Hellman Protocol Research Articles

Advance in Applied Cryptography Theory: Survey and New Results. Part 1. Key Cryptography

In the current paper, consisting from two parts, are presented both results already published before (but hard for access) and new once. Actuality of this work is firstly in a fact that recently has been obtained a number of new results in area of applied cryptography that are needed both in a clarification and be put into practice. This is namely the main goal of the current paper. The setting problem in the first paper part concerns to a complexity of symmetric cipher breaking while in the second part of the paper is discussed, so called, keyless cryptography, namely: wiretap channel concept, execution of communication channels which allow to provide information security without of key exchange procedure between legal correspondences. In the part widely used methods of applied mathematics, namely: algebra, number, probability and information theories. Computer simulation also used there. A novelty of the first part of work consists in the following: first of all it is clarified the sense of a key lifetime limitation for different symmetric cipher modes, secondly, it is explained an approach of cipher breaking by the use of quantum computers, finely, the key authentication for the Diffie ‒ Hellman protocol based on the mobile device pairing technology is investigated in detail. In the second part of the current paper has been presented a vulnerability of Dean ‒ Goldsmith cryptosystem under some extension of attacks. The main results of this paper are: estimation of the key lifetime of single key for symmetric cipher in CBC mode, clarifying of Grover’s algorithm breaking of symmetric ciphers by brute force attack, development of a method for authentication of Diffie ‒ Hellman values based on pre-distributed sequences, selection of ciphers which allow to execute with Shamir’s protocol without any key sharing in advance, breaking of Dean ‒ Goldsmith protocol under some conclusions, proof the fact regarding of a possible breakability of the key sharing protocol over noiseless communication channels. Practical application of paper results consists in the fact of stimulation the correct choice of ciphers and their parameters in order to provide their resistance to different attacks and more attention to algorithms of keyless cryptography.

Quaternary Tree Group Diffie- Hellman Based Group Key Management Protocol for Dynamic Peer Groups

Diffie-Hellman (DH) protocol for 2-party has made the key exchange to be simple yet powerful. It is widely used in many communication-oriented protocols for establishing the keys in public communication channels. With millions of internet users connected globally and using various group oriented applications, communication among them has to be in a secured manner. Due to its simplicity, DH has been further extended to group setting and number of protocols are developed. Establishing Group Key and regenerating it during membership changes is a challenging task in communication among large groups. This paper proposes a quaternary tree method that uses the key tree concept and Group Diffie Hellman protocol, GDH.3 to establish the common key. GDH.3, an extension of DH for n parties is best suited for large dynamic groups. Quaternary tree reduces the height almost by half as against binary trees, making the rekeying much easier. As the group size increases, GDH.3 outperforms other existing group protocols based on DH, since it requires much lesser number of exponentiations.

Securing Data Exchange with Elliptic Curve Cryptography: A Novel Hash-Based Method for Message Mapping and Integrity Assurance

To ensure the security of sensitive data, elliptic curve cryptography (ECC) is adopted as an asymmetric method that balances security and efficiency. Nevertheless, embedding messages into elliptic curve (EC) points poses a significant challenge. The intricacies of this process can greatly affect the overall security and efficiency of the cryptosystem, reflecting security vulnerabilities observed in many existing schemes that utilize ElGamal ECC-based encryption. In this paper, we introduce an innovative hash-based technique for securely embedding messages into EC points before encryption. A random parameter and a shared secret point generated through the EC Diffie–Hellman protocol are used to bolster the scheme’s security. The security of the proposed method is evaluated against various attack models; moreover, the complexity, and sensitivity of the encryption scheme, as well as its inputs, are analyzed. The randomness assessment of the ciphertext was performed using the NIST statistical test suite. Additionally, we propose a mechanism to ensure the integrity of the message by securely appending a tag to the ciphertext. As a consequence, a comprehensive analysis of our scheme demonstrates its effectiveness in maintaining data security and integrity against various attack models. The algorithm also meets more criteria such as the strict avalanche criterion, linear complexity, and operability.

A Hybrid Cryptosystem Incorporating a New Algorithm for Improved Entropy.

