FPGA-based Implementation of SHA-256 with Improvement of Throughput using Unfolding Transformation

Security has grown in importance as a study issue in recent years. Several cryptographic algorithms have been created to increase the performance of these information-protecting methods. One of the cryptography categories is a hash function. This paper proposes the implementation of the SHA-256 (Secure Hash Algorithm-256) hash function. The unfolding transformation approach was presented in this study to enhance the throughput of the SHA-256 design. The unfolding method is employed in the hash function by producing the hash value output based on modifying the SHA-256 structure. In this unfolding method, SHA-256 decreases the number of clock cycles required for traditional architecture by a factor of two, from 64 to 34 because of the delay. To put it another way, one cycle of the SHA-256 design can generate up to four parallel inputs for the output. As a result, the throughput of the SHA-256 design can be improved by reducing the number of cycles by 16 cycles. ModelSim was used to validate the output simulations created in Verilog code. The SHA-256 hash function factor four hardware implementation was successfully tested using the Altera DE2-115 FPGA board. According to timing simulation findings, the suggested unfolding hash function with factor four provides the most significant throughput of around 4196.30 Mbps. In contrast, the suggested unfolding with factor two surpassed the classic SHA-256 design in terms of maximum frequency. As a result, the throughput of SHA-256 increases 13.7% compared to unfolding factor two and 58.1% improvement from the conventional design of SHA-256 design.

Homogenization and Correctors for Stochastic Hyperbolic Equations in Domains with Periodically Distributed Holes

The goal of this paper is to present new results on homogenization and correctors for stochastic linear hyperbolic equations in periodically perforated domains with homogeneous Neumann conditions on the holes. The main tools are the periodic unfolding method, energy estimates, probabilistic and deterministic compactness results. The findings of this paper are stochastic counterparts of the celebrated work [D. Cioranescu, P. Donato and R. Zaki, The periodic unfolding method in perforated domains, Port. Math. (N.S.) 63 (2006) 467–496]. The convergence of the solution of the original problem to a homogenized problem with Dirichlet condition has been shown in suitable topologies. Homogenization and convergence of the associated energies results recover the work in [M. Mohammed and M. Sango, Homogenization of Neumann problem for hyperbolic stochastic partial differential equations in perforated domains, Asymptot. Anal. 97 (2016) 301–327]. In addition to that, we obtain corrector results.

Homogenization and correctors of Robin problem for linear stochastic equations in periodically perforated domains

In this paper, we present homogenization and corrector results for stochastic linear parabolic equations in periodically perforated domains with non-homogeneous Robin conditions on the holes. We use the periodic unfolding method and probabilistic compactness results. Homogenization results presented in this paper are stochastic counterparts of some fundamental work given in [Cioranescu, Donato and Zaki in Port. Math. (N.S.) 63 (2006), 467–496]. We show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized problem, which is a parabolic stochastic equation in fixed domain with Dirichlet condition on the boundary. In contrast to the two scale convergence method, the corrector results obtained in this paper are without any additional regularity assumptions on the solutions of the original problems.