Pairing-based cryptography: Difference between revisions

Revision as of 04:40, 19 February 2024

Revision as of 09:43, 7 June 2024

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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. Thus, the security level of some pairing friendly elliptic curves have been later reduced.

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