Today, safeguarding sensitive content through encryption is crucial. This work presents a hybrid cryptosystem for images that employs both asymmetric and symmetric encryption. The asymmetric component involves applying the Diffie-Hellman protocol and the ElGamal cryptosystem to securely transmit two constants. These constants are necessary for the symmetrical aspect to generate dynamic permutations, substitution boxes, and round keys. Following an encryption process with fourteen rounds, the encrypted images are processed by an algorithm proposed to enhance entropy, a critical metric for assessing encryption quality. It increases the frequencies of the basic colors to achieve a histogram closely resembling a uniform distribution, but it increases the image size by approximately 8%. This improves the entropy values achieved by the hybrid cryptosystem, bringing them remarkably close to the ideal value of 8.0. In specific instances, the entropy values were elevated from 7.99926 to 8.0. The proposed method exhibits resilience against various attacks, including differential, linear, brute force, and algebraic attacks, as evaluated through the entropy, correlation, goodness of fit, Discrete Fourier Transform (DFT), Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Avalanche Criteria (AC), contrast, energy, and homogeneity. Further, encrypted images are subjected to noise attacks ranging from 20% to 50% noise, including additive, multiplicative, occlusion noise, as well as the newly introduced χ2 noise. The noise damage is quantified using the proposed Similarity Parameter (SP), and a 3 × 3 median filter is employed to enhance the visual quality.

Advancing IoT Device Security in Smart Cities: Through Innovative Key Generation and Distribution With D_F, Gf, and Multi-Order Recursive Sequences

In today's mass communication landscape, security is a paramount concern, notably with the rapid expansion of the Internet of Things (IoT). Various methods aim to bolster IoT communication security, particularly by regulating access between IoT devices and networks. Encrypting data with a shared secret key is crucial, considering the limited capabilities of these devices, demanding a lightweight yet robust control mechanism. While traditional methods like Diffie-Hellman facilitated secure communication, vulnerabilities arose from modular and exponential equations. Our paper proposed a mathematical refinement of the Diffie Hellman (D_H) protocol. By leveraging GF finite fields and multi-order recursive sequences, this enhanced method aims to fortify confidentiality and complexity in exchanged keys, enabling secure data transmission while remaining efficient for resource restricted IoT devices. Validation using the Affine encryption method demonstrates considerable improvements in complexity, security, and speed. Incorporating Galois field (GF) and third-order sequencing enhances secrecy and complexity, ensuring swift computational processes.

Extended Diffie Hellman Protocol Based on Exponential and Multiplication Operation Over Modular Arithmetic

Extended Diffie Hellman Protocol Based on Exponential and Multiplication Operation Over Modular Arithmetic

Latin-Square-Based Key Negotiation Protocol for a Group of UAVs

Unmanned aerial vehicle mobile ad hoc networks (UAVMANETs) formed by multi-UAV self-assembling networks have rapidly developed and been widely used in many industries in recent years. However, UAVMANETs suffer from the problems of complicated key negotiations and the difficult authentication of members’ identities during key negotiations. To address these problems, this paper simplifies the authentication process by introducing a Latin square to improve the process of signature aggregation in the Boneh–Lynn–Shacham (BLS) signature scheme and to aggregate the keys negotiated via the elliptic-curve Diffie–Hellman (ECDH) protocol into new keys. As shown through security analysis and simulations, this scheme improves the efficiency of UAVMANET authentication and key negotiation while satisfying security requirements.

A Dynamic Hybrid Cryptosystem Using Chaos and Diffie–Hellman Protocol: An Image Encryption Application

Images with sensitive content require encryption for storage and transmission. Symmetric schemes can cipher them, while an asymmetric cryptosystem can distribute the secret key safely. For this reason, we propose a dynamic hybrid cryptosystem, which ciphers images and transfers its private keys. It has a symmetric algorithm that applies the Lorenz equations for generating different boxes and permutations in every encryption process and round. Since the secret key concatenates two private numbers, an asymmetric algorithm is included for its key distribution. The proposal uses the Diffie–Hellman protocol with ElGamal for obtaining a seed and building 128 strings. Then, the SHA-512 is applied in each of them a number of times associated with the secret key value in its blockchain representation. The resultant strings are concatenated to conform to the public key. Finally, the tests indicate that the cryptosystem resists differential, linear, algebraic, and brute-force attacks. Its cipher quality is high according to the entropy, correlation, DFT, NPCR, UACI, AC, texture analysis, and goodness of fit test. Additionally, occlusion, additive, multiplicative, and the proposed χ2 noise attacks are simulated on encrypted images. Finally, the sharpness loss is measured with the Similarity Parameter and improved with a filter 5 × 5.

