Public Key Exchange Protocols Research Articles

Public key exchange protocols based on tropical lower circulant and anti circulant matrices

<abstract><p>In recent years, many efficient key exchange protocols have been proposed based on matrices over the tropical semirings. The tropical addition of two elements is the minimum of the elements, while the tropical multiplication is the sum of the two elements. This paper proposes a novel key exchange protocol based on the min-plus semiring ($ \mathbb{Z}\cup\{\infty\}, \oplus, \otimes $) by introducing anti-$ s $-$ p $-circulant matrices, which forms a commutative subset of $ M_{n \times n}(\mathbb{Z}\cup \{\infty\}) $. We have given further analysis of the protocol in detail using upper or lower-$ s $-circulant matrices. Additionally, we prove that the set of all lower-$ s $-circulant matrices is a sub-semiring of the tropical semiring $ M_{n \times n}(\mathbb{Z}\cup \{\infty\}) $. We discuss the detailed security analysis of the protocol with upper or lower-$ s $-circulant matrices and provide cryptographic algorithms for both key exchange protocols with detailed explanations. We compare the protocol based on upper or lower-$ s $-circulant matrices and our proposed protocol in terms of time complexity and memory usage. Finally, we analyse the security and show that our protocol is safe against popular attacks of tropical key exchange protocols. The security of these protocols relies on the difficulty of solving tropical non-linear equations.</p></abstract>

MAKE: A matrix action key exchange

Abstract We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z p {{\mathbb{Z}}}_{p} . One of the (semi)groups is additive, and the other one is multiplicative. This allows us to take advantage of both operations on matrices to diffuse information. We note that in our protocol, no power of any matrix or of any element of Z p {{\mathbb{Z}}}_{p} is ever exposed, so standard classical attacks on Diffie–Hellman-like protocols are not applicable.

Neural synchronization of optimal structure-based group of neural networks

In this paper, a neural synchronization of the optimal structure-based group of neural networks is proposed. Asymmetric cryptography is widely used to generate a key amongst two parties and to exchange the key through an insecure channel. However, since the methods that used this strategy, like RSA, have been compromised, new methods for producing a key that can offer security must be discovered. A new group of cryptography known as neural cryptography was created to solve this issue. The primary aim of neural cryptography is to produce a secret key over an unreliable medium. The optimal neural network architecture for creating and defining a secret key between the two authorized individuals is examined in this article. Furthermore, studies into the coordination of a group of neural networks are uncommon. For the design of the public key exchange protocol, synchronization of a cluster of neural networks with Three Layer Tree Parity Machine (TLTPM) is proposed. To calculate the synchronization time, steps taken, and the number of times the attacking neural network could replicate the actions of the two accepted networks, more than 15 million simulations were run. Various parametric experiments have been conducted on the proposed methodology. Simulations of the approach show that it is correct, according to the results of the paper.

Chaos-Based Mutual Synchronization of Three-Layer Tree Parity Machine: A Session Key Exchange Protocol Over Public Channel

In this paper, a chaos-based triple-layer tree parity machine (TLTPM)-guided neural synchronization has been proposed for the development of the public key exchange protocol. A special neural network structure called tree parity machine (TPM) is used for neural synchronization. Two TPMs accept the common input and different weight vectors and update the weights using the neural learning rule by exchanging their output. In some steps, it results in complete synchronization, and the weights of the two TPMs become identical. These identical weights serve as a secret key. There is, however, hardly any investigation to investigate the randomness of the common input vector used in the synchronization process. In this paper, logistic chaos system-based TLTPM is proposed. For faster synchronization, this proposed TLTPM model uses logistic chaos-generated random common input vector. This proposed TLTPM model is faster and has better security than TPM with the same input, output, and hidden neurons. This proposed technique has been passed through a series of parametric tests. The results have been compared with some recent techniques. The results of the proposed technique have shown effective and robust potential.

Neural cryptography using optimal structure of neural networks

The asymmetric cryptography method is typically used to transfer the key via an insecure channel while creating a key between two parties. However, since the methods using this strategy, like RSA, are now breached, new strategies must be sought to generate a key that can provide security. To solve this issue, a new group of cryptography was created known as neural cryptography. The main objective of this neural cryptography is to create a secret key using an unsafe medium. This paper suggests an overview of the optimal configuration of the neural network that enables the generation and establishment of a secret key between the two approved entities. Synchronization of two neural networks with three hidden layers is proposed for the development of the public key exchange protocol. Over 15 million simulations were carried out to measure the synchronization time, the steps taken as well as the number of times the assaulting neural network can replicate the behavior of the two authorized networks. The proposed technique has been passed through different parametric tests. Simulations of the process show effectiveness in terms of cited results in the paper.

