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We designed an image encryption algorithm based on a non-degeneracy 3D chaotic map and a keyed strong S-Box, which is capable of encrypting color image with any size. First, we constructed a non-degeneracy 3D discrete hyperchaotic map (3D-DHCM), and based on it we constructed a keyed strong S-Box without fixed point, reverse fixed point or short period rings. The map is based on modular exponentiation operation, and its inverse function is the discrete logarithm problem. Finally, we applied blurring techniques to the plain image prior to encryption and employed permutation, confusion, and diffusion techniques to shuffle all pixels. Experimental and analytical results demonstrated that the NPCR and UACI are all close to their ideal values 99.6094070% and 33.4635070%, and the pixels of the cipher image are completely confused, which are all close to the ideal value 8. In addition, the chi-square values for encrypted images are significantly lower than before, with a maximum value of 255.1503. It is showed that the algorithm is superior to others in terms of its ability to encrypt images with any size and withstand common attacks. [ABSTRACT FROM AUTHOR]

A comparison and analysis of using the developed software implementation of the MontgomeryArithmetic class for computing modular exponentiation are conducted. The performance speed of the developed Montgomery modular multiplication is compared to that of the regular modular multiplication for calculating the modular exponentiation based on the right-to-left binary method for a fixed basis with precomputation of a reduced set of residues. The obtained results of modular exponentiation computing with parallelization based on multithreading on general-purpose computers speed up the computation by an average of 1.5 times using the developed modular Montgomery multiplication compared to the modular exponentiation functions of the MPIR, OpenSSL, and Crypto++ software libraries. [ABSTRACT FROM AUTHOR]

A comparison and analysis of the use of the developed software implementation of the class MontgomeryArithmetic for computing modular exponentiation are conducted. The computation speed of the developed Montgomery modular multiplication is compared to the regular modular multiplication for calculating the modular exponentiation based on the right-to-left binary elevation method for a fixed basis with a preliminary calculation of a reduced set of remainders. The obtained results of performing modular exponentiation computations with parallelization based on multithreading on general-purpose computers speed up the computations by an average of 1.5 times using the developed modular Montgomery multiplication compared to the modular exponentiation functions of the MPIR, OpenSSL, and Crypto++ software libraries. [ABSTRACT FROM AUTHOR]

Let $ N = \left\{{n}_{1}, {n}_{2}, \;\dots , {n}_{k}\right\} $ be a finite set of positive numbers. The problem of finding the minimal number of additions required to compute all elements of N starting from 1 (called the addition sequence problem) is NP-complete. It is equivalent to finding the minimum number of multiplications needed to compute a group exponentiation $ {g}^{{n}_{1}}, {g}^{{n}_{2}}, \;\dots , {g}^{{n}_{k}} $, where g is an element in a group. This paper aims to propose a new metaheuristic algorithm using a simulated annealing strategy to generate a short addition sequence. The performance of the proposed algorithm is measured by considering two parameters: The size of N and the domain of $ {n}_{\mathrm{i}}, 1\le i\le k $. The proposed algorithm is a new trade-off between the length of the generated addition sequence and the average running time of generating addition sequences. It sometimes produces longer addition sequences than exact algorithms that are slower, and it is slower than suboptimal algorithms that produce longer addition sequences.

Let N = {n1, n2, ..., nk} be a finite set of positive numbers. The problem of finding the minimal number of additions required to compute all elements of N starting from 1 (called the addition sequence problem) is NP-complete. It is equivalent to finding the minimum number of multiplications needed to compute a group exponentiation gn1, gn2, ..., gnk, where g is an element in a group. This paper aims to propose a new metaheuristic algorithm using a simulated annealing strategy to generate a short addition sequence. The performance of the proposed algorithm is measured by considering two parameters: The size of N and the domain of ni,1 ≤ i ≤ k. The proposed algorithm is a new trade-off between the length of the generated addition sequence and the average running time of generating addition sequences. It sometimes produces longer addition sequences than exact algorithms that are slower, and it is slower than suboptimal algorithms that produce longer addition sequences. [ABSTRACT FROM AUTHOR]