A Coprocessor Architecture for 80/112-bit Security Related Applications

We have proposed a flexible coprocessor key-authentication architecture for 80/112-bit security-related applications over field by employing Elliptic-curve Diffie Hellman (ECDH) protocol. Towards flexibility, a serial input/output interface is used to load/produce secret, public, and shared keys sequentially. Moreover, to reduce the hardware resources and to achieve a reasonable time for cryptographic computations, we have proposed a finite field digit-serial multiplier architecture using combined shift and accumulate techniques. Furthermore, two finite-state-machine controllers are used to perform efficient control functionalities. The proposed coprocessor architecture over and is programmed using Verilog and then implemented on Xilinx Virtex-7 FPGA (field-programmable-gate-array) device. For and , the proposed flexible coprocessor use 1351 and 1789 slices, the achieved clock frequency is 250 and 235 MHz, time for one public key computation is 40.50 and 79.20 μs and time for one shared key generation is 81.00 and 158.40 μs. Similarly, the consumed power over and is 0.91 and 1.37 mW, respectively. The proposed coprocessor architecture outperforms state-of-the-art ECDH designs in terms of hardware resources.

Signed (Group) Diffie–Hellman Key Exchange with Tight Security

We propose the first tight security proof for the ordinary two-message signed Diffie–Hellman key exchange protocol in the random oracle model. Our proof is based on the strong computational Diffie–Hellman assumption and the multiuser security of a digital signature scheme. With our security proof, the signed DH protocol can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate any security loss. We abstract our approach with a new notion called verifiable key exchange. In contrast to a known tight three-message variant of the signed Diffie–Hellman protocol (Gjøsteen and Jager, in: Shacham, Boldyreva (eds) CRYPTO 2018, Part II. LNCS, Springer, Heidelberg, 2018), we do not require any modification to the original protocol, and our tightness result is proven in the “Single-Bit-Guess” model which we know can be tightly composed with symmetric cryptographic primitives to establish a secure channel. Finally, we extend our approach to the group setting and construct the first tightly secure group authenticated key exchange protocol.

Torsion point attacks on ‘SIDH‐like’ cryptosystems

AbstractIsogeny‐based cryptography is a promising approach for post‐quantum cryptography. The best‐known protocol following that approach is the supersingular isogeny Diffie–Hellman protocol (SIDH); this protocol was turned into the CCA‐secure key encapsulation mechanism SIKE, which was submitted to and remains in the third round of NIST's post‐quantum standardisation process as an ‘alternate’ candidate. Isogeny‐based cryptography generally relies on the conjectured hardness of computing an isogeny between two isogenous elliptic curves, and most cryptanalytic work referenced on SIKE's webpage exclusively focusses on that problem. Interestingly, the hardness of this problem is sufficient for neither SIDH nor SIKE. In particular, these protocols reveal additional information on the secret isogeny, in the form of images of specific torsion points through the isogeny. This paper surveys existing cryptanalysis approaches exploiting this often called ‘torsion point information’, summarises their current impact on SIKE and related algorithms, and suggests some research directions that might lead to further impact.

LPsec: a fast and secure cryptographic system for optical connections

High capacity and low latency of optical connections are ideal for supporting current and future communication services, including 5G and beyond. Although some of those services are already secured at the packet layer using standard stream ciphers, like the Advanced Encryption Standard and ChaCha, secure transmission at the optical layer is still not implemented. To secure the optical layer, cryptographic methods need to be fast enough to support high-speed optical transmission and cannot introduce significant delay. Moreover, methods for key exchange, key generation, and key expansion are required, which can be implemented on standard coherent transponders. In this paper, we propose Light Path SECurity (LPsec), a secure cryptographic solution for optical connections that involves fast data encryption using stream ciphers and key exchange using Diffie–Hellman protocol through the optical channel. To support encryption of high-speed data streams, a fast, general-purpose pseudorandom number generator is used. Moreover, to make the scheme more secure against exhaustive search attacks, an additional substitution cipher is proposed. In contrast to the limited encryption speeds that standard stream ciphers can support, LPsec can support high-speed rates. Numerical simulation for 16 quadrature amplitude modulation (QAM), 32-QAM, and 64-QAM show that LPsec provides a sufficient security level while introducing only negligible delay.

