Security-enrichment of an asymmetric optical image encryption-based devil’s vortex Fresnel lens phase mask and lower upper decomposition with partial pivoting in gyrator transform domain

An asymmetric optical cryptosystem to encrypt images using devil’s vortex Fresnel lens (DVFLs) phase masks and lower upper decomposition with partial pivoting (LUDPP) is proposed in gyrator transform domain. The proposed cryptosystem utilizes DVFLs which are the complex phase masks designed using the combination of a phases of devil’s lens (DL), vortex lens(VL), and Fresnel lens (FL). LUDPP is an operation used to decompose the matrix and is utilized to supersede the phase-truncation (PT) task in the traditional phase-truncated Fourier transform (PTFT). Hence, the proposed method is immune to the attacks to which the PTFT-based cryptosystems are vulnerable. The cryptosystem is asymmetric as both the encryption and decryption processes are different along with different keys. The private keys generated during the encryption process are utilised in the decryption process to retrieve the original image. The encryption and decryption process can be realised with both the digital and the modified optical architecture. In order to show the strength and robustness of the proposed encryption, a conspire numerical simulation was performed.

Cryptanalysis Using Lower-Upper Decomposition and Structured Phase Mask in the Fractional Fourier Domain

Background: An asymmetric cryptosystem using Structured Phase Mask (SPM) and Random Phase Mask (RPM) in fractional Fourier transform (FrFT) using lower-Upper decomposition with partial pivoting is proposed to provide extra security to the system. The usage of structured phase mask offers additional parameter in encryption. In the encoded process the phase-truncation (PT) part is replaced by the LUDP that is by the decomposition part. Objective: Introducing an asymmetric cryptosystem with LUDP is to avert quick identification of encrypted image in the FrFT domain. Method: Input image is firstly convoluted with SPM, in FrFT and in LUDP then the obtained result is convoluted with RPM in inverse FrFT and in LUDP. Finally, the encoded image is attained. Results: The strength and legitimacy of the proposed scheme have been verified by using numerical analysis on MATLAB R2018a (9.4.0.813654). For checking the viability of the proposed scheme mathematical simulations have been carried out which determines the performance and better quality of an image based on key sensitivity, occlusion attack, noise attacks and histograms. Conclusion: A novel asymmetric cryptosystem is proposed using two phase masks one is SPM and another is RPM. LUDP is proposed in which the encoded procedure is different from the decoded procedure. Security is enhanced by increasing the number of keys and the scheme is also robust against attacks. Statistical simulations are also carried out for inspection the strength and viability of the algorithm.

Hierarchical approach for deriving a reproducible unblocked LU factorization

We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). For this purpose, we build upon Level-1/2 BLAS kernels that deliver correctly-rounded and reproducible results for the dot (inner) product, vector scaling, and the matrix-vector product. In addition, we draw a strategy to enhance the accuracy of the triangular solve via iterative refinement. Following a bottom-up approach, we finally construct a reproducible unblocked implementation of the LU factorization for GPUs, which accommodates partial pivoting for stability and can be eventually integrated in a high performance and stable algorithm for the (blocked) LU factorization.

Variability of the adiabatic parameter in monoatomic thermal and non-thermal plasmas

Context. Numerical models of the evolution of interstellar and integalactic plasmas often assume that the adiabatic parameter γ (the ratio of the specific heats) is constant (5/3 in monoatomic plasmas). However, γ is determined by the total internal energy of the plasma, which depends on the ionic and excitation state of the plasma. Hence, the adiabatic parameter may not be constant across the range of temperatures available in the interstellar medium. Aims. We aim to carry out detailed simulations of the thermal evolution of plasmas with Maxwell–Boltzmann and non-thermal (κ and n) electron distributions in order to determine the temperature variability of the total internal energy and of the adiabatic parameter. Methods. The plasma, composed of H, He, C, N, O, Ne, Mg, Si, S, and Fe atoms and ions, evolves under collisional ionization equilibrium conditions, from an initial temperature of 109 K. The calculations include electron impact ionization, radiative and dielectronic recombinations and line excitation. The ionization structure was calculated solving a system of 112 linear equations using the Gauss elimination method with scaled partial pivoting. Numerical integrations used in the calculation of ionization and excitation rates are carried out using the double-exponential over a semi-finite interval method. In both methods a precision of 10−15 is adopted. Results. The total internal energy of the plasma is mainly dominated by the ionization energy for temperatures lower than 8 × 104 K with the excitation energy having a contribution of less than one percent. In thermal and non-thermal plasmas composed of H, He, and metals, the adiabatic parameter evolution is determined by the H and He ionizations leading to a profile in general having three transitions. However, for κ distributed plasmas these three transitions are not observed for κ < 15 and for κ < 5 there are no transitions. In general, γ varies from 1.01 to 5/3. Lookup tables of the γ parameter are presented as supplementary material.