Efficient Public Key Cryptosystem Research Articles

An NTRU-like Message Recoverable Signature Algorithm

An important feature of Nyberg-Rueppel type digital signature algorithms is message recovery, this signature algorithm can recover the original information from the signature directly by the verifier in the verification phase after signing the message. However, this algorithm is currently vulnerable to quantum attacks and its security cannot be guaranteed. Number Theory Research Unit (NTRU) is an efficient public-key cryptosystem and is considered to be one of the best quantum-resistant encryption schemes. This paper proposes an NTRU-like message recoverable signature algorithm to meet the key agreement requirements in the post-quantum world. This algorithm, designed for the Internet of Things (IoT), constructs a secure system using the Group-Based Message Recoverable Signature Algorithm (NR-GTRU), by integrating a Group-Based NTRU-Like Public-Key Cryptosystem (GTRU) with an efficient Nyberg-Rueppel type of NTRU digital signature algorithm (NR-NTRU). This signature algorithm, resistant to quantum algorithm attacks, offers higher security at the cost of a slight efficiency reduction compared to traditional NTRU signature algorithms, and features Nyberg-Rueppel message recovery, making it well-suited for IoT applications.

Implementation of Elliptic Net Scalar Multiplication Computation for NIST P-192 Curve using Python

Elliptic curve cryptography is one of the most efficient public-key cryptosystems compared to the Rivest-Shamir-Addleman scheme. One of the methods to compute elliptic curve scalar multiplication is division polynomials which utilize the non-linear recurrence relation also known as the elliptic net. Previous studies were related to elliptic curve scalar multiplication via elliptic net which implemented the use of C++, GP/PARI or Java programming. This study aims to implement the Python programming in the SageMath compiler for computing elliptic net scalar multiplication based on the National Institute of Standards and Technology curve of the type P-192. The implementation could be seen at three main processes which are the scalar decomposition, the blocks of elliptic net generation namely the initial and final blocks, as well as scalar multiplication computation. The base point and prime field of the short Weierstrass curve with a large scalar are the parameters used in the process. The results showed that the implemented programming was easier while working with a large prime number field, vulnerable to errors and can be easily verified. The implemented programming can also be used to compute scalar multiplication on other standardizations of elliptic curve cryptography such as Brainpool 384-bit prime field or NUMS 256-bit prime field curves.

Provably Secure Escrow-Less Chebyshev Chaotic Map-Based Key Agreement Protocol for Vehicle to Grid Connections With Privacy Protection

Security and privacy concerns necessitate the careful management of shared keys in the vehicle to grid (V2G) networks. To do so, in recent years, several interesting key agreement protocols have been proposed to be employed in the context of V2G networks. As the efficiency is of prime significance in V2G networks, many of these protocols have been designed to be as light as possible. Nevertheless, review of the previous works indicates that the existing lightweight schemes cannot provide the desired security properties. Furthermore, the existing secure protocols are not so proper to be used by computationally limited devices in the V2G networks. Therefore, in this article, by utilizing the efficient Chebyshev chaotic map-based public key cryptosystem, we propose an anonymous key agreement scheme, which can not only provide the expected security requirements, but also has a proper level of performance. To demonstrate the security of the proposed scheme, we present a rigorous formal security proof using the random oracle model. In addition, to show its outperformance, we both compare it with several recently published well-known schemes and perform the experimental study. In general, the results indicate the efficiency of the proposed protocol in comparison to the related ones.

An Efficient Public Key Cryptosystem Based on Dihedral Group and Quantum Spin States

The enciphering schemes based on medium transformations by following the strict guidelines are almost used everywhere. We have developed the structure to simulate the digital data with quantum spin states rather than following or creating the strict guidelines. We simulate the pixels of an image with the dihedral group and spin states for a defined phase to create confusion in it. The scope of this article is concerned in the development and deployment of public key cryptosystem, its performance and security analyses.

