Public Key Cryptography Based on Ergodic Matrices over Finite Field

A new public key encryption scheme is proposed in this paper, which is based on a hard problem over ergodic matrices. The security of this scheme is equal to the MQ-problem： multivariate quadratic equations over finite fields. This problem has been shown to be NP-complete and can＇t be solved with polynomial time algorithm.

A Multivariate Public Key Cryptographic Scheme

This paper presents a multivariate public key cryptographic scheme over a finite field with odd prime characteristic.The idea of embedding and layering is manifested in its construction.The security of the scheme is analyzed in detail,and this paper indicates that the scheme can withstand the up to date differential cryptanalysis.We give heuristic arguments to show that this scheme resists all known attacks.

A New Fast Modular Arithmetic Method in Public Key Cryptography

Modular arithmetic is a fundamental operation and plays an important role in public key cryptosystem. A new method and its theory evidence on the basis of modular arithmetic with large integer modulus-changeable modulus algorithm is proposed to improve the speed of the modular arithmetic in the presented paper. For changeable modulus algorithm, when modular computation of modulo n is difficult, it can be realized by computation of modulo n-1 and n-2 on the perquisite of easy modular computations of modulo n-1 and modulo n-2. The conclusion is that the new method is better than the direct method by computing the modular arithmetic operation with large modulus. Especially, when computations of modulo n-1 and modulo n-2 are easy and computation of modulo n is difficult, this new method will be faster and has more advantages than other algorithms on modular arithmetic. Lastly, it is suggested that the proposed method be applied in public key cryptography based on modular multiplication and modular exponentiation with large integer modulus effectively

How to Integrate Abstract Algebra and Number Theory in the Teaching of Public Key Cryptography Elegantly

Different from traditional symmetric cryptography, public key cryptography allows each user to own a pair of public/private key pair. Given the public key of one user and the data to be encrypted, a ciphertext can be generated such that only the intended user is able to recover the data using his/her private key associated with public key involved in the encryption process. To really understand the philosophy behind the public key cryptography is not an easy task and sometimes it seems somewhat difficult, if not impossible, for the beginners without the knowledge of the abstract algebra and number theory. In this paper, we introduce briefly the basic definition of public key cryptography as well as the corresponding mathematical hard problems. Besides, we explain why the mathematical backgrounds, especially abstract algebra and number theory, matter in the study of public key cryptography.

A New Proxy Signature Scheme with Message Recovery Using Self-Certified Public Key

A proxy signature scheme with message recovery using self-certified public key is proposed, which withstands public key substitution attacks, active attacks, and forgery attacks. The proposed scheme accomplishes the tasks of public key verification, proxy signature verification, and message recovery in a logically single step. In addition, the proposed scheme satisfies all properties of strong proxy signature and does not use secure channel in the communication between the original signer and the proxy signature signer.

Multivariate Public-Key Encryption Scheme Based on Error Correcting Codes

Advances in quantum computers pose potential threats to the currently used public-key cryptographic algorithms such as RSA and ECC.As a promising candidate against attackers equipped with quantum computational power,Multivariate Public-Key Cryptosystems(MPKCs)has attracted increasing attention in recently years.Unfortunately,the existing MPKCs can only be used as multivariate signature schemes,and the way to construct an efficient MPKC enabling secure encryption remains unknown.By employing the basic MQ-trapdoors,this paper proposes a novel multivariate encryption scheme by combining MPKCs and code-based public-key encryption schemes.Our new construction gives a positive response to the challenges in multivariate public key cryptography.Thorough analysis shows that our scheme is secure and efficient,and its private key size is about 10 times smaller than that of McEliece-type cryptosystems.

A novel mutual authentication and key agreement protocol based on NTRU cryptography for wireless communications

In this paper, the authors present a novel mutual authentication and key agreement protocol based on the Number Theory Research Unit (NTRU) public key cryptography. The symmetric encryption, hash and “challenge-response” techniques were adopted to build their protocol. To implement the mutual authentication and session key agreement, the proposed protocol contains two stages: namely initial procedure and real execution stage. Since the lightweight NTRU public key cryptography is employed, their protocol can not only overcome the security flaws of secret-key based authentication protocols such as those used in Global System for Mobile Communications (GSM) and Universal Mobile Telecommunications System (UMTS), but also provide greater security and lower computational complexity in comparison with currently well-known public key based wireless authentication schemes such as Beller-Yacobi and M.Aydos protocols.

