Modular Addition Research Articles

Fast and Efficient Image Encryption Algorithm Based on Modular Addition and SPD.

Bit-level and pixel-level methods are two classifications for image encryption, which describe the smallest processing elements manipulated in diffusion and permutation respectively. Most pixel-level permutation methods merely alter the positions of pixels, resulting in similar histograms for the original and permuted images. Bit-level permutation methods, however, have the ability to change the histogram of the image, but are usually not preferred due to their time-consuming nature, which is owed to bit-level computation, unlike that of other permutation techniques. In this paper, we introduce a new image encryption algorithm which uses binary bit-plane scrambling and an SPD diffusion technique for the bit-planes of a plain image, based on a card game trick. Integer values of the hexadecimal key SHA-512 are also used, along with the adaptive block-based modular addition of pixels to encrypt the images. To prove the first-rate encryption performance of our proposed algorithm, security analyses are provided in this paper. Simulations and other results confirmed the robustness of the proposed image encryption algorithm against many well-known attacks; in particular, brute-force attacks, known/chosen plain text attacks, occlusion attacks, differential attacks, and gray value difference attacks, among others.

A Receding Horizon Scheduling Approach for Search & Rescue Scenarios

Many applications involving complex multi-task problems such as disaster relief, logistics and manufacturing necessitate the deployment and coordination of heterogeneous multi-agent systems due to the sheer number of tasks that must be executed simultaneously. A fundamental requirement for the successful coordination of such systems is leveraging the specialization of each agent within the team. This work presents a Receding Horizon Planning (RHP) framework aimed at scheduling tasks for heterogeneous multi-agent teams in a robust manner. In order to allow for the modular addition and removal of different types of agents to the team, the proposed framework accounts for the capabilities that each agent exhibits (e.g. quadrotors are agile and agnostic to rough terrain but are not suited to transport heavy payloads). An instantiation of the proposed RHP is developed and tested for a search and rescue scenario. Moreover, we present an abstracted search and rescue simulation environment, where a heterogeneous team of agents is deployed to simultaneously explore the environment, find and rescue trapped victims, and extinguish spreading fires as quickly as possible. We validate the effectiveness of our approach through extensive simulations comparing the presented framework with various planning horizons to a greedy task allocation scheme.

Improved Differential Fault Attack on LEA by Algebraic Representation of Modular Addition

Recently, as the number of IoT (Internet of Things) devices has increased, the use of lightweight cryptographic algorithms that are suitable for environments with scarce resources has also increased. Consequently, the safety of such cryptographic algorithms is becoming increasingly important. Among them, side-channel analysis methods are very realistic threats. In this paper, we propose a novel differential fault attack method on the Lightweight Encryption Algorithm (LEA) cipher which became the ISO/IEC international standard lightweight cryptographic algorithm in 2019. Previously proposed differential fault attack methods on the LEA used the Single Bit Flip model, making it difficult to apply to real devices. The proposed attack method uses a more realistic attacker assumption, the Random Word Error model. We demonstrate that the proposed attack method can be implemented on real devices using an electromagnetic fault injection setup. Our attack method has the weakest attacker assumption among attack methods proposed to date. In addition, the number of required fault-injected ciphertexts and the number of key candidates for which exhaustive search is performed are the least among all existing methods. Therefore, when implementing the LEA cipher on IoT deivces, designers must apply appropriate countermeasures against fault injection attacks.

Generation of the alternating group by modular additions

Abstract The paper is concerned with systems of generators of permutation groups on Cartesian products of residue rings. Each separate permutation from the system of generators is constructed on the basis of additions, is characterized by the local action, and leaves fixed the major parts of the components of the element being transformed. A criterion of 2-transitivity of the generated permutation group is given in the form of the strong connectedness of the digraph which corresponds to the system of generators and which is defined on the set of numbers of residue rings in the Cartesian product. Necessary and sufficient conditions under which this group contains an alternating group are formulated.