ONTOLOGY OF FINITE-AUTOMATION CRYPTOGRAPHY

Today, the improvement of methods for protecting information is an urgent task, therefore, the authors of the article are interested in using alternative methods of developing more robust and efficient public-key cryptosystems. Finite automata are taken as such a model. To systematize knowledge in the field of finite-state cryptography, it was decided to use ontology. This paper discusses the construction of an ontological model of finite-automaton cryptography. The proposed ontological model will have four main levels: the ontology of knowledge representation, the ontology of the top level, the domain ontology and practical ontologies. The methodology of conceptual maps was taken as the ontology of knowledge representation. The ontology of the top level contains basic information about cryptography and automata theory, the domain ontology describes directly the finite automaton cryptography. As an example of practical ontology, a public-key cryptosystem based on finite automata was considered. The presented ontology is modeled for the first time and gives a clear understanding of the use of finite automata in cryptography, systematizes the information obtained in the course of the research on this subject area, is a prerequisite in the further development of cryptosystems based on the theory of automata.

A Group-Based NTRU-Like Public-Key Cryptosystem for IoT

The Internet of things have been widely used to improve our daily life. Public-key cryptosystem plays a central role in the security of IoT. However, classic public-key cryptosystems such as RSA and ECC are not suitable for IoT because of the complicated encryption and decryption operations. NTRU is an efficient public-key cryptosystem. In this paper, we first generalize NTRU and propose a group-based NTRU-like public-key cryptosystem, namely GTRU. Then, we construct high-performance GTRU for IoT. Finally, security analysis shows that our proposed GTRU for IoT is more secure than NTRU against lattice-based attacks.

A Review on Heuristics for Addition Chain Problem: Towards Efficient Public Key Cryptosystems

Field exponentiation and scalar multiplication are the pillars of and the most computationally expensive operations in the public key cryptosystems. Optimizing the operation is the key to the efficiency of the systems. Analogous to the optimization is solving addition chain problem. In this study, we survey from the onset of the addition chain problem to the state-of-the-art heuristics for optimizing it, with the view to identifying fundamental issues that when addressed renders the heuristics most optimal mean of minimizing the two operations in various public key cryptosystems. Thus, our emphasis is specifically on the heuristics: Their various constraints and implementations efficiencies. We present possible ways forwards toward the optimal solution for the addition chain problem that can be efficiently applied for optimal implementation of the public key cryptosystems.

Multivariate Cryptography Based on Clipped Hopfield Neural Network.

Designing secure and efficient multivariate public key cryptosystems [multivariate cryptography (MVC)] to strengthen the security of RSA and ECC in conventional and quantum computational environment continues to be a challenging research in recent years. In this paper, we will describe multivariate public key cryptosystems based on extended Clipped Hopfield Neural Network (CHNN) and implement it using the MVC (CHNN-MVC) framework operated in space. The Diffie-Hellman key exchange algorithm is extended into the matrix field, which illustrates the feasibility of its new applications in both classic and postquantum cryptography. The efficiency and security of our proposed new public key cryptosystem CHNN-MVC are simulated and found to be NP-hard. The proposed algorithm will strengthen multivariate public key cryptosystems and allows hardware realization practicality.

A new cryptosystem using generalized Mersenne primes

In this paper we introduce a secure and efficient public key cryptosystem using generalized Mersenne primes based on two hard problems: the cubic root extraction modulo a composite integer and the discrete logarithm problem (DLP). These two problems are combined during the key generation, encryption and decryption phases. To break the scheme, an attacker has to solve the cubic root computation and the DLP separately which is computationally infeasible.

An efficient and practical public key cryptosystem with CCA-security on standard model

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.

A factoring and discrete logarithm based cryptosystem

This paper introduces a new public key cryptosystem based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli) and the discrete logarithm problem. These two hard problems are combined during the key generation, encryption and decryption phases. By combining the IFP and the DLP we introduce a secure and efficient public key cryptosystem. To break the scheme, an adversary may solve the IFP and the DLP separately which is computationally infeasible. The key generation is a simple operation based on the discrete logarithm modulo a composite moduli. The encryption phase is based both on the cube root computation and the DLP. These operations are computationally efficient.

Poly-Dragon: an efficient multivariate public key cryptosystem

In this paper we propose an efficient multivariate public key cryptosystem. Public key of our cryptosystem contains polynomials of total degree three in plaintext and ciphertext variables, two in plaintext variables and one in ciphertext variables. However, it is possible to reduce the public key size by writing it as two sets of quadratic multivariate polynomials. The complexity of encryption in our public key cryptosystem is O(n), where n is bit size, which is equivalent to other multivariate public key cryptosystems. For decryption we need only four exponentiations in the binary field. Our Public key algorithm is bijective and can be used for encryption as well as for signatures.

