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==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>
==Properties of hash-based signature schemes==
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