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.

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 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.

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

Trusted Certified Auditor Using Cryptography for Secure Data Outsourcing and Privacy Preservation in Fog-Enabled VANETs

With the recent technological developments,massive vehicular ad hoc networks(VANETs)have been established,enabling numerous vehicles and their respective Road Side Unit(RSU)components to communicate with oneanother.The best way to enhance traffic flow for vehicles and traffic management departments is to share thedata they receive.There needs to be more protection for the VANET systems.An effective and safe methodof outsourcing is suggested,which reduces computation costs by achieving data security using a homomorphicmapping based on the conjugate operation of matrices.This research proposes a VANET-based data outsourcingsystem to fix the issues.To keep data outsourcing secure,the suggested model takes cryptography models intoaccount.Fog will keep the generated keys for the purpose of vehicle authentication.For controlling and overseeingthe outsourced data while preserving privacy,the suggested approach considers the Trusted Certified Auditor(TCA).Using the secret key,TCA can identify the genuine identity of VANETs when harmful messages aredetected.The proposed model develops a TCA-based unique static vehicle labeling system using cryptography(TCA-USVLC)for secure data outsourcing and privacy preservation in VANETs.The proposed model calculatesthe trust of vehicles in 16 ms for an average of 180 vehicles and achieves 98.6%accuracy for data encryption toprovide security.The proposedmodel achieved 98.5%accuracy in data outsourcing and 98.6%accuracy in privacypreservation in fog-enabled VANETs.Elliptical curve cryptography models can be applied in the future for betterencryption and decryption rates with lightweight cryptography operations.

A Secure Visual Cryptography Scheme Using Private Key with Invariant Share Sizes

Visual cryptography (VC) is one of the best techniques used to secure information. It uses the human vision to decrypt the encrypted images without any cryptographic computations. The basic concept of visual cryptography is splitting the secret image into shares such that when the shares are stacked, the secret image is revealed. In this paper we proposed a method that is based on the concept of visual cryptography for color images and without any pixel expansion which requires less space. The proposed method is used to encrypt halftone color images by generating two shares, random and key shares which are the same size as the secret color image. The two shares are generated based on a private key. At the receiving side, the secret color image is revealed by stacking the two shares and exploiting the human vision system. In this paper, we produce an enhanced form of the proposed method by modifying the encryption technique used to generate the random and the key shares. Experimental results have shown that the proposed and the enhanced methods suggest an efficient way to encrypt a secret color image with better level of security, less storage space, less time of computation and with a better value of PSNR.

ELLIPTIC CURVE CRYPTOGRAPHY BASED AUTHENTICATED KEY AGREEMENT WITH PRE-SHARED PASSWORD

Based on elliptic curve Diffie-Hellman algorithm, an Elliptic Curve Authenticated Key Agreement (ECAKA) protocol with pre-shared password is proposed. Its security relies on the Elliptic Curve Discrete Logarithm Problem (ECDLP). It provides identity authentication, key validation and perfect forward secrecy, and it can foil man-in-the-middle attacks.

FORMAL PROOF OF RELATIVE STRENGTH OF SECURITY AMONG ECK2007 MODEL AND OTHER PROOF MODELS FOR KEY AGREEMENT PROTOCOLS

The differences among the extended Canetti ＆ Krawezyk 2007 model （ECK2007） and other four models, i.e., the Bellare ＆ Rogaway （1993, 1995）models （BR93,BR95）, the Bellare, Pointcheval ＆ Rogaway （2000） model （BPR2000） and the Canetti ＆ Krawczyk （2001） model （CK2001） are given. The relative strength of security among these models is analyzed. To support the implication or non-implication relation among these models, the formal proof or the counter-example is provided.

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 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.

Secure SSL/TLS Communication System Based on Quantum Keys

Secure Sockets Layer(SSL)and Transport Layer Security(TLS)protocols facilitates a secure framework for identity authentication,data encryption,and message integrity verification.However,with the recent development in quantum computing technology,the security of conventional key-based SSL/TLS protocols faces vulnerabilities.In this paper,we propose a scheme by integrating the quantum key into the SSL/TLS framework.Furthermore,the application of post-quantum algorithms is used to enhance and complement the existing encryption suites.Experimental results show that the proposed SSL/TLS communication system based on quantum keys exhibits high performance in latency and throughput.Moreover,the proposed system showcases good resilience against quantum attacks.

Development of a Post Quantum Encryption Key Generation Algorithm Using Electromagnetic Wave Propagation Theory

In today’s rapid widespread of digital technologies into all live aspects to enhance efficiency and productivity on the one hand and on the other hand ensure customer engagement, personal data counterfeiting has become a major concern for businesses and end-users. One solution to ensure data security is encryption, where keys are central. There is therefore a need to find robusts key generation implementation that is effective, inexpensive and non-invasive for protecting and preventing data counterfeiting. In this paper, we use the theory of electromagnetic wave propagation to generate encryption keys.

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 and Robust Two-Party RSA Key Generation

An efficient two party RSA secret key sharing generation scheme based on a homomorphic encryption, which is semantically secure under the prime residuosity assumption, is proposed in this paper. At the stage of computing RSA modulo N, an initial distributed primality test protocol is used to reduce the computation complexity and increase the probability of N being a two-prime product. On the other aspect, the homomorphic encryption based sharing conversion protocols is devised and adopted in multi-party computing modulus N and secret key d. Comparing to any sharing conversion protocols based on oblivious transfer protocol, the homomorphic encryption based sharing conversion protocols are of high performance. Our scheme resists the passive attack and since a method of verifying the sharing was introduced in, the scheme can resists any cheating behaviors too. Security proof, computation complexity and communication complexity analysis are given at last.

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.

STRONGER PROVABLE SECURE MODEL FOR KEY EXCHANGE

The key exchange is a fundamental building block in the cryptography. Several provable security models for the key exchange protocol are proposed. To determine the exact properties required by the protocols, a single unified security model is essential, The eCK , eCK and CK models are examined and the result is proved that the eCK＇ model is the strongest provable security model for the key exchange. The relative security strength among these models is analyzed. To support the implication or non-implication relations among these models, the formal proofs and the counter-examples are given.

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.