Big number operation has always been a bottleneck to computer system as it imposes high demand on computing power. With a limited power available, operations such as exponentiation and multiplication involving large integer belonging to encryption process requires grave scrutiny. One way to address this issue is by replacing an original complex computation into a sequence of small computations that in the end produces the same results. This paper takes an evolutionary approach to survey numerous articles that have contributed to the advancement of integer representation. Numerous representations were proposed, those that come into play concentrated on reducing non-zero digits and limiting non-zero spacing other than allowing subtraction operation. A comparison was made to distinguish the properties of each method from the others. This detailed outlook can be a guide for identifying the correct representation to be chosen for implementation within specific application. [ABSTRACT FROM AUTHOR]

Modular exponentiation is crucial for secure data exchange in cryptography, especially for resource-constrained Internet of Things (IoT) devices. These devices often rely on third-party servers to handle computationally intensive tasks like modular exponentiation. However, existing outsourcing solutions for the RSA algorithm may have security vulnerabilities. This work identifies a critical flaw in a recent outsourcing protocol for RSA proposed by Hu et al. We demonstrate how this flaw compromises the security of the entire RSA system. Subsequently, we propose a robust solution that strengthens the RSA algorithm and mitigates the identified vulnerability. Furthermore, our solution remains resilient against existing lattice-based attacks. The proposed fix offers a more secure and efficient way for IoT devices to leverage the power of third-party servers while maintaining data integrity and confidentiality. An extensive performance evaluation confirms that our solution offers comparable efficiency while significantly enhancing security compared to existing approaches. [ABSTRACT FROM AUTHOR]

With rapid development and application of artificial intelligence and block chain, the requirement of information and data security is also increased, in which the public-key cryptography, such as Rivest-Shamir-Adleman (RSA) cryptography, plays a significant role. Modular exponentiation is fundamental in computer arithmetic and is widely applied in cryptography, such as ElGamal cryptography, Diffie–Hellman key exchange protocol, and RSA cryptography. The implementation of modular exponentiation in a residue number system leads to high parallelism in computation and has been applied in many hardware architectures. While most residue number system (RNS)-based architectures utilize RNS Montgomery algorithm with two residue number systems, the recent modular multiplication algorithm with sum residues performs modular reduction in only one residue number system with about the same parallelism. In this work, it is shown that the high-performance modular exponentiation and RSA cryptography can be implemented in RNS. Both the algorithm and architecture are improved to achieve high performance with extra area overheads, where a 1024-bit modular exponentiation can be completed in 0.567 ms in Xilinx XC6VLX195t-3 platform, costing 26489 slices, 87357 LUTs, 363 dedicated multipilers of $18 \times 18$ bits, and 65 block RAMs. [ABSTRACT FROM AUTHOR]

In inter-system connections or between any two points in communication, it is necessary to make sure that the data goes securely. This is achieved by encrypting the sent data. As the disciplines of cryptography and network security matured, more practical applications were developed that were not readily available to ensure network security. Today, encryption has become a necessity in the digital environment. In this study, basic cryptography terms are mentioned. The RSA algorithm (Rivest-Shamir-Adleman) is the basis of a cryptographic system, a suite of cryptographic algorithms used for private security services or purposes, and this allows public key encryption, widely used to secure particularly sensitive data sent over an insecure network such as the internet. Commonly used methods were examined and RSA encryption method was chosen in accordance with the purpose of the study. RSA, a public key encryption technique, is built on the difficulty of generating and processing very large integers. In this study, operations with large numbers that take a long time are completed in a short time using various methods. It has been reflected in the study by creating a more secure structure by using large prime numbers for the key generation process. [ABSTRACT FROM AUTHOR]