NTRU_SSS:Anew Method Signcryption Post Quantum Cryptography Based on Shamir’s Secret Sharing

With the advent of quantum computing,numerous efforts have been made to standardize post-quantum cryptosystems with the intention of(eventually)replacing Elliptic Curve Cryptography(ECC)and Rivets-Shamir-Adelman(RSA).A modified version of the traditional N-Th Degree Truncated Polynomial Ring(NTRU)cryptosystem called NTRU Prime has been developed to reduce the attack surface.In this paper,the Signcryption scheme was proposed,and it is most efficient than others since it reduces the complexity and runs the time of the code execution,and at the same time,provides a better security degree since it ensures the integrity of the sent message,confidentiality of the data,forward secrecy when using refreshed parameters for each session.Unforgeability to prevent the man-in-the-middle attack from being active or passive,and non-repudiation when the sender can’t deny the recently sent message.This study aims to create a novel NTRU cryptography algorithm system that takes advantage of the security features of curve fitting operations and the valuable characteristics of chaotic systems.The proposed algorithm combines the(NTRU Prime)and Shamir’s Secret Sharing(SSS)features to improve the security of the NTRU encryption and key generation stages that rely on robust polynomial generation.Based on experimental results and a comparison of the time required for crucial exchange between NTRU-SSS and the original NTRU,this study shows a rise in complexity with a decrease in execution time in the case when compared to the original NTRU.It’s encouraging to see signs that the suggested changes to the NTRU work to increase accuracy and efficiency.

A New Self-Generated-Certificate Public Key Encryption Scheme with Flexible Public Key

Self-Generated-Certificate Public Key Cryptography(SGC-PKC) ,is the enhanced version of Certificateless Public Key Cryptography(CL-PKC) . It preserves all advantages of CL-PKC. Similar to CL-PKC,every user is given a partial private key by the KGC and generates his own private key and corresponding public key. In addition,it can defend against the Denial-of-Decryption(DoD) Attack. In this paper,we propose a new approach to construction SGC-PKE scheme that derived from a new application of chameleon hash and give a concrete scheme. It is the first scheme which has flexible public key and reaches Girault's trusted level 3,the same level as is enjoyed in a traditional PKI.

Applying Evolutionary Algorithm to Public Key Cryptosystems

A best algorithm generated scheme is proposed in the paper by making use of the thought of evolutionary algorithm, which can generate dynamically the best algorithm of generating primes in RSA cryptography under different conditions. Taking into account the factors of time, space and security integrated, this scheme possessed strong practicability. The paper also proposed a model of multi-degree parallel evolutionary algorithm to evaluate synthetically the efficiency and security of the public key cryptography. The model contributes to designing public key cryptography system too.

Efficient Certificateless Authenticated Key Agreement Protocol from Pairings

In the area of secure Web information system, mutual authentication and key agreement are essential between Web clients and servers. An efficient certificateless authenticated key agreement protocol for Web client/server setting is proposed, which uses pairings on certain elliptic curves. We show that the newly proposed key agreement protocol is practical and of great efficiency, meanwhile, it satisfies every desired security require ments for key agreement protocols.

Provable Efficient Certificateless Group Key Exchange Protocol

Certificateless public key cryptography （CL-PKC） avoids the inherent escrow of identity-based cryptography and does not require certificates to guarantee the authenticity of public keys. Based on CL-PKC, we present an efficient constant-round group key exchange protocol, which is provably secure under the intractability of computation Diffie-Hellman problem. Our protocol is a contributory key exchange with perfect forward secrecy and has only two communication rounds. So it is more efficient than other protocols. Moreover, our protocol provides a method to design efficient constant-round group key exchange protocols and most secret sharing schemes could be adopted to construct our protocol.

On the Group Based Cryptography

There are quite more applications of group theory. The recent application of group theory is public key （asymmetric） cryptography. All cryptographic algorithms have some weaknesses. To avoid its weakness, some special groups and methods can applied on. We will touch on group based public key cryptography and will give some suggestions in this area.

