We have implemented the Miller’s algorithm to compute Tate pairings below, based on ourelliptic curve arithmetic library. //Tate pairing e(P, Q) in pairing contractstaticfunctionmillerLoop(PointP,PointQ):int{PointT=P;intf=1;// main miller looploop(N):i{f=f*f*linefunc(T,T,Q);T=EC...
In the recent years, pairing based cryptographic schemes on elliptic curve have been a very active field of research in cryptography. It has also recently become extremely useful in cryptologic constructions related to these objects. The present paper consists of brief survey on pairing based schemes...
Pairing-based cryptography is based on pairing functions that map pairs of points on an elliptic curve into a finite field. The unique properties of these pairing functions have enabled many new cryptographic protocols that had not been previously feasible. ...
简介 基于配对的密码学(Pairing-based cryptography2) (PBC) 建立在一个叫做椭圆曲线配对(elliptic curve pairing3)的数学对象存在的椭圆曲线密码学(elliptic curve cryptography4)之上。虽然配对的定义相对复杂,但它们是零知识密码学现代发展的许多加密对象的基础: BLS 数字签名、 KZG 多项式承诺和 zkSNARKs。 由于ZK ...
如果将参与方扩展到3个,很自然的问题是这种3方单次交互的协议是否可以抵抗eve。该问题在2000年是被Joux通过一个相当简单的bilinear pairing的方式解决。 Three-party two-round key agreement protocol 自此,基于pairings的方案变得非常流行。 【1】Alfred Menezes An Introduction to Pairing-Based Cryptography ...
In recent years cryptographic protocols based on the Weil and Tate pairings on elliptic curves have attracted much attention. A notable success in this area was the elegant solution by Boneh and Franklin [8] of the problem of efficient identity-based enc
基于配对的密码学(Pairing-based cryptography2) (PBC)建立在一个叫做椭圆曲线配对(elliptic curve pairing3)的数学对象存在的椭圆曲线密码学(elliptic curve cryptography4)之上。虽然配对的定义相对复杂,但它们是零知识密码学现代发展的许多加密对象的基础: BLS 数字签名、 KZG 多项式承诺和 zkSNARKs。
Towards practical lattice-based cryptography(走向实用的基于格的密码学) 热度: improving reliability in dna based computations with applications to cryptography 热度: LectureNotesinComputerScience5209 CommencedPublicationin1973 FoundingandFormerSeriesEditors: ...
gnark-crypto provides elliptic curve and pairing-based cryptography on BN, BLS12, BLS24 and BW6 curves. It also provides various algorithms (algebra, crypto) of particular interest to zero knowledge proof systems. - holiman/gnark-crypto
Forarandomellipticcurve,k≈n,whichistoolarge.Theorem:IfEisasupersingularellipticcurve,thenk≤6.(RecallEissupersingularif#E(Fpr)≡1modp.)Thereareordinarycurveswithlowembeddingdegree(MNTcurveshavek=2,3,or4.)CryptographicApplications •MOVattack-TransfersthediscretelogarithmproblemonEtoadiscretelogarithminFqk....