Modular exponentiation is crucial for secure data exchange in cryptography, especially for resource-constrained Internet of Things (IoT) devices. These devices often rely on third-party servers to handle computationally intensive tasks like modular exponentiation. However, existing outsourcing solutions for the RSA algorithm may have security vulnerabilities. This work identifies a critical flaw in a recent outsourcing protocol for RSA proposed by Hu et al. We demonstrate how this flaw compromises the security of the entire RSA system. Subsequently, we propose a robust solution that strengthens the RSA algorithm and mitigates the identified vulnerability. Furthermore, our solution remains resilient against existing lattice-based attacks. The proposed fix offers a more secure and efficient way for IoT devices to leverage the power of third-party servers while maintaining data integrity and confidentiality. An extensive performance evaluation confirms that our solution offers comparable efficiency while significantly enhancing security compared to existing approaches.

Evolutionary computation techniques have always provided fascinating results in all the fields of science and engineering. However in the area of computer security, their contribution has been comparatively very less. More specifically if we consider the side-channel attacks, use of these nature based techniques have been very nominal. Therefore, we proposed a secure protocol in this paper to combat against the Higher Order Differential Power Analysis attacks on modular exponentiation based cryptosystems using one of the popular evolutionary computation techniques. The proposed work first uses Genetic Algorithm for splitting the huge exponent within the modular exponentiation into multiple non-uniform shares. Then, this shares are randomly chosen for computing individual modular exponentiation with the help of nearest neighbor algorithm. Using Genetic Algorithm, our proposed protocol can generate reasonable number of shares which exposes secret exponent at the least. As a result, it provides significant resistance to Higher Order Differential Power Analysis attacks. Moreover, randomization in computing individual modular exponentiation secures the cryptosystem from generic power analysis attacks like SPA and DPA.

The aim of this paper is to present a new design for a pseudorandom number generator (PRNG) that is cryptographically secure, passes all of the usual statistical tests referenced in the literature and hence generates high-quality random sequences, that is compact and easy to implement in practice, of portable design and offering reasonable execution times. Our procedure achieves those objectives through the use of a sequence of modular exponentiations followed by the application of Feistel-like boxes that mix up bits using a nonlinear function. The results of extensive statistical tests on sequences of about 2 40 bits in size generated by our algorithm are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method of using Montgomery multiplication in the computation of binary Bailey–Borwein–Plouffe (BBP)-type formulas for mathematical constants. The most time-consuming part of the computation of a BBP-type formula is modular exponentiation. It is known that modular exponentiation can be performed efficiently using binary modular exponentiation and Montgomery multiplication. When computing a Montgomery multiplication in binary, the modulus of the modular exponentiation must be an odd number. However, if the denominator of the fraction in a binary BBP-type formula, excluding the power of the base, is an even number, then the modulus of the modular exponentiation is also an even number, so Montgomery multiplication cannot be used directly. The proposed method makes it possible to use Montgomery multiplication for binary BBP-type formulas even in such a case. [ABSTRACT FROM AUTHOR]

With the development of the Internet of Things, smart grids have become indispensable in our daily life and can provide people with reliable electricity generation, transmission, distribution and control. Therefore, how to design a privacy-preserving data aggregation protocol has been a research hot-spot in smart grid technology. However, these proposed protocols often contain some complex cryptographic operations, which are not suitable for resource-constrained smart meter devices. In this paper, we combine data aggregation and the outsourcing of computations to design two privacy-preserving outsourcing algorithms for the modular exponentiation operations involved in the multi-dimensional data aggregation, which can allow these smart meter devices to delegate complex computation tasks to nearby servers for computing. By utilizing our proposed outsourcing algorithms, the computational overhead of resource-constrained smart meter devices can be greatly reduced in the process of data encryption and aggregation. In addition, the proposed algorithms can protect the input's privacy of smart meter devices and ensure that the smart meter devices can verify the correctness of results from the server with a very small computational cost. From three aspects, including security, verifiability and efficiency, we give a detailed analysis about our proposed algorithms. Finally, through carrying out some experiments, we prove that our algorithms can improve the efficiency of performing the data encryption and aggregation on the smart meter device side. [ABSTRACT FROM AUTHOR]

