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In a wireless sensor network, we often require the deployment of new nodes to extend the lifetime of the network because some sensor nodes may be lost due to power exhaustion problem or they may be also malicious nodes. In order to protect malicious nodes from joining the sensor network, access control mechanism becomes a major challenging problem in the design of sensor network protocols. Existing access control protocols designed for wireless sensor networks require either high communication overheads or they are not scalable due to involvement of the base station during authentication and key establishment processes. In this paper, we propose a new access control scheme for large-scale distributed wireless sensor networks, which not only identifies the identity of each node but it has also ability to differentiate between old nodes and new nodes. The proposed scheme does not require involvement of the base station during authentication and key establishment processes, and it can be easily implemented as a dynamic access control protocol. In addition, our scheme significantly reduces communication costs in order to authenticate neighbor nodes among each other and establish symmetric keys between neighbor nodes as compared with existing approaches. Further, our scheme is secure against different attacks and unconditionally secure against node capture attacks. The simulation results of our scheme using the AVISPA (Automated Validation of Internet Security Protocols and Applications) tool ensure that our scheme is safe.

Let $(n=pq,e=n^{\beta })$ be an RSA public key with private exponent $d=n^{\delta },$ where $p$ and $q$ are large primes of the same bit size. At Eurocrypt 96, Coppersmith presented a polynomial-time algorithm for finding small roots of univariate modular equations based on lattice reduction and then succussed to factorize the RSA modulus. Since then, a series of attacks on the key equation $ed-k\varphi (n)=1$ of RSA have been presented. In this paper, we show that many of such attacks can be unified in a single attack using a new notion called Coppersmith’s interval. We determine a Coppersmith’s interval for a given RSA public key $(n,e).$ The interval is valid for any variant of RSA, such as Multi-Prime RSA, that uses the key equation. Then we show that RSA is insecure if $\delta <\beta +\frac{1}{3}\alpha -\frac{1}{3}\sqrt{12\alpha \beta +4{\alpha }^2}$ provided that we have approximation $p_0\ge \sqrt{n}$ of $p$ with $\left|p-p_0\right|\le \frac{1}{2}{n}^{\alpha },$$\alpha \le \frac{1}{2}.$ The attack is an extension of Coppersmith’s result.

This paper presents an implementation of Rivest, Shamir and Adleman (RSA) cryptosystem based on hardware/software (HW/SW) co-design. The main operation of RSA is the modular exponentiation (ME) which is performed by repeated modular multiplications (MMs). In this work, the right-to-left (R2L) algorithm is used for the implementation of the ME as a programmable system on chip (PSoC). The processor MicroBlaze of Xilinx is used for flexibility. The R2L method is often suggested to improve the timing performance, since it is based on parallel computations of MMs. However, if the optimization of HW resources is a constraint, this method can be executed sequentially using a single modular multiplier as a custom intellectual property (IP). Consequently, the execution time of the ME becomes dependent of three factors, namely the capability of the custom IP to perform the MMs, the nonzero bit string of the exponent and the communication link between the processor and the custom IP. In order to achieve the best trade-off between area, speed and flexibility, we propose three implementations in this work. The first one is a pure software solution. The second one takes benefit of a HW accelerator dedicated to the MM execution. The last one is based on a dual strategy. Two parallel MMs are implemented within a custom IP and local memories are used close to the arithmetic units to minimize the communication link influence. The results show that in the application to RSA 1024-bits, the ME runs in 22,25 ms, while using only 1,848 slices.

One of the most common algorithms in a digital signature is the RSA-CRT. Several side channel attacks have been presented on the RSA-CRT’s embedded design. Such attacks are divided into two categories: attack in the modular reduction step and attack in the recombination step. The former are plaintext attacks and based on the modular reduction on equidistant data attack, which is introduced in [B. den Boer, et al., “A DPA attack against the modular reduction within a CRT implementation of RSA,” in CHES 2002]. In these attacks, instead of using random plaintext, an equidistant series of input data is used. In a chosen and equidistant plaintext attack, the attacker needs a higher level of accessibility, and it is more difficult than a nonchosen plaintext attack. In this paper, we present a nonequidistant plaintext (but chosen plaintext) differential power analysis attack on the modular reduction in RSA-CRT, named NEMR (nonequidistant plaintext on modular reduction). We also present a new countermeasure on NEMR attack, which is resistant against equidistant and nonequidistant data attack on reduction step in RSA-CRT. In order to prove the idea, the NEMR attack is applied on the RSA-CRT 2048-bit implementation on SAKURA-G board, and the result is evaluated. Then, the presented countermeasure on NEMR attack is tested, and practical results demonstrate the validity of the proposed approach.