A New Adaptive Security Architecture with Extensible Computation Complexity for Generic Ciphers

Among recent developments on ciphers, attacks involving polynomial cryptanalysis have gained prominent attention in evaluating encryption algorithms for both stream and block ciphers. Algebraic cryptanalysis is also a tool to measure the strength of a cipher in terms of its resistance against different types of polynomial attacks. A contemporary way of representing such ciphers is in terms of multivariate equations over $\mathbb {GF}(2)$, which are highly vulnerable to algebraic cryptanalysis. Algebraic cryptanalysis, in its general form, aims to recover the internal secret state bits of the registers of the cipher by solving non-linear algebraic equations. Recent trends in algebraic cryptanalysis tend to use modular addition 2n over logic XOR as a mixing operator to guard against such malicious attacks. Nonetheless, it has been observed that the complexity of modular addition can be drastically decreased with the appropriate formulation of polynomial equations and probabilistic conditions. This article outlines a new design framework for modular addition with added security enhancements to address these issues. Inspiring from this framework, we show that the new design is characterized by user-specified extendable security for stronger encryption and does not impose changes in existing layout of ciphers including stream ciphers such as SNOW2.0, BIVIUM, and grain family, and block ciphers like IDEA, SAFER, AES, and DES. Our proposed design framework can be rapidly scaled to use-specific requirements which boosts the algebraic degree of the overall structure. This, in turn, thwarts the probabilistic conditions by retaining the original hardware complexity sans critical modifications of modular addition 2n.

Efficient Modular Adder Designs Based on Thermometer and One-Hot Coding

Residue number systems (RNSs) are efficient alternatives to positional number systems, providing fast and power-efficient computational systems. The key feature of the RNS benefitting modern embedded systems and the Internet-of-Thing (IoT) edge devices is its energy efficiency. Modular addition is the most important and frequent operation applied on the components of RNS, including arithmetic units in the channels as well as forward and reverse converters. The small and medium dynamic range requirements of low-power embedded and edge devices make the usage of the thermometer coding (TC) and one-hot coding (OHC) viable, reducing the power consumption and improving the energy efficiency of modulo addition in comparison to regular binary representations. Based on these techniques, this paper presents two new energy-efficient modular adders, which, due to the carry-free internal computations, are also highly performing. The proposed modular adders based on the TC and OHC result in average improvements of 38% and 34.5% for the delay, 27% and 14.5% for the circuit area, 29.5% and 6.3% for energy consumption, and about 54.9% and 44.2% for the area-delay product (ADP), respectively, in comparison with the related state of the art.

Implementation of Reversible Circuits in Modular Adders

Reversible logic is a computing paradigm that has attracted significant attention in recent years due to its properties that lead to ultra-low power and reliable circuits. Reversible circuits are fundamental, for example, for quantum computing .Since addition is a fundamental operation, designing efficient adders is a cornerstone in the research of reversible circuits. Residue Number Systems (RNS) has been as a powerful tool toprovide parallel and fault-tolerant implementations of computations where additions and multiplications are dominant. In this paper, for the first time in the literature, we propose the combination of RNS and reversible logic. The parallelism of RNS is leveraged to increase the performance of reversible computational circuits. Being the most fundamental part in any RNS, in this work we propose the implementation of different adders, namely ripple carry adder, carry save adder, carry look ahead adder using reversible logic. Analysis and comparison with different adders for modular addition are designed using reversible gates with minimum overhead in comparison to regular Brunt Kung modulo-adders.