With the advancements of communication technology, security threats are also increasing. RSA is a robust cryptosystem to protect classified information. The efficiency of RSA cryptosystem depends on the efficient execution of Montgomery modular multiplication. A low latency and throughput efficient Montgomery modular multiplier is proposed in this paper. The input and final output of this multiplier are binary, but intermediate input and output are carry-saved i.e. sum and carry bits are stored in separate registers. Sum and carry bits are obtained from the addition of operands using carry-save adder (CSA). Montgomery multipliers require quotient calculation for subsequent iteration. The proposed multiplier computes two subsequent quotients in parallel with carry-save addition. Output of carry-save addition is right shifted by two bits to obtain the next-to-next intermediate output. This calculation also requires integer multiples of the inputs. Computation of next output is skipped. Format conversion of output is performed using a carry look-ahead unit (CLU). CLU along with one cycle of carry save addition is also utilized for pre-computation of integer multiples of inputs. The proposed multiplier is implemented on NEXYS4DDR and VIRTEX VII FPGA and the following result is obtained. NEXYS4DDR: Area (LUT + REG): 38903, Delay: 5.84 ns, Cycles: 1158, Latency: 6.76 µs, Throughput: 302.96 Mbps. VIRTEX VII: Area (LUT): 16447, Delay: 1.62 ns, Cycles: 1158, Latency: 1.88 µs, Throughput: 1089.4 Mbps. Results verify the improved area, latency and throughput performance of the proposed work.

Copyright of Radio Electronics, Computer Science, Control is the property of Zaporizhzhia National Technical University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

With the growing popularity of cloud computing in recent years, data owners (DOs) now prefer to outsource their data to cloud servers and allow the specific data users (DUs) to retrieve the data. Searchable encryption is an important tool to provide secure search over the encrypted cloud data without infringing data confidentiality and data privacy. In this work, we consider a secure search service providing fine-grained and search functionality, called attribute-based multiple keyword search (ABMKS), which can be seen as an extension of searchable encryption. In the existing ABMKS schemes, the computation operations in the encrypted keyword index generation are time-consuming modular exponentiation, and the number of which is linearly growing with the factor $m$ . Here $m$ is the number of keywords embedded in a file. To reduce the computation overhead, in this paper, we propose an ABMKS with only multiplication operations in encrypted keyword index generation. As a result, the computation cost of the encrypted keyword index generation is more efficient than the existing schemes. In addition, the encrypted keyword indexes are aggregated into one item, which is regardless of the number of underlying keywords in a file data. Finally, the security and the performance analysis demonstrate that our scheme is both efficient and secure.

Edge computing provides users with nearby services, promotes the development of the Internet of Things and transforms the mode of traditional electronic medical system that improves the speed and accuracy of medical diagnosis. However, edge computing has introduced new security challenges, such as the difficulty in applying standard encryption algorithms because of the limited computing capability of devices on the edge and concerns of privacy leakage. In this article, we propose a data access scheme by employing a lightweight attribute-based encryption (ABE) to address the security weaknesses of edge computing for e-health. Our novel modular exponential outsourcing algorithm outsources the shared data to the untrusted edge server and verifies the correctness of the returned results while achieving a lightweight computational load. The proposed Mask Algorithm along with blind pairs conceals the bases and exponents of the encrypted data, thus preserving the privacy of sensitive data in the process of outsourced computing. Security analysis and performance evaluation confirmed the security and efficiency of the proposed method.