Multiple RGB images encryption algorithm based on elliptic curve, improved Diffie Hellman protocol

Multiple RGB images encryption algorithm based on elliptic curve, improved Diffie Hellman protocol

Blockchain-based cross-user data shared auditing

In cloud storage, public auditing is a more popular data integrity verification technique since it allows users to delegate auditing tasks to a fully trusted third-party auditor (TPA). However, it is difficult to find such a TPA in practical application. Besides, the centralised auditing model makes TPA have to bear burdensome work pressure, which limits the practicability of existing schemes. In this paper, we firstly proposed a blockchain-based generalised shared auditing mechanism BCSA in the cross-user scenario, which aims at achieving available public auditing with a non-fully trusted TPA, and reducing the user's auditing fees and TPA's work pressure by allowing data users to share their auditing procedure with others. Furthermore, we initialise a concrete construction BCSAD with Diffie–Hellman protocol for the cross-user auditing scenario with different data. Likewise, we also propose a novel construction BCSAI for the cross-user auditing scenario with identical data, which utilises a password-authenticated key exchange (PAKE) protocol to achieve shared auditing and ciphertext deduplication, reducing data storage and auditing fees for data users and alleviating service pressure on the cloud server and TPA. Security and performance analysis evaluate the practicability of the proposed scheme.

Some results of development of cryptographic transformations schemes using non-abelian groups

Implementation of a successful attack on classical public key cryptosystems becomes more and more real with the advent of practical results in the implementation of Shor's and Grover's algorithms on quantum computers. Modern results in tackling the problem of building a quantum computer of sufficiently power justify the need to revise the existing approaches and determine the most effective in terms of solving problems of post-quantum cryptography. One of these promising research priorities is the study of the cryptosystems based on non-abelian groups.
 The problems of conjugacy search, membership search, and others are difficult to solve in the theory of non-abelian groups and are the basis for building provably secure public key cryptosystems. This paper gives an overview of the most frequently discussed algorithms using non-abelian groups: matrix groups braid groups, semi direct products, and algebraic erasers (AE). The analysis of the construction of encryption and decryption schemes, key establishment mechanisms is given. Many non-abelian group-based key establishment protocols are associated with the Diffie – Hellman (DH) protocol. The paper analyzes the properties of non-abelian group public key encryption schemes. Various cryptographic primitives using non-commutative groups as a basis for post-quantum schemes are considered.

CE-SKE: cost-effective secure key exchange scheme in Fog Federation

Security in cyberspace has become an important problem in the modern world. Security threats are a disadvantage for jobbers on cloud computing, thus using different levels of information security in different contexts, is required more than ever. In distributed systems, encryption and key exchange are used to create security. The Diffie–Hellman protocol is one of the first methods, which allows the users, two people or two organizations, to create a shared key without any prior knowledge and exchange it through an insecure communication path. This research shows that the Diffie–Hellman protocol is vulnerable to active and passive attacks. We have provided a secure key Exchange scheme Based on the Diffie–Hellman for Fog Federation. The scheme is then compared with other protocols in terms of security requirements, and the Automated Validation of Internet Security Protocols and Applications (AVISPA) tool is used for security analysis. The results show that the scheme is safe against active and passive attacks and has a low communication cost and a medium computation cost compared to other protocols.

A quantum key distribution on qudits using quantum operators

Cryptography is processing for securing communication between two people. The opponent wants to know the message that is encrypted using a secret key. Although the opponent can eavesdrop the message sent between the sender and the receiver, the opponent is unable to decrypt to read the message. Therefore, the secret key is very important. The sender and the receiver agree with the secret key in an insecure channel by using key distribution protocol such as the Diffie–Hellman protocol. Since quantum computer is coming soon, Diffie–Hellman protocol is not secure. We will develop a quantum key distribution protocol. The benefit of the quantum system is the quantum state that cannot copy by no‐cloning theorem. Thus, the opponent does not copy and keeps the message that is quantum. In this paper, a novel quantum key distribution protocol between two people (Alice and Bob) based on quantum operators is developed. The opponent (Eve) wants to know the secret key. Although Eve knows this quantum key distribution protocol, Eve does not behave similarly to Alice and Bob. For example, Eve eavesdrops Alice's quantum state that was sent to Bob, and Eve sends another quantum state. Therefore, we cannot control Eve's behavior. So we give the upper bound of mutual information between the user and opponent by using Holevo's bound. We verify the usual security definition for quantum key distribution that is equality‐and‐uniformity and privacy in the mutual information sense.

