Search Results (3)

With the development of mobile communication, digital signatures with low latency, low area, and high security are in increasing demand. Elliptic curve cryptography (ECC) is widely used because of its security and lightweight. Elliptic curve scalar multiplication (ECSM) is the basic arithmetic in ECC. Based on this background information, we propose our own research objectives. In this paper, a low-latency and low-area ECSM architecture based on the comb algorithm is proposed. The detailed methodology is as follows. The recoding-k algorithm and randomization-Z algorithm are used to improve security, which can resist sample power analysis (SPA) and differential power analysis (DPA). A low-area multi-functional architecture for comb is proposed, which takes into account different stages of the comb algorithm. Based on this, the data dependency is considered and the comb architecture is optimized to achieve a uniform and efficient execution pattern. The interleaved modular multiplication algorithm and modified binary inverse algorithm are used to achieve short clock cycle delay and high frequency while taking into account the need for a low area. The proposed architecture has been implemented on Xilinx Virtex-7 series FPGA to perform ECSM on 256-bits prime field $GF\left(p\right)$. In the hardware architecture with only 7351 slices of resource usage, a single ECSM only takes 0.74 ms, resulting in an area-time product (ATP) of 5.41. The implementation results show that our design can compete with the existing state-of-the-art engineering in terms of performance and has higher security. Our design is suitable for computing scenarios where security and computing speed are required. The implementation of the overall architecture is of great significance and inspiration to the research community. Full article

For a finite field GF($p^L$) with prime p and $L>1$, one of the standard representations is $L\times L$ matrices over GF(p) so that the arithmetic of GF($p^L$) can be realized by the arithmetic among these matrices over GF(p). Based on the matrix representation of GF($p^L$), a conventional linear network coding scheme over GF($p^L$) can be transformed to an L-dimensional vector LNC scheme over GF(p). Recently, a few real implementations of coding schemes over GF($2^L$), such as the Reed–Solomon (RS) codes in the ISA-L library and the Cauchy-RS codes in the Longhair library, are built upon the classical result to achieve matrix representation, which focuses more on the structure of every individual matrix but does not shed light on the inherent correlation among matrices which corresponds to different elements. In this paper, we first generalize this classical result from over GF($2^L)$ to over GF($p^L$) and paraphrase it from the perspective of matrices with different powers to make the inherent correlation among these matrices more transparent. Moreover, motivated by this correlation, we can devise a lookup table to pre-store the matrix representation with a smaller size than the one utilized in current implementations. In addition, this correlation also implies useful theoretical results which can be adopted to further demonstrate the advantages of binary matrix representation in vector LNC. In the following part of this paper, we focus on the study of vector LNC and investigate the applications of matrix representation related to the aspects of random and deterministic vector LNC. Full article

A scheme for the Fourier–Galois spectrum analyzer for the field GF(31) is proposed. It is shown that this analyzer allows for solving a wide enough range of problems related to image processing, in particular those arising in the course of experimental studies in the field of physical chemistry. Such images allow digital processing when divided into a relatively small number of pixels, which creates an opportunity to use Galois fields of relatively small size. The choice of field GF(31) is due to the fact that the number 31 is a Mersenne prime number, which considerably simplifies the algorithm of calculating the Fourier–Galois transform in this field. The proposed scheme of the spectrum analyzer is focused on the use of threshold sensors, at the output of which signals corresponding to binary logic are formed. Due to this fact, further simplification of the proposed analyzer scheme is achieved. The constructiveness of the proposed approach is proven using digital modeling of electronic circuits. It is concluded that when solving applied problems in which an image can be divided into a relatively small number of pixels, it is important to take into account the specificity of particular Galois fields used for their digital processing. Full article