Publicly Verifiable Spatial and Temporal Aggregation Scheme Against Malicious Aggregator in Smart Grid

We propose a privacy-preserving aggregation scheme under a malicious attacks model, in which the aggregator may forge householders’ billing, or a neighborhood aggregation data, or collude with compromised smart meters to reveal object householders’ fine-grained data. The scheme can generate spatially total consumption in a neighborhood at a timestamp and temporally a householder’s billing in a series of timestamps. The proposed encryption scheme of imposing masking keys from pseudo-random function (PRF) between pairwise nodes on partitioned data ensures the confidentiality of individual fine-grained data, and fends off the power theft of n-2 smart meters at most (n is the group size of smart meters in a neighborhood). Compared with the afore-mentioned methods of public key encryption in most related literatures, the simple and lightweight combination of PRF with modular addition not only is customized to the specific needs of smart grid, but also facilitates any node’s verification for local aggregation or global aggregation with low cost overhead. The publicly verifiable scenarios are very important for self-sufficient, remote places, which can only afford renewable energy and can manage its own energy price according to the energy consumption circumstance in a neighborhood.

Efficient Hardware Implementation of Modular Arithmetic and Group Operation Over Prime Field

The need for secure communication over the network has increased drastically over recent years, and Elliptic Curve Cryptography (ECC) carries out a significant role in moving secured information. In this work, a hardware implementation of modular arithmetic and group operations over the prime field for an Elliptic Curve Cryptography Processor (ECP) for an efficient security system is proposed. The modular addition or subtraction operation takes only one clock cycle and the modular multiplication, which is designed using the interleaved modular multiplication method, requires 257 clock cycles. For elliptic curve group operation separate point doubling (PD) and point addition (PA) architectures are implemented in Jacobean coordinates. These new architectures are simulated in a Xilinx ISE 14.7. After that, the architectures are implemented in Xilinx Virtex-7 field-programmable gate array (FPGA) with the VHDL language. Proposed modular arithmetic and group operations can be utilized to design an Elliptic Curve Point Multiplication (ECPM).

Differential Cryptanalysis of Round-Reduced SPECK Suitable for Internet of Things Devices

In this paper, we focus on differential cryptanalysis of a lightweight ARX cipher. These ciphers use three simple arithmetic operations, namely, modular addition, bitwise rotation, and exclusive-OR, and therefore, are designed very well to perform over the Internet-of-Things (IoT) devices. We choose a very well-known ARX cipher designed by the National Security Agency (NSA) of the United States of America in June 2013, named SPECK. SPECK was subjected to several years of detailed cryptanalytic analysis within NSA and has been subjected to academic analysis by researchers worldwide. SPECK is specially optimized for low-cost processors like those used in the IoT devices. We first find the differential paths for all the variants of SPECK, and based on that differential path, we attack the round-reduced variant of the cipher. Finding differential paths in ARX is one of the most difficult and time-consuming problems due to the huge state space. We use a nested-based heuristic technique to find a differential path which is inspired by the nested Monte Carlo search (NMCS) algorithm. NMCS was successfully applied before for different games: Morpion Solitaire, SameGame, and $16\times 16$ Sudoku, but the use of such heuristic techniques in cryptography is entirely new and time-saving.

Anatomically constrained tractography facilitates biologically plausible fiber reconstruction of the optic radiation in multiple sclerosis.

Diffusion-weighted magnetic resonance imaging (dMRI) enables the microstructural characterization and reconstruction of white matter pathways in vivo non-invasively. However, dMRI only provides information on the orientation of potential fibers but not on their anatomical plausibility. To that end, recent methodological advances facilitate the effective use of anatomical priors in the process of fiber reconstruction, thus improving the accuracy of the results. Here, we investigated the potential of anatomically constrained tracking (ACT), a modular addition to the tractography software package MRtrix3, to accurately reconstruct the optic radiation, a commonly affected pathway in multiple sclerosis (MS). Diffusion MRI data were acquired from 28 MS patients and 22 age- and sex-matched healthy controls. For each participant, the optic radiation was segmented based on the fiber reconstruction obtained using ACT. When implementing ACT in MS, it proved essential to incorporate lesion maps to avoid incorrect reconstructions due to tissue-type misclassifications in lesional areas. The ACT-based results were compared with those obtained using two commonly used probabilistic fiber tracking procedures, based on FSL (FMRIB Software Library) and MRtrix3 without ACT. All three procedures enabled a reliable localization of the optic radiation in both MS patients and controls. However, for FSL and MRtrix3 without ACT it was necessary to place an additional waypoint halfway between the lateral geniculate nucleus and the primary visual cortex to filter out anatomically implausible tracks. In the case of ACT, the results with and without an additional waypoint were virtually identical, presumably because the employed anatomical constraints already prevented the occurrence of the most implausible tracks. Irrespective of the employed tractography procedure, increased diffusivity and decreased anisotropy were found in the optic radiation of the MS patients compared to the controls.

