Anissa Sghaier

The use of resource-constrained devices is rising nowadays, and these devices mostly operate with sensitive data. Consequently, security is a key issue for these devices. In this paper, we propose a compact ECC (elliptic curve cryptography) architecture for resource-constrained devices based on López–Dahab (LD) projective point arithmetic operations on GF(2^m). To achieve an efficient area-power hardware ECC implementation, an efficient digit-serial multiplier is developed. The proposed multiplier is built on a Bivariate Polynomial Basis representation and a modified Radix-n Interleaved Multiplication (mRnIM) method (for area and power complexities reduction). Furthermore, the LD-Montgomery point multiplication algorithm is adjusted for accurate scheduling in the compact ECC architecture to eliminate data reliance and improve signal management. Meanwhile, the area complexity is reduced by reuse of resources, and clock gating and asynchronous counter are exploited to reduce the power consumption. Finally, the proposed compact ECC architecture is implemented over GF(2^m) (m = 163, 233, 283, 409, and 571) on Xilinx FPGAs’ (Field-Programmable Gate Array) Virtex 5, Virtex 6, and Virtex 7, showing that the efficiency of this design outperforms to date when compared to reported works individually. It utilizes less area and consumes low power. The FPGA results clearly demonstrate that the proposed ECC architecture is appropriate for constraint-resources devices.

The Elliptic Curve Digital Signature Algorithm(ECDSA) is the analog to the Digital Signature Algorithm(DSA). Based on the elliptic curve, which uses a small key compared to the others public-key algorithms, ECDSA is the most suitable scheme for environments where processor power and storage are limited. This paper focuses on the hardware implementation of the ECDSA over elliptic curveswith the 163-bit key length recommended by the NIST (National Institute of Standards and Technology). It offers two services: signature generation and signature verification. The proposed processor integrates an ECC IP, a Secure Hash Standard 2 IP (SHA-2 Ip) and Random Number Generator IP (RNG IP). Thus, all IPs will be optimized, and different types of RNG will be implemented in order to choose the most appropriate one. A co-simulation was done to verify the ECDSA processor using MATLAB Software. All modules were implemented on a Xilinx Virtex 5 ML 50 FPGA platform; they require respectively 9670 slices, 2530 slices and 18,504 slices. FPGA implementations represent generally the first step for obtaining faster ASIC implementations. Further, the proposed design was also implemented on an ASIC CMOS 45-nm technology; it requires a 0.257 mm2 area cell achieving a maximum frequency of 532 MHz and consumes 63.444 (mW). Furthermore, in this paper, we analyze the security of our proposed ECDSA processor against the no correctness check for input points and restart attacks.

Because it offers several benefits over other public-key cryptosystems much effort are done to make Hyper Elliptic Curve Cryptosystems (HECC) more practical, such as RSA, it offers a comparable level of security with a smaller key size. For this reason, HECCs can be used in embedded environments where speed, energy, power, chip and memory area are constrained. However, HEC use a complex mathematical background, so it's difficult to be implemented on hardware. They can be defined over real numbers, complex numbers and any other field. So we need arithmetic operations (addition, subtraction, multiplication and division) which have much application in cryptography and coding theory. We have to note that the overall performance of HECC is mainly determined by the speed of arithmetic operations. The most algorithms that manipulate these operations use polynomial coefficients in base 2 and they are defined over finite fields. But, the problem is clearly viewed over real field and simple to be presented. Arithmetic operations are based on the complexity of a mathematical problem, and to have an optimized architecture we need to optimize arithmetic operations. In this paper we describe a high performance, area efficient implementation of arithmetic operations in HECC over real field and a new design methodology is presented. The proposed architectures operations are implemented in FPGA.