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 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

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 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.

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.

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.

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.

Weak-Keys in Public Key Cryptosystems Based on Discrete Logarithms

The discrete logarithm method is the foundation of many public key algorithms. However, one type of key, defined as a weak-key, reduces the security of public key cryptosystems based on the discrete logarithm method. The weak-key occurs if the public key is a factor or multiple of the primitive element, in which case the user＇s private key is not needed but can be obtained based on the character of the public key. An algorithm is presented that can easily test whether there is a weak-key in the cryptosystem. An example is given to show that an attack can be completed for the Elgamal digital signature if a weak-key exists, therefore validating the danger of weak-keys. Methods are given to prevent the generation of these weak-keys.

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.

Weakness in Projected C＊- Scheme

This paper presents an algebraic method to attack the projected C*? cryptographic scheme.The attack applies the affine parts of the private keys and the weakness caused by the structures of the private keys to find a large number of linear equations.The attack can recover the private keys efficiently when the parameters are small enough.Meanwhile,the weak keys of the scheme are found and the private keys can be recovered efficiently once the weak keys are used.The paper also proposes a new modification of C*? cryptographic scheme,which is not only as efficient as original projected C*? scheme,but also resistant to the differential attack and the attack proposed in this paper.

Hyper Elliptic Curve Based Certificateless Signcryption Scheme for Secure IIoT Communications

Industrial internet of things (IIoT) is the usage of internet of things(IoT) devices and applications for the purpose of sensing, processing andcommunicating real-time events in the industrial system to reduce the unnecessary operational cost and enhance manufacturing and other industrial-relatedprocesses to attain more profits. However, such IoT based smart industriesneed internet connectivity and interoperability which makes them susceptibleto numerous cyber-attacks due to the scarcity of computational resourcesof IoT devices and communication over insecure wireless channels. Therefore, this necessitates the design of an efficient security mechanism for IIoTenvironment. In this paper, we propose a hyperelliptic curve cryptography(HECC) based IIoT Certificateless Signcryption (IIoT-CS) scheme, with theaim of improving security while lowering computational and communicationoverhead in IIoT environment. HECC with 80-bit smaller key and parameterssizes offers similar security as elliptic curve cryptography (ECC) with 160-bitlong key and parameters sizes. We assessed the IIoT-CS scheme security byapplying formal and informal security evaluation techniques. We used Realor Random (RoR) model and the widely used automated validation of internet security protocols and applications (AVISPA) simulation tool for formalsecurity analysis and proved that the IIoT-CS scheme provides resistance tovarious attacks. Our proposed IIoT-CS scheme is relatively less expensivecompared to the current state-of-the-art in terms of computational cost andcommunication overhead. Furthermore, the IIoT-CS scheme is 31.25% and 51.31% more efficient in computational cost and communication overhead,respectively, compared to the most recent protocol.

Enabling Space-Air integration:A Satellite-UAV networking authentication scheme

One of the goals of sixth-generation mobile networks(6G)is to achieve a larger network coverage area.Satellite networks enable global coverage and aerial nodes such as Unmanned Aerial Vehicle(UAV)can serve as a supplement to ground networks in remote environments.Therefore,6G networks are gradually evolving towards Space-AirGround integrated networks.The combination of UAV networks and satellite networks is a research hotspot in the field of Space-Air integrated networks.However,the combination of UAV networks and satellite networks currently faces many challenges in terms of security.The characteristics of large propagation delay and unstable communication links in satellite networks make them vulnerable to various attacks,including eavesdropping,tampering,and impersonation.Meanwhile,existing research on UAV networks mainly focuses on UAV-Ground networking authentication mechanisms,which are not suitable for resourceconstrained nodes in the Space-Air integration scenario.Therefore,based on elliptic curve public key cryptography and Chebyshev polynomial,we propose a secure networking authentication scheme for satellite nodes and UAV nodes in the Space-Air integration scenario.The security analysis indicates that our scheme possesses security attributes such as mutual authentication,key agreement,identity anonymity,unlinkability,perfect forward-backward security,and resistance against various protocol attacks,among other security properties.Performance analysis also indicates certain advantages of our scheme over existing schemes in terms of signaling,bandwidth,and computational overhead.

