Oswald|editor-first=Elisabeth|editor-link= Elisabeth Oswald |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|citeseerx = 10.1.1.690.6403}}</ref><ref>{{cite web|title=SPHINCS: Introduction|url=http://sphincs.cr.yp.to/}}</ref> hash-based signature schemes were introduced in 2011 and 2015, respectively. XMSS was developed by a team of researchers under the direction of [[Johannes Buchmann]] and 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|language=en|doi-access=free}}</ref> A multi-tree variant of XMSS, XMSS^''MT'', was described in 2013.<ref>{{cite book|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|pages=194–208|doi=10.1007/978-3-642-40588-4_14|language=en|isbn=978-3-642-40587-7}}</ref>

== One-time signature schemes ==