Pairing-based cryptography: Difference between revisions

Revision as of 03:15, 21 August 2023

Revision as of 21:58, 3 November 2023

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; [[Bilinear map|Bilinearity]]: <math> \forall a,b \in F_q^*, P\in G_1, Q\in G_2:\ e\left(aP, bQ\right) = e\left(P, Q\right)^{ab}</math>

; [[Degeneracy (mathematics)|Non-degeneracy]]: <math>e \neq 1</math>

; Computability: There exists an efficient [[algorithm]] to compute <math>e</math>.

== Classification ==

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== Cryptanalysis ==

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 |last1=Kim |first1=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 |last1=Barbulescu |first1=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 ==

{{Reflist}}