Cryptographic Applications Research Articles

An efficient high throughput BCH module for multi-bits error correction mechanism on hardware platform

The bose-chaudhuri-hocquenghem (BCH) codes are a cyclic error correction codes (ECC) class. The BCH is constructed by using a polynomial over the Galois field. The BCH codes can detect and correct the multi-bits with an easy decoding mechanism. The BCH codes are used in most of the storage device's cryptography, disk drives, and satellite applications. This manuscript presents an efficient high-throughput BCH module with an encoding and decoding mechanism for multi-bit corrections. The BCH code of (15, k) is used to construct the encoder and decoder architectures. The BCH encoder decoder (ED) module with single error correction (SEC), double error correction (DEC), and triple-error correction (TEC) are discussed in detail. The BCH encoder module uses a linear feedback shift register (LFSR). The BCH decoder with SEC and DEC is constructed using the syndrome generator module (SGM) and chien search module (CSM). The BCH decoder with TEC is designed using SGM, inversion-based berlekamp-massey-algorithm (BMA), and CSMs. The BCH-ED module with SEC, DEC, and TEC utilizes <1 % chip area on Artix-7 FPGA. The BCH-ED with SEC, DEC, and TEC achieves a throughput of 7.13 Gbps, 1.2 Gbps, and 0.803 Gbps, respectively. Lastly, the BCH module is compared with existing BCH approaches with better improvement in chip area, frequency, and throughput parameters.

A Plasmonic Optoelectronic Resistive Random-Access Memory for In-Sensor Color Image Cryptography.

The optoelectronic resistive random-access memory (RRAM) with the integrated function of perception, storage and intrinsic randomness displays promising applications in the hardware level in-sensor image cryptography. In this work, 2D hexagonal boron nitride based optoelectronic RRAM is fabricated with semitransparent noble metal (Ag or Au) as top electrodes, which can simultaneous capture color image and generate physically unclonable function (PUF) key for in-sensor color image cryptography. Surface plasmons of noble metals enable the strong light absorption to realize an efficient modulation of filament growth at nanoscale. Resistive switching curves show that the optical stimuli can impede the filament aggregation and promote the filament annihilation, which originates from photothermal effects and photogenerated hot electrons in localized surface plasmon resonance of noble metals. By selecting noble metals, the optoelectronic RRAM array can respond to distinct wavelengthsand mimic the biological dichromatic cone cells to perform the color perception. Due to the intrinsic and high-quality randomness, the optoelectronic RRAM can produce a PUF key in every exposure cycle, which can be applied in the reconfigurable cryptography. The findings demonstrate an effective strategy to build optoelectronic RRAM for in-sensor color image cryptography applications.

Failing to Hash Into Supersingular Isogeny Graphs

Abstract An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of ‘hard supersingular curves’ that is equations for supersingular curves for which computing the endomorphism ring is as difficult as it is for random supersingular curves. A related open problem is to produce a hash function to the vertices of the supersingular $\ell $-isogeny graph, which does not reveal the endomorphism ring, or a path to a curve of known endomorphism ring. Such a hash function would open up interesting cryptographic applications. In this paper, we document a number of (thus far) failed attempts to solve this problem, in the hope that we may spur further research, and shed light on the challenges and obstacles to this endeavour. The mathematical approaches contained in this article include: (i) iterative root-finding for the supersingular polynomial; (ii) gcd’s of specialized modular polynomials; (iii) using division polynomials to create small systems of equations; (iv) taking random walks in the isogeny graph of abelian surfaces, and applying Kummer surfaces and (v) using quantum random walks.