Cryptanalysis and improvement of a certificateless signcryption scheme without bilinear pairing

As an improtant cryptographic scheme, signcryption scheme has been widely used in applications since it could provide both of signature and encryption. With the development of the certificateless public key cryptography （CLPKC）, many certificatelss signcryption （CLSC） schemes using bilinear pairing hve been proposed. Comparated other operations, the bilinear pairing operaion is much more compulicated. Therefore, CLSC scheme without bilinear pairing is more suitable for applications. Recently, Jing et al. proposed a CLSC scheme without bilinear pairing and claimed their scheme is secure against two types of adversaries. In this paper, we will show their scheme provide neither unforgeability property nor confidentiality property. To improve security, we also propose a new CLSC scheme without pairing and demonstrate it is provably secure in the random oracle model.

Secure proxy signature scheme with fast revocation in the standard model

Proxy signature is an important cryptographic primitive and has been suggested in numerous applications, Tne revocation oI delegated rights is an essential issue of the proxy signature schemes. In this article, a security model of proxy signature schemes with fast revocation is formalized. Under the formal security framework, a proxy signature scheme with fast revocation based on bilinear pairings is proposed. A security mediator （SEM）, which is an on-line partially trusted server, is introduced to examine whether a proxy signer signs according to the warrant or he/she exists in the revocation list. Moreover, the proxy signer must cooperate with the SEM to generate a valid proxy signature, thus the proposed scheme has the property of fast revocation. The proposed scheme is provably secure based on the computational Diffie-Hellman （CDH） intractability assumption without relying on the random oracles, and satisfies all the security requirements for a secure proxy signature.

Efficient Tate pairing computation using double-base chains

Pairing-based cryptosystems have developed very fast in the last few years. The efficiencies of these cryptosystems depend on the computation of the bilinear pairings, In this paper, a new efficient algorithm based on double-base chains for computing the Tate pairing is proposed for odd characteristic p 〉 3. The inherent sparseness of double-base number system reduces the computational cost for computing the Tate pairing evidently. The new algorithm is 9% faster than the previous fastest method for the embedding degree k = 6.

New Multivariate-Based Certificateless Hybrid Signcryption Scheme for Multi-Recipient

With the development of quantum computer, multivariate public key cryptography withstanding quantum attack has became one of the research focus. The existed signcryption schemes from discrete logarithm and bilinear paring are facing the serious threats. Based on multivariate public key cryptography, a new certificateless multi-receiver hybrid signcryption scheme has been proposed. The proposal reduced the cipher text and could handle arbitrary length messages by employing randomness reusing and hybrid encryption, as well as keeping security. In the random oracle model, the scheme＇s confidentiality could withstand the IND-CCA2 adversary and its unforgeability could withstand the UF-CMA adversary under the hardness of multivariat quadratic （MQ） problem and isomorphism of polynomials （IP） assumption. It has less computation overhead and higher transmission efficiency than others. It reduced 33% cipher data compared with the existed similar scheme.

CCA2 secure biometric identity based encryption with constant-size ciphertext

We propose a new biometric identity based encryption scheme （Bio-IBE）, in which user biometric information is used to generate the public key with a fuzzy extractor. This is the first Bio-IBE scheme that achieves constant size ciphertext. This is also a scheme that is secure against the adaptive chosen ciphertext attack （CCA2）. Details are presented along with a discussion of Shamir＇s threshold secret sharing and fuzzy extraction of biometrics, which is based on error correction codes. We also define a security model and prove that the security of the proposed scheme is reduced to the decisional bilinear Diffie-Hellman proposed scheme has better efficiency and stronger security （DBDH） assumption. The comparison shows that the compared with the available Bio-IBE schemes.

Cryptanalysis and improvement of a certificateless encryption scheme in the standard model

Certificateless public key cryptography elimi- nates inherent key escrow problem in identity-based cryptog- raphy, and does not yet requires certificates as in the tradi- tional public key infrastructure. In this paper, we give crypt- analysis to Hwang et al.＇s certificateless encryption scheme which is the first concrete certificateless encryption scheme that can be proved to be secure against ＂malicious-but- passive＂ key generation center （KGC） attack in the stan- dard model. Their scheme is proved to be insecure even in a weaker security model called ＂honest-but-curious＂ KGC at- tack model. We then propose an improved scheme which is really secure against ＂malicious-but-passive＂ KGC attack in the standard model.