The aim of this paper is to propose the alternative algorithm to finish the process in public key cryptography. In general, the proposed method can be selected to finish both of modular exponentiation and point multiplication. Although this method is not the best method in all cases, it may be the most efficient method when the condition responds well to this approach. Assuming that the binary system of the exponent or the multiplier is considered and it is divided into groups, the binary system is in excellent condition when the number of groups is small. Each group is generated from a number of 0 that is adjacent to each other. The main idea behind the proposed method is to convert the exponent or the multiplier as the subtraction between two integers. For these integers, it is impossible that the bit which is equal to 1 will be assigned in the same position. The experiment is split into two sections. The first section is an experiment to examine the modular exponentiation. The results demonstrate that the cost of completing the modular multiplication is decreased if the number of groups is very small. In tables 7 – 9, four modular multiplications are required when there is one group, although number of bits which are equal to 0 in each table is different. The second component is the experiment to examine the point multiplication process in Elliptic Curves Cryptography. The findings demonstrate that if the number of groups is small, the costs to compute point additions are low. In tables 10 – 12, assigning one group is appeared, number of point addition is one when the multiplier of a point is an even number. However, three-point additions are required when the multiplier is an odd number. As a result, the proposed method is an alternative way that should be used when the number of groups is minimal in order to save the costs. [ABSTRACT FROM AUTHOR]

Copyright of Radio Electronics, Computer Science, Control is the property of Zaporizhzhia National Technical University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

On account of the high computational cost of modular exponentiation, the local clients with limited resources can delegate the modular exponentiation to the cloud servers with strong computing capacity. This paper mainly studied the outsourcing algorithm of the modular exponentiation like u" ( mod N), where N is the product of two large prime numbers. The method used Euler theorem to design a new modular exponentiation outsourcing scheme based on two servers model. In the process of computing and outsourcing, it guaranteed the privacy protection of base u, exponent a and calculation results for the two severs. The safety and efficiency analysis and experimental simulation show that compared with the existing schemes, the proposed new scheme has better execution efficiency and verifiability, the efficiency is higher on the client side, and the probability of verifiability of the new scheme is 1. [ABSTRACT FROM AUTHOR]

Attribute-based encryption (ABE) is a promising cryptographic tool for data owner (DO) to realize fine-grained date sharing in the cloud computing. In the encryption of most existing ABE schemes, a substantial number of modular exponentiations are often required; the computational cost of it is growing linearly with the complexity of the access policy. Besides, in the most existing ABE with outsourced decryption, the computation cost of generating transformation key is growing linearly with the number of attributes associated with user private key; these computations are prohibitively high for mobile device users, which becomes a bottleneck limiting its application. To address the above issues, we propose a secure outsourcing algorithm for modular exponentiation in one single untrusted server model and a new method to generate the transformation key. Based on these techniques and Brent Waters's ciphertext-policy ABE scheme, we propose an ABE scheme with verifiable outsourced both encryption and decryption, which can securely outsource encryption and decryption to untrusted encryption service provider (ESP) and decryption service provider (DSP), respectively, leaving only a constant number of simple operations for the DO and eligible users to perform locally. In addition, both DO and the eligible users can check the correctness of results returned from the ESP and the DSP with a probability, respectively. Finally, we provide the experimental evaluation and security analysis of our scheme, which indicates that our construction is suitable for the mobile environment.

With the development of the Internet of Things, smart grids have become indispensable in our daily life and can provide people with reliable electricity generation, transmission, distribution and control. Therefore, how to design a privacy-preserving data aggregation protocol has been a research hot-spot in smart grid technology. However, these proposed protocols often contain some complex cryptographic operations, which are not suitable for resource-constrained smart meter devices. In this paper, we combine data aggregation and the outsourcing of computations to design two privacy-preserving outsourcing algorithms for the modular exponentiation operations involved in the multi-dimensional data aggregation, which can allow these smart meter devices to delegate complex computation tasks to nearby servers for computing. By utilizing our proposed outsourcing algorithms, the computational overhead of resource-constrained smart meter devices can be greatly reduced in the process of data encryption and aggregation. In addition, the proposed algorithms can protect the input’s privacy of smart meter devices and ensure that the smart meter devices can verify the correctness of results from the server with a very small computational cost. From three aspects, including security, verifiability and efficiency, we give a detailed analysis about our proposed algorithms. Finally, through carrying out some experiments, we prove that our algorithms can improve the efficiency of performing the data encryption and aggregation on the smart meter device side.