Cryptographic Application of Elliptic Curve Generated through Centered Hexadecagonal Numbers

Background/Objectives: Elliptic Curve Cryptography (ECC) is a public-key encryption method that is similar to RSA. ECC uses the mathematical concept of elliptic curves to achieve the same level of security with significantly smaller keys, whereas RSA's security depends on large prime numbers. Elliptic curves and their applications in cryptography will be discussed in this paper. The elliptic curve is formed by the extension of a Diophantine pair of Centered Hexadecagonal numbers to a Diophantine triple with property D(8). Method: The Diffie–Hellman key exchange, named for Whitfield Diffie and Martin Hellman, was developed by Ralph Merkle and is a mathematical technique for safely transferring cryptographic keys over a public channel. Based on the Diffie–Hellman key exchange, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography. The generation of keys, encryption and decryption are the three main operations of the ElGamal cryptosystem. Findings: Given the relative modesty of our objectives, the fundamental algebraic and geometric characteristics of elliptic curves shall be delineated. Then the behaviour of elliptic curves modulo p: ultimately, there is a fairly strong analogy between the structure of the points on an elliptic curve modulo p and the integers modulo n will be studied. In the end, elliptic curve ElGamal encryption analogues of Diffie–Hellman key exchange will be created. Novelty: Elliptic curves are encountered in a multitude of mathematical contexts and have a varied and fascinating history. Elliptic curves are very significant in number theory and are a focus of much recent work. The earlier research works in Elliptic Curve Cryptography has concentrated on computer algorithms and pairing – based algorithms. In this paper, the concept of polygonal numbers and its extension from Diophantine pair to triples is encountered, thus forming an elliptic curve and perform the encryption-decryption process. MSC Classification Number: 11D09, 11D99,11T71,11G05. Keywords: Elliptic curves, Cryptography, Encryption, Decryption, Centered polygonal numbers

The boomerang uniformity of three classes of permutation polynomials over 𝔽2n

Permutation polynomials with low boomerang uniformity have wide applications in cryptography. In this paper, by utilizing the Weil sums technique and solving some certain equations over [Formula: see text], we determine the boomerang uniformity of these permutation polynomials: (1) [Formula: see text], where [Formula: see text], [Formula: see text] with [Formula: see text]; (2) [Formula: see text], where [Formula: see text], [Formula: see text] with [Formula: see text]; (3) [Formula: see text], where [Formula: see text], [Formula: see text] with [Formula: see text]. The results show that the boomerang uniformity of [Formula: see text], [Formula: see text] and [Formula: see text] can attain [Formula: see text].

Multi-key and Multi-input Predicate Encryption (for Conjunctions) from Learning with Errors

We put forward two natural generalizations of predicate encryption (PE), dubbed multi-key and multi-input PE. More in details, our contributions are threefold.Definitions. We formalize security of multi-key PE and multi-input PE following the standard indistinguishability paradigm, and modeling security both against malicious senders (i.e., corruption of encryption keys) and malicious receivers (i.e., collusions).Constructions. We construct adaptively secure multi-key and multi-input PE supporting the conjunction of poly-many arbitrary single-input predicates, assuming the sub-exponential hardness of the learning with errors (LWE) problem.Applications. We show that multi-key and multi-input PE for expressive enough predicates suffices for interesting cryptographic applications, including non-interactive multi-party computation (NI-MPC) and matchmaking encryption (ME). In particular, plugging in our constructions of multi-key and multi-input PE, under the sub-exponential LWE assumption, we obtain the first ME supporting arbitrary policies with unbounded collusions, as well as robust (resp. non-robust) NI-MPC for so-called all-or-nothing functions satisfying a non-trivial notion of reusability and supporting a constant (resp. polynomial) number of parties. Prior to our work, both of these applications required much heavier tools such as indistinguishability obfuscation or compact functional encryption.

A new 2D-HELS hyperchaotic map and its application on image encryption using RNA operation and dynamic confusion

Chaotic systems are commonly being researched for applications in cryptography. In this study, a novel chaotic two-dimensional hyperchaotic exponential adjusted Logistic and sine map (2D-HELS) is derived from the well-known two-dimensional Logistic map and Sine maps. The resulting chaotic system is demonstrated with the help of bifurcation diagram, chaos trajectories, Lyapunov exponent, sample entropy, permutation entropy, and 0–1 test. A new image encryption algorithm (IEA) is proposed utilizing the 2D-HELS to ensure the essential characteristics of a good cryptographic structure “permutation-diffusion”. The IEA utilizes dynamic confusion strategy and RNA operation to achieve a highly secure cipher-image. Theoretical analysis and simulation results are compared with some recently developed cryptosystems. It demonstrates that the 2D-HELS-IEA has splendid achievement in well-known security indicators. Hence, the 2D-HELS-IEA is highly secure as a conclusion.