Generative adversarial network guided mutual learning based synchronization of cluster of neural networks

Neural synchronization is a technique for establishing the cryptographic key exchange protocol over a public channel. Two neural networks receive common inputs and exchange their outputs. In some steps, it leads to full synchronization by setting the discrete weights according to the specific rule of learning. This synchronized weight is used as a common secret session key. But there are seldom research is done to investigate the synchronization of a cluster of neural networks. In this paper, a Generative Adversarial Network (GAN)-based synchronization of a cluster of neural networks with three hidden layers is proposed for the development of the public-key exchange protocol. This paper highlights a variety of interesting improvements to traditional GAN architecture. Here GAN is used for Pseudo-Random Number Generators (PRNG) for neural synchronization. Each neural network is considered as a node of a binary tree framework. When both i-th and j-th nodes of the binary tree are synchronized then one of these two nodes is elected as a leader. Now, this leader node will synchronize with the leader of the other branch. After completion of this process synchronized weight becomes the session key for the whole cluster. This proposed technique has several advantages like (1) There is no need to synchronize one neural network to every other in the cluster instead of that entire cluster can be able to share the same secret key by synchronizing between the elected leader nodes with only logarithmic synchronization steps. (2) This proposed technology provides GAN-based PRNG which is very sensitive to the initial seed value. (3) Three hidden layers leads to the complex internal architecture of the Tree Parity Machine (TPM). So, it will be difficult for the attacker to guess the internal architecture. (4) An increase in the weight range of the neural network increases the complexity of a successful attack exponentially but the effort to build the neural key decreases over the polynomial time. (5) The proposed technique also offers synchronization and authentication steps in parallel. It is difficult for the attacker to distinguish between synchronization and authentication steps. This proposed technique has been passed through different parametric tests. Simulations of the process show effectiveness in terms of cited results in the paper.

Secure exchange of information using artificial intelligence and chaotic system guided neural synchronization

In this paper, a chaos-based neural synchronization has been proposed for the development of the public-key exchange protocol. A special neural network structure called Tree Parity Machine (TPM) is used for neural synchronization. Two TPMs accept the common input and different weight vector and update the weights using neural learning rule by exchanging their output. In some steps, it results in complete synchronization, and the weights of the two TPMs become identical. These identical weights serve as a secret key. There is, however, hardly some investigation to investigate the randomness of the common input vector used in the synchronization process. In this paper, logistic Chaos system based Tree Parity Machine (CTPM) is proposed. For faster synchronization, this proposed CTPM model uses logistic chaos generated random common input vector. This proposed CTPM model is faster and has better security than TPM with the same input, output, and hidden neurons. This proposed technique has been passed through a series of parametric tests. The results have been compared with some recent techniques. The results of the proposed technique have shown effective and robust potential.

Neural Cryptography Based on Generalized Tree Parity Machine for Real-Life Systems

Traditional public key exchange protocols are based on algebraic number theory. In another perspective, neural cryptography, which is based on neural networks, has been emerging. It has been reported that two parties can exchange secret key pairs with the synchronization phenomenon in neural networks. Although there are various models of neural cryptography, called Tree Parity Machine (TPM), many of them are not suitable for practical use, considering efficiency and security. In this paper, we propose a Vector-Valued Tree Parity Machine (VVTPM), which is a generalized architecture of TPM models and can be more efficient and secure for real-life systems. In terms of efficiency and security, we show that the synchronization time of the VVTPM has the same order as the basic TPM model, and it can be more secure than previous results with the same synaptic depth.

A closer look at the tropical cryptography

We examine two recently proposed public key exchange protocols that are based upon tropical matrix algebras. We observe the first protocol to exhibit a pattern. We introduce a fast attack on the first protocol that exploits this pattern to extract a private parameter of the protocol, and consequently the shared key, in seconds. We go on to show that the second protocol cannot be implemented as it is described in the proposal. The protocol is reliant on an operation being associative. We prove by counterexample that this operation is not associative.