LUT‐based high‐speed point multiplier for Goldilocks‐Curve448

Recent studies have shown that existing elliptic curve-based cryptographic standards provide backdoors for manipulation and hence compromise the security. In this regard, two new elliptic curves known as Curve448 and Curve25519 are recently recommended by IETF for transport layer security future generations. Hence, cryptosystems built over these elliptic curves are expected to play a vital role in the near future for secure communications. A high-speed elliptic curve cryptographic processor (ECCP) for the Curve448 is proposed in this study. The area of the ECCP is optimised by performing different modular operations required for the elliptic curve Diffie–Hellman protocol through a unified architecture. The critical path delay of the proposed ECCP is optimised by adopting the redundant-signed-digit technique for arithmetic operations. The segmentation approach is introduced to reduce the required number of clock cycles for the ECCP. The proposed ECCP is developed using look-up-tables (LUTs) only, and hence it can be ported to any field-programmable gate array family or standard ASIC libraries. The authors' ECCP design offers higher speed without any significant area overhead to recent designs reported in the literature.

An Alternative Diffie-Hellman Protocol

The Diffie–Hellman protocol, ingenious in its simplicity, is still the major solution in protocols for generating a shared secret in cryptography for e-trading and many other applications after an impressive number of decades. However, lately, the threat from a future quantum computer has prompted successors resilient to quantum computer-based attacks. Here, an algorithm similar to Diffie–Hellman is presented. In contrast to the classic Diffie–Hellman, it involves floating point numbers of arbitrary size in the generation of a shared secret. This can, in turn, be used for encrypted communication based on symmetric cyphers. The validity of the algorithm is verified by proving that a vital part of the algorithm satisfies a one-way property. The decimal part is deployed for the one-way function in a way that makes the protocol a post-quantum key generation procedure. This is concluded from the fact that there is, as of yet, no quantum computer algorithm reverse engineering the one-way function. An example illustrating the use of the protocol in combination with XOR encryption is given.

FPGA implementation of a wireless sensor node with built-in security coprocessors for secured key exchange and data transfer

The technological advances in wireless sensor nodes and the appearance of the Internet of Things (IoT) concept have reinforced interest in wireless sensor networks (WSN), as one of the basic elements, the IoT relies on Bhoyar et al. (2019) [1]. However, the security of data exchanged between nodes, which are susceptible to several types of attack, is still one of the challenges WSNs face. The aim of this work is to design and implement, in a field-programmable gate array (FPGA) circuit, a wireless sensor node with some customised built-in coprocessors to make data transfer and key-exchange operations secure and, especially, faster. These coprocessors allow us to establish secure communication using symmetric and asymmetric cryptography. In addition, we implement a reliable key-exchange protocol, to authenticate a new node before sharing the symmetric encryption key with it. This key exchange is based on the Diffie Hellman protocol, and enhanced with a lightweight defence mechanism against man-in-the-middle (MITM) attacks. The implemented security coprocessors are: the Advanced Encryption Standard (AES-128), to perform the symmetric cryptography; elliptic-curve cryptography (ECC-163), to perform elliptic-curves operations for asymmetric cryptography; and a secure hash algorithm (SHA-256), to perform a hash function that can be used for digital signature, authentication, and random-keys generation. All these coprocessors are supervised by the soft-core processor MicroBlaze. The hardware implementation of these algorithms makes their execution times shorter, which allows us to reduce the time needed for key exchange significantly to less than 12 ms and to accelerate the data encryption. The developed wireless node is equipped with the nRF24L01 + 2.4 GHz transceiver module, implemented and tested in an Artix-7 XC7A35T FPGA with a maximum resources consumption of less than 55%.