Performance Evaluation of Genetic Algorithm-Driven Blockchain Encryption for EHR Management and Validation

In the realm of electronic health record (EHR) management, ensuring robust security and validation mechanisms is paramount due to the sensitive nature of healthcare data. This research focuses on the performance evaluation of a genetic algorithm-driven blockchain encryption approach for enhancing EHR security and validation. The proposed method leverages genetic algorithms to optimize encryption parameters within a blockchain framework, aiming to safeguard patient privacy and prevent unauthorized access. By integrating advanced cryptographic techniques like Elliptic Curve Cryptography (ECC) and Keyed-Hash Message Authentication Code (HMAC)-based authentication, along with machine learning for data classification. The evaluation of the approach holds significant promise in advancing secure EHR management practices, addressing critical challenges in data privacy and integrity within healthcare environments. Finally, as a result, this study presents a comparative analysis of cryptographic systems genetic algorithm-driven blockchain encryption (GADBE)+ECC and GADBE+ Advanced Encryption Standard (AES), focusing on the scaling of encryption and decryption times relative to key sizes and data volumes. Results show that both systems exhibit increasing times with larger key sizes and data sizes. ECC consistently demonstrates superior speed over AES, with decryption times ranging from 0.4 to 3.5 seconds for key sizes from 128 to 512 bits, indicating potential performance advantages of ECC in cryptographic applications.

Binary and ternary leading-systematic LCD codes from special functions

Linear complementary dual codes (LCD codes for short) are an important subclass of linear codes which have nice applications in communication systems, cryptography, consumer electronics and information protection. In the literature, it has been proved that an [n,k,d] Euclidean LCD code over Fq with q>3 exists if there is an [n,k,d] linear code over Fq, where q is a prime power. However, the existence of binary and ternary Euclidean LCD codes has not been totally characterized. Hence it is interesting to construct binary and ternary Euclidean LCD codes with new parameters. In this paper, we construct new families of binary and ternary leading-systematic Euclidean LCD codes from some special functions including semibent functions, quadratic functions, almost bent functions, and planar functions. These LCD codes are not constructed directly from such functions, but come from some self-orthogonal codes constructed with such functions. Compared with known binary and ternary LCD codes, the LCD codes in this paper have new parameters.

Thinking about the application of commercial cryptography in intelligent connected vehicles

As an important part of intelligent transportation, the information security of connected vehicles has become increasingly prominent. As a key technology to ensure the information security of networked vehicles, commercial cryptography plays an important role in vehicle identity authentication, data encryption and secure communication. In this paper, the status quo, challenges and future development trend of commercial cryptography application in connected vehicles are discussed, and some suggestions are put forward to strengthen technology research and development, standardization and industry cooperation. By continuously optimizing the application strategy of commercial cryptography, the information security level of connected vehicles can be effectively improved, providing strong support for the security development of the industry.

Four-Dimensional Physical Unclonable Functions and Cryptographic Applications Based on Time-Varying Chaotic Phosphorescent Patterns.

Physical unclonable functions (PUFs) have attracted interest in demonstrating authentication and cryptographic processes for Internet of Things (IoT) devices. We demonstrated four-dimensional PUFs (4D PUFs) to realize time-varying chaotic phosphorescent randomness on MoS2 atomic seeds. By forming hybrid states involving more than one emitter with distinct lifetimes in 4D PUFs, irregular lifetime distribution throughout patterns functions as a time-varying disorder that is impossible to replicate. Moreover, we established a bit extraction process incorporating multiple 64 bit-stream challenges and experimentally obtained physical features of 4D PUFs, producing countless random 896 bit-stream responses. Furthermore, the weak and strong PUF models were conceptualized and demonstrated based on 4D PUFs, exhibiting superior cryptological performances, including randomness, uniqueness, degree of freedom, and independent bit ratio. Finally, the data encryption and decryption in pictures were performed by a single 4D PUF. Therefore, 4D PUFs could enhance the counterfeiting deterrent of existing optical PUFs and be used as an anticounterfeiting security strategy for advanced authentication and cryptographic processes of IoT devices.