Fast Large Integer Modular Addition in GF(p) Using Novel Attribute-Based Representation

Addition is an essential operation in all cryptographic algorithms. Higher levels of security require larger key sizes and this becomes a limiting factor in GF(p) using large integers because of the carry propagation problem. We propose a novel and efficient attribute-based large integer representation scheme suitable for large integers commonly used in cryptography such as the five NIST primes and the Pierpont primes used in supersingular isogeny Diffie-Hellman (SIDH) for post-quantum cryptography. Algorithms are proposed for this new representation to implement arithmetic operations such as two's complement, addition/subtraction, comparison, sign detection, and modular reduction. Algorithms are also developed for converting binary numbers to attribute representation and vice versa. The extensive numerical simulations were done to verify the performance of the new number representation. Results show that addition is done faster in our proposed representation when compared with binary and residue number system (RNS)-based additions. Attribute addition outperformed RNS addition for all values of m where 128 ≤ m ≤ 32768 bits for all machine word sizes w where 4 ≤ w ≤ 128 bits. Attribute-based addition outperforms Kogge-Stone binary adders for a wide range of m when w is small. For increasing values of w, the speed advantages are evident only for large values of m. This makes the proposed number representation suitable for implementing cryptographic applications in embedded processors for IoT and consumer electronic devices where w is small.

FIR Filter Realization via Deferred End-Around Carry Modular Addition

Hardware realization of FIR filters that are based on residue number systems leads to increased speed and reduced power, where besides the popular Mersenne numbers, several moduli of the form ${2}^{n} \pm \delta (\delta \ge 3)$ are commonly used. However, additional weighted ${2}^{i}(i>1)$ end-around carries (EACs) slow down and complicate the required modular adders in comparison to modulo-( ${2}^{n}-1$ ) adders. For example, for $\delta =3$ , the modular sum is obtained via $A+B\mp 3{c}_{\mathrm {out}}$ , where ${A}$ and ${B}$ are modulo-( ${2}^{n}\pm 3$ ) operands and ${c}_{\mathrm {out}}$ is the carryout of binary addition $A+B$ . In this paper, a new multioperand modular adder is proposed, where the key improvement is that all the required EAC additions (e.g., $+ 3c_{\mathrm {out}}$ ) are postponed until after the last filter tap, whereby tens of addition operations take place without the EAC secondary addition; hence considerable savings of time, area consumption, and power dissipation. The proposed deferred EAC addition scheme has been applied to three previous relevant works. The corresponding synthesis results showed over 11%–32%, 27%–29%, and 21%–37%, reductions in delay, area, and power measures, respectively. This is achieved despite area and power overhead of the few appended stages into the pipelined architecture of the filter, which are nevertheless shown to become less significant as the number of filter taps grows.

Efficient Side-Channel Protections of ARX Ciphers

The current state of the art of Boolean masking for the modular addition operation in software has a very high performance overhead. Firstly, the instruction count is very high compared to a normal addition operation. Secondly, until recently, the entropy consumed by such protections was also quite high. Our paper significantly improves both aspects, by applying the Threshold Implementation (TI) methodology with two shares and by reusing internal values as randomness source in such a way that the uniformity is always preserved. Our approach performs considerably faster compared to the previously known masked addition and subtraction algorithms by Coron et al. and Biryukov et al. improving the state of the art by 36%, if we only consider the number of ARM assembly instructions. Furthermore, similar to the masked adder from Biryukov et al. we reduce the amount of randomness and only require one bit additional entroy per addition, which is a good trade-off for the improved performance. We applied our improved masked adder to ChaCha20, for which we provide two new first-order protected implementations and achieve a 36% improvement over the best published result for ChaCha20 using an ARM Cortex-M4 microprocessor.

