Pairing-based cryptography: Difference between revisions

Revision as of 17:32, 28 March 2023

Revision as of 08:28, 18 June 2023

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For example, in groups equipped with a [[Bilinear map|bilinear mapping]] such as the [[Weil pairing]] or [[Tate pairing]], generalizations of the [[Diffie–Hellman problem|computational Diffie–Hellman problem]] are believed to be infeasible while the simpler [[decisional Diffie–Hellman assumption|decisional Diffie–Hellman problem]] can be easily solved using the pairing function. The first group is sometimes referred to as a '''Gap Group''' because of the assumed difference in difficulty between these two problems in the group.

While first used for [[cryptanalysis]],<ref>{{cite journal|last1=Menezes|first1=Alfred J. Menezes|last2=Okamato|first2=Tatsuaki|last3=Vanstone|first3=Scott A.|title=Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field|journal=IEEE Transactions on Information Theory|date=1993|volume=39|issue=5|pages=1639–1646 |doi=10.1109/18.259647 }}</ref> pairings have also been used to construct many cryptographic systems for which no other efficient implementation is known, such as [[identity-based encryption]] or [[attribute-based encryption]] schemes.

Pairing-based cryptography is used in the [[Cryptographic commitment#KZG commitment|KZG cryptographic commitment scheme]].

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In June 2012 the [[National Institute of Information and Communications Technology]] (NICT), [[Kyushu University]], and [[Fujitsu#Fujitsu Laboratories|Fujitsu Laboratories Limited]] improved the previous bound for successfully computing a discrete logarithm on a [[supersingular elliptic curve]] from 676 bits to 923 bits.<ref>{{cite web |work=Press release from NICT |date=June 18, 2012 |url=http://www.nict.go.jp/en/press/2012/06/18en-1.html |title=NICT, Kyushu University and Fujitsu Laboratories Achieve World Record Cryptanalysis of Next-Generation Cryptography }}</ref>

In 2016, the Extended Tower Number Field Sieve algorithm<ref>{{Cite journal |lastlast1=Kim |firstfirst1=Taechan |last2=Barbulescu |first2=Razvan |date=2015 |title=Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case |url=https://eprint.iacr.org/2015/1027 |journal=Cryptology ePrint Archive |language=en}}</ref> allowed to reduce the complexity of finding discrete logarithm in some resulting groups of pairings. Thus, the security level of some pairing friendly elliptic curves have been later reduced.<ref>{{Cite journal |lastlast1=Barbulescu |firstfirst1=Razvan |last2=Duquesne |first2=Sylvain |date=2019-10-01 |title=Updating Key Size Estimations for Pairings |url=https://doi.org/10.1007/s00145-018-9280-5 |journal=Journal of Cryptology |language=en |volume=32 |issue=4 |pages=1298–1336 |doi=10.1007/s00145-018-9280-5 |s2cid=253635514 |issn=1432-1378}}</ref>

== References ==