On Patarin's Attack against the <i>l</i>IC Scheme

In 2007, Ding et al. proposed an attractive scheme, which is called the l-Invertible Cycles (lIC) scheme. lIC is one of the most efficient multivariate public-key cryptosystems (MPKC); these schemes would be suitable for using under limited computational resources. In 2008, an efficient attack against lIC using Grobner basis algorithms was proposed by Fouque et al. However, they only estimated the complexity of their attack based on their experimental results. On the other hand, Patarin had proposed an efficient attack against some multivariate public-key cryptosystems. We call this attack Patarin's attack. The complexity of Patarin's attack can be estimated by finding relations corresponding to each scheme. In this paper, we propose an another practical attack against the lIC encryption/signature scheme. We estimate the complexity of our attack (not experimentally) by adapting Patarin's attack. The attack can be also applied to the lIC- scheme. Moreover, we show some experimental results of a practical attack against the lIC/lIC- schemes. This is the first implementation of both our proposed attack and an attack based on Grobner basis algorithm for the even case, that is, a parameter l is even.

Fast public-key encryption scheme based on Chinese remainder theorem

Traditional public-key cryptosystems suffer from a relatively low encryption/decryption speed, which hampers their applications in resource-constrained environments. A fast public-key cryptosystem is proposed to remedy this drawback. The new algorithm uses Chinese remainder theorem to hide the trapdoor information. The encryption of the system only carries out several modular multiplication operations, and the decryption only needs a modular multiplication and a low-dimensional matrixvector multiplication, which makes the speed of the encryption and the decryption of the scheme very high. The security of the system is based on two difficult number-theoretic problems. The attacker has to solve the integer factorization problem and the simultaneous Diophantine approximation problem simultaneously to recover the secret key from the public key. The proposed cryptosystem is also shown to be secure against lattice attack. The analysis shows that the encryption algorithm is a secure, fast and efficient public-key cryptosystem.

A More Compact Representation of XTR Cryptosystem

XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup Fq2 of extension field Fq6, so that the compression ratio of XTR cryptosystem is 1/3. On the other hand, Dijk et al. proposed an efficient public-key cryptosystem using a torus over Fq30 whose compression ratio is 4/15. It is an open problem to construct an efficient public-key cryptosystem whose compression ratio is smaller than 4/15. In this paper we propose a new variant of XTR cryptosystem over finite fields with characteristic three whose compression ratio is 1/6. The key observation is that there exists a trace map from Fq6 to Fq in the case of characteristic three. Moreover, the cost of compression and decompression algorithm requires only about 1% overhead compared with the original XTR cryptosystem. Therefore, the proposed variant of XTR cryptosystem is one of the fastest public-key cryptosystems with the smallest compression ratio.

Compression in Finite Fields and Torus-Based Cryptography

We present efficient compression algorithms for subgroups of multiplicative groups of finite fields, we use our compression algorithms to construct efficient public key cryptosystems called $\T_2$ and CEILIDH, we disprove some conjectures, and we use the theory of algebraic tori to give a better understanding of our cryptosystems, the Lucas-based, XTR, and Gong–Harn cryptosystems, and conjectured generalizations.

Elliptic curve scalar multiplication algorithm using complementary recoding

Elliptic curve based cryptosystem is an efficient public key cryptosystem, which is more suitable for limited environments. The very expensive operation in elliptic curve based cryptographic protocol is the scalar multiplication. In this paper, scalar multiplication using complementary recoding method is proposed. The intermediate operations carried out in conversion are less than the other existing scalar multiplication algorithm. The efficiency of our proposed method is tested and found that our method is an efficient than the other methods.

Utilisation des modules de Drinfeld en cryptologie

We present in this Note a new and efficient public-key cryptosystem based on Drinfeld modules. The details will appear elsewhere. To cite this article: R. Gillard et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Efficient probabilistic public-key cryptosystem based on the diffie-hellman problem

An efficient probabilistic public-key cryptosystem based on the Diffie-Hellman problem is proposed. The new scheme is similar to the Elgamal public-key cryptosystem (1985), but is more efficient than Elgamal's scheme in its transmission efficiency and computational complexity.