Tropical cryptography II: Extensions by homomorphisms

We use extensions of tropical algebras as platforms for very efficient public key exchange protocols.

Crypto-Steganographic LSB-based System for AES-Encrypted Data

The purpose of this work is to increase the level of concealment of information from unauthorized access by pre-encrypting and hiding it in multimedia files such as images. A crypto-steganographic information protection algorithm with LSB-method was implemented. The algorithm hides AES pre-encrypted confidential information in the form of text or images into target containing image files. This method uses the concept of data concealing in the least significant pixel bits of the target image files. The proposed method relies on the use of Diffie-Hellman public key exchange protocol for securely exchanging the stego-key used for LSB as well as the public key used for encrypting the secret information. The algorithm ensures that the visual quality of the image remains unchanged, with no distortions perceived by the human eye. The algorithm also complicates the detection of concealed information embedded in the target image with use of PRNG as an enhancement for LSB. The proposed system scheme achieved competitive results. On an average, the system achieved a Peak Signal-to-Noise Ratio (PSNR) of 96.3 dB and a Mean Square Error (MSE) of 0.00408. The results obtained demonstrate that the proposed system offers high payload capabilities with immunity against visual degradation of resultant stego images.

Portable Implementation of Postquantum Encryption Schemes and Key Exchange Protocols on JavaScript-Enabled Platforms

Quantum computers have the potential to solve some difficult mathematical problems efficiently and thus will inevitably exert a more significant impact on the traditional asymmetric cryptography. The National Institute of Standards and Technology (NIST) has opened a formal call for the submission of proposals of quantum-resistant public-key cryptographic algorithms to set the next-generation cryptography standards. Compared to powerful machines with ample amount of hardware resources such as racks of servers and IoT devices, including the massive number of microcontrollers, smart terminals, and sensor nodes with limited computing capacity, should also have some postquantum cryptography features for security and privacy. To ensure the correct execution of encryption algorithms on any platforms, the portability of implementation becomes more important. As distinguished from C/C++, JavaScript is a popular cross-platform language that can be used for the web applications and some hardware platforms directly, and it could be one of the solutions of portability. Therefore, we investigate and implement several recent lattice-based encryption schemes and public-key exchange protocols including Lizard, ring-Lizard, Kyber, Frodo, and NewHope in JavaScript, which are the active candidates of postquantum cryptography due to their applicabilities and efficiencies. We show and compare the performance of our JavaScript implementation on web browsers, embedded device Tessel2, Android phone, and several JavaScript-enabled platforms on PC and Mac. Our work shows that implementing lattice-based cryptography on JavaScript-enabled platforms is achievable and results in desirable portability.

Cryptanalysis of Xinyu et al.'s NTRU-lattice based key exchange protocol

Xinyu et al. proposed a public key exchange protocol, which is based on the NTRU-lattice based cryptography. In this paper, we show that how Xinyu et al.'s NTRU-KE: A lattice based key exchange protocol can be broken, under the assumption that a man-in-the middle attack is used for extracting private keys of users who participated in the key exchange protocol.

On Frobenius groups of order q(q – 1)

In this article, we consider a Frobenius group G of order q(q – 1) whose Frobenius complement H is of order q, where q is a prime power. In this case, right loop structures on right transversals to H in G determine new kinds of algebraic structures termed as generalised right near domains and right near domains respectively. We also determine a reasonable lower bound of their non-isomorphic classes (with their explicit structures). In last section, we gave an idea of public key exchange protocol for right near domains.

Selective opening security of practical public‐key encryption schemes

The authors show that two well-known and widely employed public-key encryption schemes – RSA optimal asymmetric encryption padding (RSA-OAEP) and Diffie–Hellman integrated encryption scheme (DHIES), instantiated with a one-time pad, – are secure under (the strong, simulation-based security notion of) selective opening security against chosen-ciphertext attacks in the random oracle model. Both schemes are obtained via known generic transformations that transform relatively weak primitives (with security in the sense of one-wayness) to indistinguishability (IND)-CCA secure encryption schemes. The authors also show a similar result for the well-known Fujisaki–Okamoto transformation that can generically turn a one-way secure public key encryption system and a one-time pad into a IND-CCA-secure public-key encryption system. The authors prove that selective opening security comes for free in these transformations. Both DHIES and RSA-OAEP are important building blocks in several standards for public key encryption and key exchange protocols. The Fujisaki–Okamoto transformation is very versatile and has successfully been utilised to build efficient lattice-based cryptosystems. The considered schemes are the first practical cryptosystems that meet the strong notion of simulation-based selective opening (SIM-SO-CCA) security.