A side-channel attack (SCA) hardened AES-128 and RSA crypto-processor in 14-nm CMOS with measured resistance to correlation power/electromagnetic analysis (CPA/CEMA) in both time and frequency domains is demonstrated. While previously reported linear low-dropout regulators (LDOs) offer improvements in minimum-time-to-disclose (MTD) of extracted key bytes in the time domain, their transformations are less effective against frequency-domain attacks. This article describes a non-linear digital LDO (NL-DLDO) with control loop randomizations that bolster SCA resistance in the frequency domain. The NL-DLDO cascaded with an AES engine augmented with arithmetic countermeasures enables > 250 K × improvement in MTD, with no CPA/CEMA/DNN attacks detected after 1-B encryptions, with 8% power and 10% area overheads incurred by arithmetic techniques. The RSA-4K crypto-processor implements exponent magnitude and timing randomizations along with dynamic memory addressing to mitigate time- and frequency-domain attacks. The countermeasures enable 711 × suppression in means separation in current/EM magnitudes from 3.1 mV to 4.35 μV, reducing attacker’s accuracy to an ineffective random guess classification, while limiting area and performance overheads to < 0.05% and 3.25%, respectively. [ABSTRACT FROM AUTHOR]

This paper presents a secured computation of modular exponentiation to resist higher-order differential power analysis (HODPA) attacks in asymmetric cryptosystems like RSA. HODPA attacks can be resisted by segmenting secret sensitive data and its intermediate values into multiple shares. In modular exponentiation-based cryptosystems, the exponent plays a significant part in the secret key. We have used inner product with differential evolution algorithm to segment the exponent into multiple shares. Using entropy-based nearest neighbor algorithm, we have randomly computed independent modular exponentiation to resist SPA and DPA attacks. Analysis was done on 1024, 1536 and 2048 bit RSA. With a pre-computation complexity, the proposed approach can provide significant resistance to SPA, DPA and HODPA attacks against modular exponentiation-based cryptosystems. [ABSTRACT FROM AUTHOR]

Due to the computational limitations at present, there is no efficient integer factorization algorithm that can break at least 2048 bits of RSA with strong prime factors in polynomial time. Although Shor’s algorithm based on a quantum computer has been presented, the quantum computer is still in its early stages of the development. As a result, the integer factorization problem (IFP) is a technique that is still being refined. Pollard’s p − 1 is an integer factorization algorithm based on all prime factors of p − 1 or q − 1, where p and q are two distinct prime factors of modulus. In fact, Pollard’s p − 1 is an efficient method when all prime factors of p − 1 or q − 1 are small. The aim of this paper is to propose a variant of Pollard’s p − 1 in order to decrease the computation time. In general, the proposed method is very efficient when all prime factors of p − 1 or q − 1 are the members of B-smooth. Assuming this condition exists, the experimental results demonstrate that the proposed method is approximately 80 to 90 percent faster than Pollard’s p − 1. Furthermore, the proposed technique is still faster than Pollard’s p − 1 for some values of modulus in which at least one integer is a prime factor of p − 1 or q − 1 while it is not a member of B-smooth. In addition, it is demonstrated that the proposed method’s best-case running time is O(x),where x is represented as bits length of n.

At present,in discrete-log based cryptographic protocols,most of the computational models of modular exponentiation are for primes,while less work has been done for composite.What’s more,most schemes are based on two servers,in which it requires at least one server to be honest.However,there may not be a fully trusted cloud server in the actual environment.Then a new secure method for outsourcing exponentiation modular a composite which based on a single server was proposed.The scheme used a new mathematical division method,it could ensure the privacy of the base and exponentiation.Compared with the existing schemes,the checkability of our scheme can be greatly improved.The user can detect the error result with the probability of 119/120.