Focused electrical stimulation using a single current source

Objective. Cochlear implants, while providing significant benefits to recipients, remain limited due to broad neural activation. Focussed multipolar stimulation (FMP) is an advanced stimulation strategy that uses multiple current sources to produce highly focussed patterns of neural excitation in order to overcome these shortcomings. Approach. This report presents single-source multipolar stimulation (SSMPS), a novel form of stimulation based on a single current source and a passive current divider. Compared to conventional FMP with multiple current sources, SSMPS can be implemented as a modular addition to conventional (i.e. single) current source stimulation systems facilitating charge balance within the cochlea. As with FMP, SSMPS requires the determination of a transimpedance matrix to allow for focusing of the stimulation. The first part of this study therefore investigated the effects of varying the probe stimulus (e.g. current level and pulse width) on the measurement of the transimpedance matrix. SSMPS was then studied using in vitro based measurements of voltages at non-stimulated electrodes along an electrode array in normal saline. The voltage reduction with reference to monopolar stimulation was compared to tripolar and common ground stimulation, two clinically established stimulation modes. Finally, a proof of principle in vivo test of SSMPS in a feline model was performed. Main results. A probe stimulus of at least 40 nC is required to reliably measure the transimpedance matrix. In vitro stimulation using SSMPS resulted in a significantly greater voltage reduction compared to monopolar, tripolar and common ground stimulation. Interestingly, matching measurement and stimulation parameters did not lead to an improved focussing performance. Compared to monopolar stimulation, SSMPS resulted in reduced spread of neural activity in the inferior colliculus, albeit with increased thresholds. Significance. The present study demonstrates that SSMPS successfully limits the broadening of the excitatory field along the electrode array and a subsequent reduction in the spread of neural excitation.

A Vendor-Neutral Unified Core for Cryptographic Operations in GF(p) and GF(2m) Based on Montgomery Arithmetic

In the emerging IoT ecosystem in which the internetworking will reach a totally new dimension the crucial role of efficient security solutions for embedded devices will be without controversy. Typically IoT-enabled devices are equipped with integrated circuits, such as ASICs or FPGAs to achieve highly specific tasks. Such devices must have cryptographic layers implemented and must be able to access cryptographic functions for encrypting/decrypting and signing/verifying data using various algorithms and generate true random numbers, random primes, and cryptographic keys. In the context of a limited amount of resources that typical IoT devices will exhibit, due to energy efficiency requirements, efficient hardware structures in terms of time, area, and power consumption must be deployed. In this paper, we describe a scalable word-based multivendor-capable cryptographic core, being able to perform arithmetic operations in prime and binary extension finite fields based on Montgomery Arithmetic. The functional range comprises the calculation of modular additions and subtractions, the determination of the Montgomery Parameters, and the execution of Montgomery Multiplications and Montgomery Exponentiations. A prototype implementation of the adaptable arithmetic core is detailed. Furthermore, the decomposition of cryptographic algorithms to be used together with the proposed core is stated and a performance analysis is given.

Automatic search of impossible differentials and zero-correlation linear hulls for ARX ciphers

