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On the isomorphism classes of Legendre elliptic curves over finite fields

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Science China Mathematics 2011年第9期54卷 1885-1890页

作者： WU Hongfeng feng rongquan College of Science North China University of technology Beijing 100144 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

In this paper,the number of isomorphism classes of Legendre elliptic curves over finite field is enumerated.

关键词： elliptic curve Legendre curve isomorphism classes cryptography

Verifiable random functions with Boolean function constraints

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Science China(Information Sciences) 2018年第3期61卷 243-245页

作者： Qianwen WANG rongquan feng Yan ZHU School of Mathematical Sciences Peking University School of Computer and Communication Engineering University of Science and Technology Beijing

Dear editor,Verifiable random functions(VRFs)[1]are cryptographic functions that behaves like a random function for producing a random string y for any variant x,but also allows for efficient verification of uniqueness of y for a valid witness *** this work,we extend the concept of VRFs to a notion of a conditionally verifiable random function

关键词： VRF Verifiable random functions with Boolean function constraints

Lattice-based key exchange on small integer solution problem

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Science China(Information Sciences) 2014年第11期57卷 150-161页

作者： WANG ShanBiao ZHU Yan MA Di feng rongquan School of Mathematical Sciences Peking University School of Computer and Communication Engineering University of Science and Technology Beijing Department of Computer and Information Science University of Michigan-Dearborn

In this paper, we propose a new hard problem, called bilateral inhomogeneous small integer solution(Bi-ISIS), which can be seen as an extension of the small integer solution problem on lattices. The main idea is that, instead of choosing a rectangle matrix, we choose a square matrix with small rank to generate Bi-ISIS problem without affecting the hardness of the underlying SIS problem. Based on this new problem, we present two new hardness problems: computational Bi-ISIS and decisional problems. As a direct application of these problems, we construct a new lattice-based key exchange(KE) protocol, which is analogous to the classic DiffieHellman KE protocol. We prove the security of this protocol and show that it provides better security in case of worst-case hardness of lattice problems, relatively efficient implementations, and great simplicity.

关键词： cryptography lattices small integer solutions key exchange protocol secure communications

Identity-Based Encryption on RSA Without Pairings and Key Escrow

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Chinese Journal of Electronics 2014年第4期23卷 842-850页

作者： ZHU Yan WANG Shanbiao MA Di feng rongquan School of Computer and Communication Engineering University of Science and Technology Beijing School of Mathematical Sciences Peking University Department of Computer and Information Science University of Michigan-Dearborn

We propose a new construction of identitybased encryption without key escrow over the tradition RSA cryptosystems. The security of our scheme follows from the decisional Diffie-Hellman assumption and the difficulty of Modular inversion hidden number problem with error(MIHNPw E), which can be seen as a generalization of the modular inversion hidden number problem. We give an analysis on the hardness of MIHNPw E by lattice techniques. In our construction, we generate each user’s partial private key in the form of an MIHNPw E instance. The hardness of MIHNPw E provides our scheme with resistance against key-collusion attacks from any number of traitors. Our prototype implementation of the proposed scheme shows that it can be more computation efficient and easy-to-implementation than the influential pairingfriendly elliptic-curve based IBE scheme.

关键词： Identity-based encryption Key escrow Hidden number problem with error

New instant confirmation mechanism based on interactive incontestable signature in consortium blockchain

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Frontiers of Computer Science 2019年第6期13卷 1182-1197页

作者： Yan ZHU Khaled RIAD Ruiqi GUO Guohua GAN rongquan feng School of Computer&Communication Engineering University of Science and Technology BeijingBeijing 100083China Mathematics Department Faculty of ScienceZagazig UniversityZagazig 44519Egypt School of Mathematical Sciences Peking UniversityBeijing 100871China

The blockchain is a radical innovation that has a considerable effect on payments,stock exchanges,cybersecurity,and computational ***,its limitations in terms of the uncertainty involved in transaction confirmation are *** this paper,we describe the design of a decentralized voting protocol for the election of a block generator in a consortium blockchain and propose a new system framework that allows fast and exact confirmation of all *** addition,to replace a transaction’s owner signature,a new interactive incontestable signature between the dealer and owner is used to confirm a *** means of this signature,the dealer can assure the owner that a transaction will be permanently included in the blockchain in a non-repudiation ***,the signatures of all transactions in a block share only one witness that provides membership proof between the block and these ***,a security and performance analysis shows that the proposed schemes are provably secure and highly efficient.

关键词： security blockchain signature consortium interactive proof

Full automorphism group of the generalized symplectic graph

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Science China Mathematics 2013年第7期56卷 1509-1520页

作者： ZENG LiWei CHAI Zhao feng rongquan MA ChangLi LMAM School of Mathematical Sciences Peking University Science China Press College of Mathematics and Information Science Hebei Normal University

Let Fq be a finite field of odd characteristic, m, v the integers with 1 ≤ m ≤ v and K a 2v × 2v nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2v（q, m） relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2v-dimensional symplectic space Fq（2v） as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQw is 1 and the dimension of P ∩ Q is m - 1. It is proved that the full automorphism group of the graph GSp2v（q, m） is the projective semilinear symplectic group P∑p（2v, q）.

关键词： generalized symplectic graph automorphism projective generalized symplectic group totally isotropic subspace generalized dual polar graph

Elliptic Curves in Huff's Model

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Wuhan University Journal of Natural Sciences 2012年第6期17卷 473-480页

作者： WU Hongfeng feng rongquan College of Sciences North China University of TechnologyBeijing 00China School of Mathematical Sciences/Laboratory of Mathematics and Applied Mathematics(LMAM) Peking UniversityBeijing 100871China

In this paper,we present the generalized Huff curves that contain Huff＇s model as a special ***,it is proved that every elliptic curve with three points of order 2 is isomorphic to a generalized Huff ***,the fast and explicit formulae are derived for generalized Huff curves in projective *** paper also enumerates the number of isomorphism classes of generalized Huff curves over finite ***,the explicit formulae are presented for the doubling step and addition step in Miller＇s algorithm to compute the Tate pairing on generalized Huff elliptic curves.

关键词： elliptic curve Huff curve cryptography scalar multiplication isomorphism classes

A Complete Set of Addition Laws for Twisted Jacobi Intersection Curves

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Wuhan University Journal of Natural Sciences 2011年第5期16卷 435-438页

作者： WU Hongfeng feng rongquan College of Sciences North China University of TechnologyBeijing 100144 China School of Mathematical Sciences and Laboratory ofMathematics and Applied Mathematics (LMAM) Peking UniversityBeijing 100871 China

A complete system of addition laws on an elliptic curve E is a collection of addition laws with the property that for any pair of points P1, P2 on E at least one of the addition laws in the collection can be used to compute P1＋P2. This paper proposes a complete set of the addition laws for arbitrary twisted Jacobi intersection curve.

关键词： elliptic curve twisted Jacobi intersection curve complete addition law point multiplication cryptography

The ranks of Maiorana-McFarland bent functions

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Science China Mathematics 2008年第9期51卷 1726-1731页

作者： WENG GuoBiao feng rongquan QIU WeiSheng ZHENG ZhiMing LMAM School of Mathematical SciencesPeking UniversityBeijing 100871China

In this paper, the ranks of a special family of Maiorana-McFarland bent functions are discussed. The upper and lower bounds of the ranks are given and those bent functions whose ranks achieve these bounds are determined. As a consequence, the inequivalence of some bent functions are derived. Furthermore, the ranks of the functions of this family are calculated when t 6.

关键词： p-rank bent function difference set 06E30 11T71 94C10