Hash Function Based Keyword Searchable Encryption Framework in Cloud Server Using MD5 and MECC

Cloud Computing expands its usability to various fields that utilize data and store it in a common space that is required for computing and the purpose of analysis as like the IoT devices.These devices utilize the cloud for storing and retrieving data since the devices are not capable of storing processing data on its own.Cloud Computing provides various services to the users like the IaaS,PaaS and SaaS.The major drawback that is faced by cloud computing include the Utilization of Cloud services for the storage of data that could be accessed by all the users related to cloud.The use of Public Key Encryptions with keyword search(PEKS)provides security against the untrustworthy third-party search capability on publicly encryption keys without revealing the data’s contents.But the Security concerns of PEKs arise when Inside Keywords Guessing attacks(IKGA),is identified in the system due to the untrusted server presume the keyword in trapdoor.This issue could be solved by using various algorithms like the Certificateless Hashed Public Key Authenticated Encryption with Keyword Search(CL-HPAEKS)which utilizes the Modified Elliptic Curve Cryptography(MECC)along with the Mutation Centred flower pollinations algorithm(CM-FPA)that is used in enhancing the performance of the algorithm using the Optimization in keys.The additional use of Message Digests 5(MD5)hash function in the system enhances the security Level that is associated with the system.The system that is proposed achieves the security level performance of 96 percent and the effort consumed by the algorithm is less compared to the other encryption techniques.

Identity-based key distribution for mobile Ad Hoc networks

An identity-based cryptosystem can make a special contribution to building key distribution and management architectures in resource-constrained mobile ad hoc networks since it does not suffer from certificate management problems. In this paper, based on a light- weight cryptosystem, elliptic curve cryptography （ECC）, we propose an identity-based distributed key-distribution protocol for mobile ad hoc networks. In this protocol, using secret sharing, we build a virtual private key generator which calculates one part of a user＇s secret key and sends it to the user via public channels, while, the other part of the secret key is generated by the user. So, the secret key of the user is generated collaboratively by the virtual authority and the user. Each has half of the secret information about the secret key of the user. Thus there is no secret key distribution problem. In addition, the user＇s secret key is known only to the user itself, therefore there is no key escrow.

J2EE平台双因素认证的设计与实现

网络信息安全技术的发展,使得单一的用户口令(PIN)认证方式认证强度已经不能满足用户的安全要求.本文分析了单一认证的弱安全性,结合PKCS 11标准和J2EE平台的EJB组件技术,设计并实现了基于用户口令(PIN)认证和硬件USBKey数字证书身份认证的双重因素认证系统.在所建系统模型基础上,重点构建了双因素认证系统的安全认证协议和签名、认证算法.最后的测试结果显示,在与单一认证系统性能相近的基础上,安全性较高.

A threshold key escrow scheme based on public key cryptosystem

In key escrow field it is important to solve the problem thatuser's secret key completely depends on the trusted escrow agency. In 1995, some methods of solving the problem were presented. But these methods are no better than that of directly using threshold cryptography. In this paper, we present a common pattern of threshold key escrow scheme based on public key cryptosystem, and a detailed design based on the improved RSA algorithm is given. The above problem is solved by this scheme.

Cryptanalysis of Public Key Cryptosystems Based on Non-Abelian Factorization Problems

Advances in quantum computers threaten to break public-key cryptosystems （e.g., RSA, ECC, and EIGamal）, based on the hardness of factoring or taking a discrete logarithm. However, no quantum algorithms have yet been found for solving certain mathematical problems in non-commutative algebraic structures. Recently, two novel public-key encryption schemes, BKT-B cryptosystem and BKT-FO cryptosystem, based on factorization problems have been proposed at Security and Communication Networks in 2013. In this paper we show that these two schemes are vulnerable to structural attacks and linearization equations attacks, and that they only require polynomial time complexity to obtain messages from associated public keys. We conduct a detailed analysis of the two attack methods and show corresponding algorithmic descriptions and efficiency analyses. In addition, we provide some improvement suggestions for the two public-key encryption schemes.

Security Architecture on the Trusting Internet of Things

By analyzing existed Internet of Things＇ system security vulnerabilities, a security architecture on trusting one is constructed. In the infrastructure, an off-line identity authentication based on the combined public key （CPK） mechanism is proposed, which solves the problems about a mass amount of authentications and the cross-domain authentication by integrating nodes＇ validity of identity authentication and uniqueness of identification. Moreover, the proposal of constructing nodes＇ authentic identification, valid authentication and credible communication connection at the application layer through the perception layer impels the formation of trust chain and relationship among perceptional nodes. Consequently, a trusting environment of the Internet of Things is built, by which a guidance of designing the trusted one would be provided.

New Public-Key Cryptosystem Based on the Morphism of Polynomials Problem

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.