From semigroup action to homomorphic encryption and some related problems in cryptography

In some recent papers, the authors have showed some homomorphic cryptosystems which are particular cases of split exact sequences of groups. By connecting the relation between these ideas to the concept of group action, in this paper, we build a public key exchange protocol based on actions to a group, from its automorphism group and semigroup ℤ under usual multiplication.

Approach to design neural cryptography: A generalized architecture and a heuristic rule

Neural cryptography, a type of public key exchange protocol, is widely considered as an effective method for sharing a common secret key between two neural networks on public channels. How to design neural cryptography remains a great challenge. In this paper, in order to provide an approach to solve this challenge, a generalized network architecture and a significant heuristic rule are designed. The proposed generic framework is named as tree state classification machine (TSCM), which extends and unifies the existing structures, i.e., tree parity machine (TPM) and tree committee machine (TCM). Furthermore, we carefully study and find that the heuristic rule can improve the security of TSCM-based neural cryptography. Therefore, TSCM and the heuristic rule can guide us to designing a great deal of effective neural cryptography candidates, in which it is possible to achieve the more secure instances. Significantly, in the light of TSCM and the heuristic rule, we further expound that our designed neural cryptography outperforms TPM (the most secure model at present) on security. Finally, a series of numerical simulation experiments are provided to verify validity and applicability of our results.

Two-layer tree-connected feed-forward neural network model for neural cryptography

Neural synchronization by means of mutual learning provides an avenue to design public key exchange protocols, bringing about what is known as neural cryptography. Two identically structured neural networks learn from each other and reach full synchronization eventually. The full synchronization enables two networks to have the same weight, which can be used as a secret key for many subsequent cryptographic purposes. It is striking to observe that after the first decade of neural cryptography, the tree parity machine (TPM) network with hidden unit $K=3$ appears to be the sole network that is suitable for a neural protocol. No convincingly secure neural protocol is well designed by using other network structures despite considerable research efforts. With the goal of overcoming the limitations of a suitable network structure, in this paper we develop a two-layer tree-connected feed-forward neural network (TTFNN) model for a neural protocol. The TTFNN model captures the notion that two partners are capable of exchanging a vector with multiple bits in each time step. An in-depth study of the dynamic process of TTFNN-based protocols is then undertaken, based upon which a feasible condition is theoretically obtained to seek applicable protocols. Afterward, according to two analytically derived heuristic rules, a complete methodology for designing feasible TTFNN-based protocols is elaborated. A variety of feasible neural protocols are constructed, which exhibit the effectiveness and benefits of the proposed model. With another look from the perspective of application, TTFNN-based instances, which can outperform the conventional TPM-based protocol with respect to synchronization speed, are also experimentally confirmed.

Public key exchange using matrices over group rings

We offer a public key exchange protocol in the spirit of Diffie–Hellman, but we use (small) matrices over a group ring of a (small) symmetric group as the platform. This “nested structure” of the platform makes computation very efficient for legitimate parties. We discuss security of this scheme by addressing the Decision Diffie–Hellman (DDH) and Computational Diffie–Hellman (CDH) problems for our platform.

Network based Security model using Symmetric Key Cryptography (AES 256- Rijndael Algorithm) with Public Key Exchange Protocol (Diffie-Hellman Key Exchange Protocol)

The main aim of this paper is to strengthen secured communication over the Network by enhancing the strength of the AES algorithm with Diffie-Hellman key exchange Protocol. The Rijndael is a block cipher with variable block and key size is believed to provide much more security. The Rijndael with 128 bit block size is adopted as the Advanced Encryption Standard (AES) in 2001 and has become widely used in the bulk data encryption. The security strength of the AES algorithm can be enhanced by increasing the key length to 256 bit and thereby increasing the number of rounds in order to provide a stronger encryption method for secure communication. For the secured communication over network, AES can be more strengthen by Diffie-Hellman Key Exchange Protocol which allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel. Keywords: AES, Rijndael, Diffie-Hellman, Primitive root, MIM