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An Efficient and Practical public key cryptosystem with CCA-Security on Standard Model

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Tsinghua Science and Technology 2014年第5期19卷 486-495页

作者： Zhen Liu Xiaoyuan Yang Weidong Zhong Yiliang Han Department of Network and Information Security key Laboratory Engineering University of the Armed PoliceForce

Chosen Ciphertext Attack （CCA） security on the standard model is widely accepted as the standard security notion for the public key cryptosystem. The existing CCA-secure public key cryptosystems on the standard model are expensive in terms of efficiency and practicality. In this paper, an efficient and practical public key cryptosystem is presented over the group of signed quadratic residues. It is provably secure against CCA on the standard model. Furthermore, public verifiability for this scheme is also realized in the way that projects the verification privacy key into public key on trapdoor pretending. It will be useful to devise efficient CCA-secure threshold and proxy re-encryption schemes on the standard model.

关键词： public key cryptosystem standard model Chosen Ciphertext Attack (CCA)-security public verifiability

public key cryptosystem Based on Two Sided Action of Different Exotic Semirings

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Journal of Mathematics and System Science 2014年第1期4卷 6-13页

作者： Mariana Durcheva Faculty of Applied Mathematics and Informatics Technical University of Sofia Sofia 1756 Bulgaria

The idempotent semirings Rmax and Rmin play a crucial role in several areas of mathematics and their applications such as discrete mathematics, algebraic geometry, computer science, computer languages, linguistic problems, optimization theory, discrete event systems, fuzzy logics. In this paper we consider the expansion of the semirings Rmax and Rmin with residuals and describe how to use these expended semirings in public key cryptography.

关键词： public key cryptosystem exotic semirings semiring action residuals.

New public-key cryptosystem Based on the Morphism of Polynomials Problem

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Tsinghua Science and Technology 2016年第3期21卷 302-311页

作者： Houzhen Wang Huanguo Zhang Shaowu Mao Wanqing Wu Liqiang Zhang Computer School of Wuhan University Wuhan 430079China the State key Laboratory of Cryptology Beijing 100878China

During the last two decades, there has been intensive and fast development in Multivariate public key Cryptography （MPKC）, which is considered to be an important candidate for post-quantum cryptography. However, it is universally regarded as a difficult task, as in the Knapsack cryptosystems, to design a secure MPKC scheme （especially an encryption scheme） employing the existing trapdoor construction. In this paper, we propose a new key-exchange scheme and an MPKC scheme based on the Morphism of Polynomials （MP） problem. The security of the proposed schemes is provably reducible to the conjectured intractability of a new difficult problem, namely the Decisional Multivariate Diffie-Hellman （DMDH） problem derived from the MP problem. The proposed key agreement is one of several non-number-theory-based protocols, and is a candidate for use in the post-quantum era. More importantly, by slightly modifying the protocol, we offer an original approach to designing a secure MPKC scheme. Furthermore, the proposed encryption scheme achieves a good tradeoff between security and efficiency, and seems competitive with traditional MPKC schemes.

关键词： public key cryptosystem key exchange Multivariate public key Cryptography (MPKC) Morphism ofPolynomials (MP) problem

New public key cryptosystems from Combinatorial Group Theory

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Wuhan University Journal of Natural Sciences 2006年第5期11卷 1267-1270页

作者： TANG Xueming WANG Xiaofei HONG Fan CUI Guohua College of Computer Science and Technology HuazhongUniversity of Science and Technology Wuhan 430074Hubei China

External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in the quantum computing epoch. Three hard problems on this new platform, Subgroup Root Problem, Multi-variant Subgroup Root Problem and Subgroup Action Problem are presented and well analyzed, which all have no relations with conjugacy. New secure public key encryption system and key agreement protocol are designed based on these hard problems. The new cryptosystems can be implemented in a general group environment other than in braid or Artin groups.

关键词： public key cryptosystem key agreement protocol combinatorial group theory Artin group external direct product quantum computing

Constructing Finite Automata with Invertibility bytransformation Method

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Journal of Computer Science & Technology 2000年第1期15卷 10-26页

作者：陶仁骥陈世华 LaboratoryforComputerScience InstituteofSoftwareChineseAcademyofSciencesP.O.Box8718Beijing100080P.R.China LaboratoryforComputerScience InstituteofSoftwareChineseAcademyofScienc

Ra, Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In aprevious paper, the authors generalized R., Rb transformations to deal with nonlinear memory finite automata, and gave sufficient conditions for weak inverse andfor weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automatasatisfying one of these sufficient conditions were also given. This paper extends theconcepts, methods and results to general finite automata, in which states consist offinite input history, finite output history and finite 'inner state' history.

