Calculation And Application Of Bilinear Pairs In Hyperelliptic Curve Cryptosystem

With the development of identity-based cryptosystem,the use of bilinear pairings on elliptic curves has become a hotspot of cryptography experts.The elliptic curve(ECC)is a hyperelliptic curve(HECC)with a genus 1,and HECC has a better advantage over ECC: a smaller hyperplane can be found in the smaller domain,which can make the operation of HECC The HECC has been a lot of development since the scholars at home and abroad have the original ECC-based bilinear pair of identity encryption scheme transplanted to the HECC on the basis of the bilinear pair of HECC A variety of identity encryption solutions emerge in an endless stream.Therefore,the use of bilinear pairings on hyperelliptic curve(HECC)to achieve identity-based public key cryptosystem has become a hotspot in the field of cryptography research.We extend the oblique-Frobenius mapping on elliptic curves to hyperelliptic curves.By studying the oblique-Frobenius mapping on hyperelliptic curves with genus 2 and genus 3,we construct a skew-Frobenius mapping on hyperelliptic curves with a genus of 4,and propose an oblique-Frobenius mapping on hyperelliptic curves,General Form of Frobenius Mapping.A new scalar multiplication algorithm is constructed based on the general form of the oblique-Frobenius mapping on the hyperelliptic curve.The Weil pairs of the optimized variants are constructed by using the auto-isomorphism and hyper-elliptic curve with high distortion,a new Miller algorithm is constructed based on the optimized variant Weil.We propose a new multi-party fair exchange protocol based on bilinear pairing.By using the identity-based signature scheme based on hyperelliptic curve bilinear pairing,the efficiency of the protocol is improved.The threshold secret sharingtechnique of HECC ensures the security of the transaction process.And the formal analysis of the new multi-party fair exchange protocol by improved Kailar logic.Based on the hyperelliptic curve cryptosystem and bilinear pairings on hyperelliptic curves,we propose a ring signature based on attributes on hyperelliptic curves Program.The computation efficiency and security of the ring signature scheme based on attribute are greatly improved,and the signature length is shortened.Finally,the security proofs of our proposed scheme are presented in the standard model.