RSA-CRT is one of the most common algorithms in the digital signature. Several side-channel attacks have been presented on the implementation of RSA-CRT. One of the most important side-channel attacks on RSA-CRT is Modular Reduction on Equidistant Data (MRED). The implementation of RSA-CRT has too many challenges in the multiplications when the key size is too long (e.g. 2048 bits). Montgomery multiplication is one of the common methods for executing the RSA multiplication, which has many implementation problems and side-channel leakage challenges. This article first implements an RSA-CRT algorithm based on the Montgomery multiplication with the high-speed and low area hardware. The implementation is named RSA-CRT-MMB (Montgomery Method Based). Next, a new power analysis side-channel attack on RSA-CRT-MMB is presented. We name our attack MRED on MMB. The attack utilizes new side-channel leakage information about the CRT reduction algorithm implemented by the MMB, for the first time. The previous articles do not investigate the MRED attack on Montgomery multiplication in RSA-CRT. Finally, a new countermeasure is presented to prevent the MREDM attack. The countermeasure does not have any overload in the hardware area or running time of the RSA algorithm. The correctness of our scheme, the 2048-bit RSA-CRT-MMB, is investigated by the implementation of the scheme on the SASEBO-W board in our DPA laboratory. The total running time of 2048-bit RSA is 250ms and the RSA algorithm occupies only 23% of LUT slice on Spartan-6 FPGA. The proposed countermeasures are also verified by practical experiments.

In this paper, we design a cellular automaton and a discrete-time cellular neural network (DTCNN) using nonlinear passive memristors. They can perform a number of applications, such as logical operations, image processing operations, complex behaviors, higher brain functions, RSA algorithm, etc. By modifying the characteristics of nonlinear memristors, the memristor DTCNN can perform almost all functions of memristor cellular automaton. Furthermore, it can perform more than one function at the same time, that is, it allows multitasking.

Herein, an asymmetric image encryption algorithm based on RSA cryptosystem and a fractional-order chaotic system is proposed. Its security depends on RSA algorithm. First, a pair of public and private keys is generated by RSA algorithm. Subsequently, a random message shown as plaintext key information is encrypted by the public key and RSA to achieve ciphertext key information. Next, a new transformation map is established to generate the initial key according to the ciphertext key information. Subsequently, the initial key is substituted into a fractional hyperchaotic system equation to calculate the keystream. Finally, permutation and diffusion operations are employed to encrypt a plain image to obtain the final cipher image. In the proposed algorithm, different keys for encryption and decryption are designed under an asymmetric architecture. The RSA algorithm and fractional chaotic system are combined to encrypt images; in particular, a fast algorithm for computing power multiplication is employed, which significantly improves the encryption effect and enhances the security. Simulation results show that the proposed algorithm is effective and applicable to image protection.

The nickel molybdate carbon nanotube composites $({\mathrm{\text{NiMoO}}}_4/\mathrm{\text{CNTs}})$ were synthesized by solution blending method. The ${\mathrm{\text{NiMoO}}}_4/\mathrm{\text{CNTs}}$ were characterized by scanning electron microscopy (SEM), Raman spectroscopy and UV–Vis absorption spectroscopy. The $({\mathrm{\text{NiMoO}}}_4/\mathrm{\text{CNTs}})/\mathrm{\text{PMMA}}$ organic glasses were obtained by dispersing ${\mathrm{\text{NiMoO}}}_4/\mathrm{\text{CNTs}}$ in methyl methacrylate (MMA) and polymerizing in a water bath at 75°C for 1h. The nonlinear optical (NLO) properties were measured via $Z$-scan technique. By testing we obtained that $({\mathrm{\text{NiMoO}}}_4/\mathrm{\text{CNTs}})/\mathrm{\text{PMMA}}$ has a reverse saturation absorption (RSA) effect and optical limiting (OL) performance. In addition, the RSA effect is enhanced compared to other similar materials. The OL threshold ${(F}_{\mathrm{\text{th}}})$ and the normalized transmittance clamping value $(T_c)$ are calculated and fitted to be ${0.83\mathrm{\text{J}}\mathrm{\text{cm}}}^{-2}$ and ${0.48\mathrm{\text{J}}\mathrm{\text{cm}}}^{-2}$, respectively. Consequently, ${\mathrm{\text{NiMoO}}}_4/\mathrm{\text{CNTs}}$ have significant research value in the direction of extending new materials for laser protection.