A Flexible Hardware Accelerator for Booth Polynomial Multiplier

This article presents a parameterized/flexible hardware accelerator design tailored for the Booth polynomial multiplication method. The flexibility is achieved by allowing users to compute multiplication operations across various operand lengths, reaching up to 212 or 4096 bits. Our optimization strategy involves resource reuse, effectively minimizing the overall area cost of the Booth accelerator design. A comprehensive evaluation compares the proposed multiplier design with several non-digitized bit-serial polynomial multiplication accelerators. Implementation is realized in Verilog HDL using the Vivado IDE tool, featuring diverse operand sizes, and post-place and route assessments are performed on the Xilinx Virtex-7 field-programmable gate array device. For the largest considered operand size of 1024 × 1024, our Booth accelerator utilizes 1434 slices and can operate on a maximum frequency of 523.56 MHz. A single polynomial multiplication operation requires 0.977 μs and the total power consumption is 927 mW. Moreover, a comparison to state-of-the-art accelerators reveals that the proposed flexible accelerator is 1.34× faster in computation time and 1.05× more area-efficient than the recent dedicated polynomial multiplication design. Therefore, the implementation results and comparison to the state of the art show that the proposed accelerator is suitable for a wide range of cryptographic applications.

Hiding Data using LSB in Combination with AES

In our increasingly digital age, steganography has emerged as one of the most trustworthy methods for the transmission of confidential information. This new research improves upon earlier LSB approaches by demonstrating how they may be utilized to efficiently encode secret data into a covert object without causing any obvious distortion. This opens the door for future applications of these methods. A safe data-hiding model will be produced by combining LSB-based steganography with AES; an LSB-based AES-256 encryption has been created and implemented in MATLAB.First, encrypted picture data is produced by encrypting the original image using a 256-bit AES technique. This process takes place before the image is used. The subsequent step includes sending a LSB-based steganography picture to the objective, which additionally contains the scrambled information. Interpreting the steganography picture information and reestablishing the first picture have both been achieved through the work of a similar strategy at the less than desirable finish of the transmission. We have examined and assessed an expansive range of sources of info and results from a few emphasess of the procedure applied to an assortment of picture information types. It is feasible to involve it in numerous useful cryptography applications to go through with steganography picture exchanges in a safer way.

Chemical unclonable functions based on operable random DNA pools

Physical unclonable functions (PUFs) based on unique tokens generated by random manufacturing processes have been proposed as an alternative to mathematical one-way algorithms. However, these tokens are not distributable, which is a disadvantage for decentralized applications. Finding unclonable, yet distributable functions would help bridge this gap and expand the applications of object-bound cryptography. Here we show that large random DNA pools with a segmented structure of alternating constant and randomly generated portions are able to calculate distinct outputs from millions of inputs in a specific and reproducible manner, in analogy to physical unclonable functions. Our experimental data with pools comprising up to >1010 unique sequences and encompassing >750 comparisons of resulting outputs demonstrate that the proposed chemical unclonable function (CUF) system is robust, distributable, and scalable. Based on this proof of concept, CUF-based anti-counterfeiting systems, non-fungible objects and decentralized multi-user authentication are conceivable.