The CMERE algorithm was designed to resist DPA attacks on modular exponentiation. It was implemented and tested at the algorithmic level for different key sizes of the RSA cryptosystems. The strength of CMERE lied on the facts that it could be implemented both on left-to-right and right-to-left binary methods for modular exponentiation without any changes in the original algorithm. Also, the execution of modular exponentiation was completely bit independent making it a very strong countermeasure against simple and differential power analysis attacks. In this paper, we have verified the CMERE algorithm at hardware level using VHDL. During formal verification with VHDL on FPGA, the algorithm was modified for practical implementation. However, the overall strength of the improved CMERE algorithm remains the same as the original algorithm. [ABSTRACT FROM AUTHOR]

Verifiable computation (VC) enables a computationally weak client to outsource the computation of a function f to a more powerful but untrusted server. The server returns an answer that allows the client to recover the correct result, accompanied by a proof of correctness. The basic requirement of a VC scheme is efficiency, i.e., the time consuming in preparing its input and verifying the server's proof must be less than the time required to compute the function on its own. In this paper, we propose a novel outsourcing scheme for modular exponentiation from shareable functions, which is secure even in the presence of adaptive adversaries. Compared with previous works, our algorithm is superior in both efficiency and checkability. In order to keep the exponent privacy, our algorithm invokes the less subroutine, which accounts for the largest proportion of the time spent. The client can detect the error with overwhelming probability. We then gave a comparation that demonstrates the efficiency of the proposed outsourcing algorithm and scheme. Finally, we propose a generic scheme for shareable function family, and analyze the concrete security. [ABSTRACT FROM AUTHOR]

This paper presents an approach to resist modular exponentiation-based cryptosystems like RSA from higher-order DPA attacks. The best way to prevent higher-order DPA attacks is by splitting the sensitive data into independent shares and execute them individually. We have incorporated the concept of inner product to split the large exponent or secret key in modular exponentiation into multiple shares. With these independent shares, individual modular exponentiation has been computed using multiply-always binary method. These shares have also been arithmetically blinded with a 32-bit blinding factor prior to computation. The entire analysis has been executed in RSA of sizes: 1024 bits, 1536 bits and 2048 bits. The results show that the proposed work can provide significant resistance to SPA, DPA and higher-order DPA attacks on modular exponentiation-based cryptosystems. [ABSTRACT FROM AUTHOR]

This paper presents an approach to compute secured modular exponentiation to mitigate power analysis attacks. Two processes have been designed based on 'multiply-always' binary method, which injects dummy multiplications so that the original multiplications can remain intact. The two processes are being invoked based on a random variable, which generated either 0 or 1. With these randomised modular exponentiation, the proposed approach can resist simple and differential power analysis attacks to a large extent. The proposed approach has been implemented using conventional 'squaring-multiplication' and 'Montgomery-Ladder' methods. Further, the work has also been extended to CRT-RSA, which is widely used for fast computation. The proposed method has been implemented for different key sizes of 1024-bit, 1536-bit and 2048-bit RSA & CRT-RSA. The analysis and results show that with a complexity of O (n) , the proposed approach can resist some of the standard DPA attacks on modular exponentiation. [ABSTRACT FROM AUTHOR]

This paper presents an FPGA implementation of the most critical operations of Public Key Cryptography (PKC), namely the Modular Exponentiation (ME) and the Modular Multiplication (MM). Both operations are integrated as Programmable System on Chip (PSoC) where the processor Microblaze of Xilinx is used for flexibility. Our objective is to achieve a best trade-off between time execution, occupied area and flexibility. The implementation of these operations on such environment requires taking into account several criteria. Indeed, the Hardware (HW) architectures data bus should be smaller than the input data length. The design must be scalable to support different security levels. The implementation achieves optimums execution time and HW resources number. In order to satisfy these constraints, Montgomery Power Ladder (MPL) and Montgomery Modular Multiplication (MMM) algorithms are utilized for the ME and the MM implementations as HW accelerators, respectively. Our implementation approach is based on the digit-serial method for performing the basic arithmetic operations. Efficient parallel and pipeline strategies are developed at the digit level for the optimization of the execution times. The application for 1024-bits data length shows that the MMM run in 6.24 μ s and requires 647 slices. The ME is executed in 6.75 ms using 2881 slices. [ABSTRACT FROM AUTHOR]