关键词： finite automata invertibility public key cryptosystem

New designing of cryptosystems based on quadratic fields

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Science in China(Series F) 2008年第8期51卷 1106-1116页

作者： DONG XiaoLei CAO ZhenFu WANG LiCheng Department of Computer Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China

This paper proposes a method to construct new kind of non-maximal imaginary quadratic order （NIQO＊） by combining the technique of Diophantine equation and the characters of non-maximal imaginary quadratic order. It is proved that in the class group of this new kind of NIQO＊, it is very easy to design provable secure cryptosystems based on quadratic field （QF）. With the purpose to prove that this new kind of QF-based cryptosystems are easy to implement, two concrete schemes are presented, i.e., a Schnorr-like signature and an EIGamel-like encryption, by using the proposed NIQO＊. In the random oracle model, it is proved that：（1） under the assumption that the discrete logarithm problem over class groups （CL-DLP） of this new kind of NIQO＊ is intractable, the proposed signature scheme is secure against adaptive chosen-message attacks, i.e., achieving UF-CMA security; （2） under the assumption that the decisional Diffie-Hellman problem over class groups （CL-DDH） of this new kind of NIQO＊ is intractable, the enhanced encryption in this paper is secure against adaptive chosen-ciphertext attacks, i.e., reaching IND-CCA2 security.

关键词： public key cryptosystem quadratic field cryptography quadratic fields provable security

public key based uniform access framework in 3G systems

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Journal of Harbin Institute of Technology(New Series) 2006年第4期13卷 404-408页

作者：王弈谷大武白英彩 Dept. of Computer Science and Engineering Shanghai Jiaotong University

This paper compares two types of access methods in 3G telecommunication systems, registration based access method and alternative access method. Through analyzing their common ground, we establish a public-key based uniform access framework, which combines different access methods into one unified model and provides more scalability and flexibility. Then an improved wireless authentication protocol is introduced into the framework, which gives an example of how unification is obtained by using public key technology. Since original protocol has flaws, an improved one is proposed based on security investigation. Improved authentication protocol overcomes the weakness of the original one, and maintains all the security features owned by old protocol. Finally, the feasibility of this framework is analyzed with consideration of current development in mobile telecommunication fields and the future trend of 3G systems. The result shows that public key technology has a promising future in 3G and Beyond 3G systems. It points out a new way for key management in future telecommunication systems.

关键词： 3G telecommunication systems public key cryptosystem network access

Fast VLSI Implementation of Modular Inversion in Galois Field GF(p)

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Tsinghua Science and Technology 2003年第5期8卷 628-632页

作者：周涛吴行军白国强陈弘毅 Institute of Microelectronics

Modular inversion is one of the key arithmetic operations in public key cryptosystems, so low-cost, high-speed hardware implementation is absolutely necessary. This paper presents an algorithm for prime fields for hardware implementation. The algorithm involves only ordinary addition/subtraction and does not need any modular operations, multiplications or divisions. All of the arithmetic operations in the algorithm can be accomplished by only one adder, so it is very suitable for fast very large scale integration (VLSI) implementation. The VLSI implementation of the algorithm is also given with good performance and low silicon penalty.

关键词： modular inverse Galois field very large scale integration (VLSI) public key cryptosystem

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New Weak keys in RSA

Wuhan University Journal of Natural Sciences 2006年第6期11卷 1529-1532页

作者： WANG Baocang LIU Shuanggen HU Yupu key Laboratory of Computer Network and Information Security Ministry of Edueation Xidian University Xi＇an 710071 Shaanxi China College of Computer Information Engineering Jiangxi Normal University Nanchang 330022 Jiangxi China

The security of the RSA system with the prime pairs of some special form is investigated. A new special-purpose algorithm for factoring RSA numbers is proposed. The basic idea of the method is to factor RSA numbers by factoring a well-chosen quadratic polynomial with integral coefficients. When viewed as a general-purpose algorithm, the new algorithm has a high computational complexity. It is shown thai the RSA number n = pq can be easily factored if p and q have the special form of p = as＋b, q=cs＋d, where a, b, c, d are relatively small numbers. Such prime pairs （p, q） are the weak keys of RSA, so when we generate RSA modulus, we should avoid using such prime pairs （p, q）.

关键词： integer factorization RSA number public key cryptosystem special-purpose algorithm