Symmetry and symmetric transformations in mathematical imaging

The article delves into the intricate relationship between symmetry and mathematical imaging, spanning various mathematical disciplines. Symmetry, a concept deeply ingrained in mathematics, manifests in art, nature, and physics, providing a powerful tool for understanding complex structures. The paper explores three types of symmetriesreflection, rotational, and translationalexemplified through concrete mathematical expressions. Evariste Galoiss Group Theory emerges as a pivotal tool, providing a formal framework to understand and classify symmetric operations, particularly in the roots of polynomial equations. Galois theory, a cornerstone of modern algebra, connects symmetries, permutations, and solvability of equations. Group theory finds practical applications in cryptography, physics, and coding theory. Sophus Lie extends group theory to continuous spaces with Lie Group Theory, offering a powerful framework for studying continuous symmetries. Lie groups find applications in robotics and control theory, streamlining the representation of transformations. Benoit Mandelbrots fractal geometry, introduced in the late 20th century, provides a mathematical framework for understanding complex, self-similar shapes. The applications of fractal geometry range from computer graphics to financial modeling. Symmetrys practical applications extend to data visualization and cryptography. The article concludes by emphasizing symmetrys foundational role in physics, chemistry, computer graphics, and beyond. A deeper understanding of symmetry not only enriches perspectives across scientific disciplines but also fosters interdisciplinary collaborations, unveiling hidden order and structure in the natural and designed world. The exploration of symmetry promises ongoing discoveries at the intersection of mathematics and diverse fields of study.

Quantum random number generation using an on-chip nanowire plasmonic waveguide

Quantum random number generators employ the inherent randomness of quantum mechanics to generate truly unpredictable random numbers, which are essential in cryptographic applications. While a great variety of quantum random number generators have been realized using photonics, few exploit the high-field confinement offered by plasmonics, which enables device footprints an order of magnitude smaller in size. Here we integrate an on-chip nanowire plasmonic waveguide into an optical time-of-arrival based quantum random number generation setup. Despite loss, we achieve a random number generation rate of 14.4Mbitss−1 using low light intensity, with the generated bits passing industry standard tests without post-processing. By increasing the light intensity, we were then able to increase the generation rate to 41.4Mbitss−1 , with the resulting bits only requiring a shuffle to pass all tests. This is an order of magnitude increase in the generation rate and decrease in the device size compared to previous work. Our experiment demonstrates the successful integration of an on-chip nanoscale plasmonic component into a quantum random number generation setup. This may lead to new opportunities in compact and scalable quantum random number generation.

Chat Secure-Messaging Application Based on Secure Encryption Algorithm

Abstract: This study aims to explore the application of cryptography in various chat interfaces. Utilizing a systematic literature review methodology, we examine research conducted across various scientific platforms that bridge cryptography and the chat sector, as well as the intersection of cryptograph and database. The potential for advanced encryption algorithms to enhance the security of the user data is enormous. Implementing cryptography in chat interface presents competitive advantages, as numerous researchers have proposed and validated models that effectively optimize the use of cryptography in sharing data b/w the users

Redefining GCM’s resistance to cryptanalysis with offset mechanisms

The research paper proposes an enhancement to the Galois/Counter Mode (GCM) of authenticated encryption by introducing an “offset” mechanism. This modification aims to improve privacy and resist differential cryptanalysis without significantly impacting the mode’s efficiency and simplicity. The improved GCM maintains its original features, such as minimal block cipher invocations, the use of a single cryptographic key, and efficient offset computation. It provides a detailed analysis of the operational framework, including the integration and calculation of offsets in encryption and decryption processes. By complicating the predictability of differential cryptanalysis through unique offsets, the paper asserts this enhancement significantly increases GCM’s security within a concrete security model. The discussion emphasizes the benefits of the offset-enhanced GCM over other modes, highlighting its suitability for high-speed, parallelizable cryptographic applications while bolstering resistance against cryptanalytic attacks.

Applications of automaton groups in cryptography

In 1991, the first public key protocol involving automaton groups has been proposed. In this paper, we give a survey about algorithmic problems around automaton groups which may have potential applications in cryptography. We then present a new public key protocol based on the conjugacy search problem in some families of automaton groups. At the end, we offer open problems that could be of interest to group theorists and computer scientists in this direction.

New cyclic groups based on the generalized order-k Pell sequences in the Heisenberg group and their application in cryptography

New cyclic groups based on the generalized order-k Pell sequences in the Heisenberg group and their application in cryptography