In lightweight cryptographic primitives, round functions with only simple operations XOR, modular addition and rotation are widely used nowadays. This kind of ciphers is called ARX ciphers. For ARX ciphers, impossible differential cryptanalysis and zero-correlation linear cryptanalysis are among the most powerful attacks, and the key problems for these two attacks are discovering more and longer impossible differentials (IDs) and zero-correlation linear hulls (ZCLHs). However, finding new IDs and ZCLHs for ARX ciphers has been a manual work for a long time, which has been an obstacle in improving these two attacks. This paper proposes an automatic search method to improve the efficiency of finding new IDs and ZCLHs for ARX ciphers. In order to prove the efficiency of this new tool, we take HIGHT, LEA, SPECK three typical ARX algorithms as examples to explore their longer and new impossible differentials and zero-correlation linear hulls. To the best of our knowledge, this is the first application of automatic search method for ARX ciphers on finding new IDs and ZCLHs. For HIGHT, we find more 17 round IDs and multiple 17 round ZCLHs. This is the first discovery of 17 round ZCLHs for HIGHT. For LEA, we find extra four 10 round IDs and several 9 round ZCLHs. In the specification of LEA, the designers just identified three 10 round IDs and one 7 round ZCLH. For SPECK, we find thousands of 6 round IDs and forty-four 6 round ZCLHs. Neither IDs nor ZCLHs of SPECK has been proposed before. The successful application of our new tool shows great potential in improving the impossible differential cryptanalysis and zero-correlation linear cryptanalysis on ARX ciphers.

Nonlinear diffusion layers

In the practice of block cipher design, there seems to have grown a consensus about the diffusion function that designers choose linear functions with large branch numbers to achieve provable bounds against differential and linear cryptanalysis. In this paper, we propose two types of nonlinear functions as alternative diffusing components. One is based on a nonlinear code with parameters (16,256,6) which is known as a Kerdock code. The other is a general construction of nonlinear functions based on the T-functions, in particular, two automatons with modular addition operations. We show that the nonlinear functions possess good diffusion properties; specifically, the nonlinear function based on a Kerdock code has a better branch number than any linear counterparts, while the automatons achieve the same branch number as a linear near-MDS matrix. The advantage of adopting nonlinear diffusion layers in block ciphers is that, those functions provide extra confusion effect while a comparable performance in the diffusion effect is maintained. As an illustration, we show the application of the nonlinear diffusion functions in two example ciphers, where a 4-round differential characteristic with the optimal number of active Sboxes has a probability significantly lower ( $$2^{16}$$ and $$2^{10}$$ times, respectively) than that of a similar cipher with a linear diffusion layer. As a result, it sheds light upon an alternative strategy of designing lightweight building blocks.

Branched Glycerol-Based Copolymer with Ultrahigh p65 siRNA Delivery Efficiency for Enhanced Cancer Therapy.

The small interfering RNA (siRNA) is emerging as a potential therapeutic for the treatment of various diseases because of the targeted gene silencing capability. The suppression of p65 expression has shown great potential in various cancer treatments. However, various substantial obstacles limit its clinical applications, including low cellular uptake, instability, and cytotoxicity of delivery vehicles. We show a highly branched and biocompatible glycerol-based copolymer (HBGC) to effectively deliver siRNA for excellent p65 gene silencing and safe lung cancer treatment in vitro and in vivo. HBGCs could be synthesized through a facile and modular one-spot Michael addition. HBGCs effectively protect siRNA in serum, enhance cellular uptake of siRNA, and show negligible cytotoxicity in various cells (A549, HeLa, HepG2, and C2C12). Additionally, the HBGC-siRNA complex potently downregulates the p65 expression in A549 cancer cells (almost the highest value of 96% in reported references) and enhances the cellular apoptosis compared to that of commercial transfection agents polyethyleneimine 25 kDa and Lipofectamine 2000. The HBGC-siRNA complex demonstrated significantly increased accumulation in the tumor sites and enhanced downregulation of p65 gene and cancer cell apoptosis. Furthermore, the tumor growth could be significantly inhibited in a subcutaneous lung tumor model with negligible adverse effects.

Analysis of the Use of Frame Construction and Modular Additions in City Centre

The living urban fabric can be characterized by the continuous introduction of changes and additions. The city centre is subject to specific restrictions due to the conservation protection and high demand on aesthetics aspect, thermal insulation, construction cost and the ratio of usable area of the building area. This article presents a comparative analysis of traditional construction with light frame and modular construction for the above-mentioned issues. Timber frame structure technology was suggested as effective, economic and innovative solutions for modular additions on buildings in city centres.