Discovery of Multiple-Valued Bent Functions in Galois Field and Reed-Muller-Fourier Domains

Radmanovic, Milos; Stanković, Radomir S.

doi:10.1109/ismvl.2017.17

Cited by 3 publications

(5 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The presented algorithm is compared with our previous algorithm with exhaustive search for random discovering of bent functions in both domains [7]. The proposed algorithm using GF or RMF subsets reduces the number of possible positions of non-zero coefficients in the spectrum.…”

Section: Resultsmentioning

confidence: 99%

“…Since the algebraic degree of bent functions in the GF and RMF domains is restricted, the spectral search space for discovering of bent functions in the GF and RMF domains is discussed in [7]. It is shown that in the GF and RMF domains the discovery is extended to ternary bent functions with 6 variables, and to quaternary bent functions with 4 variables.…”

Section: Copyright Cmentioning

confidence: 99%

See 1 more Smart Citation

Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains

Cacute

2021

IEICE Trans. Inf. & Syst.

View full text Add to dashboard Cite

Multiple-valued bent functions are functions with highest nonlinearity which makes them interesting for multiple-valued cryptography. Since the general structure of bent functions is still unknown, methods for construction of bent functions are often based on some deterministic criteria. For practical applications, it is often necessary to be able to construct a bent function that does not belong to any specific class of functions. Thus, the criteria for constructions are combined with exhaustive search over all possible functions which can be very CPU time consuming. A solution is to restrict the search space by some conditions that should be satisfied by the produced bent functions. In this paper, we proposed the construction method based on spectral subsets of multiple-valued bent functions satisfying certain appropriately formulated restrictions in Galois field (GF) and Reed-Muller-Fourier (RMF) domains. Experimental results show that the proposed method efficiently constructs ternary and quaternary bent functions by using these restrictions.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Copyright Cmentioning

confidence: 99%

Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains

Cacute

2021

IEICE Trans. Inf. & Syst.

View full text Add to dashboard Cite

show abstract

“…Therefore, ternary FPRM circuit optimization, which combines ternary logic and FPRM logic, has become a research hotspot in the field of integrated circuit logic synthesis. 12 Different polarities correspond to different circuit expressions, which in turn correspond to different circuit delays. Therefore, polarity is an important factor affecting circuit delay.…”

Section: Introductionmentioning

confidence: 99%

Delay optimization for ternary fixed polarity Reed–Muller circuits based on multilevel adaptive quantum genetic algorithm

Xiaoqian

Wang

et al. 2021

Int J Intell Syst

View full text Add to dashboard Cite

Delay optimization has now emerged as an important optimization goal in logic synthesis. The delay optimization for ternary fixed polarity Reed-Muller (FPRM) circuits aims to find a ternary FPRM circuit with a minimum delay. Because the delay optimization for ternary FPRM circuits is a combinatorial optimization problem, in this paper, we first propose a multilevel adaptive quantum genetic algorithm (MAQGA), which divides individuals into three-level populations: high-level population, intermediate-level population, and low-level population and uses the proposed ternary quantum rotation gate, proposed ternary quantum correction gate, and proposed multi-operator adaptive mutation mechanism to make the three-level populations evolve. Moreover, based on the proposed delay decomposition strategy, we propose a delay optimization approach (DOA) for ternary FPRM circuits under the unit delay model, which searches for a ternary FPRM circuit with a minimum delay using the MAQGA. Experimental results demonstrated the effectiveness and superiority of the DOA in optimizing the delay of ternary FPRM circuits.

show abstract

“…Fortunately, accelerators such as General Purpose Graphical Processing Unit (GPGPU), 1,2,[9][10][11] Many Integrated Core (MIC), [12][13][14] Digital Signal Processing (DSP), 3,4,[15][16][17][18] and Field Programmable Gate Array (FPGA) 5,6,[19][20][21][22][23][24][25][26][27][28] have recently proved to be a more promising platform to solve FFT prob-lems, since accelerators have much more parallel computing resources and can often achieve an order of magnitude performance improvement over CPUs.…”

Section: Introductionmentioning

confidence: 99%

“…Efforts have been popularly focused on GPGPU accelerating FFTs such as CUFFT from Nvidia, 29 a GPU-based out-ofcard FFT library from Gu et al, 30 FFT implementation based on a GPU cluster, Hybrid GPU/CPU FFT for Large FFT problems, 8,9,25,31 and FFT accelerated using MICs. [12][13][14] However, literature has cited the huge computing resources used by accelerators and have barely taken computing complexity and specified restrictions on the size of FFTs into account.…”

Section: Introductionmentioning

confidence: 99%

Customizing FFT with FMA for China Accelerator

Gan

Guo

et al. 2021

AATCC Journal of Research

View full text Add to dashboard Cite

Recently, Fast Fourier Transform (FFT) was introduced to study pattern characterization in textiles. Accelerators are a promising platform to accelerate large-scale FFT computation. However, current accelerating FFT only uses the accelerator to compute, but uses a CPU as a mere task controller. Additionally, a specified interface for FFT is built into the China accelerator (CA), which severely restricts FFT parallelization and performance. Hence, we transform four multiplications and six additions into six Fused Multiply Add (FMA) operations, then reduce total float operations by 40%, assisted by FMAs equipped with a Vector Processing Unit (VPE). Moreover, we propose an Interface Adapter (IA) to cater to a specified interface and a Fused Algorithm for Interface Adapter (FAIA) to fully use both the CA and CPU to compute large-scale FFT with coordination. Experimental results validated successful performance.

show abstract

Discovery of Multiple-Valued Bent Functions in Galois Field and Reed-Muller-Fourier Domains

Cited by 3 publications

References 4 publications

Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains

Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains

Delay optimization for ternary fixed polarity Reed–Muller circuits based on multilevel adaptive quantum genetic algorithm

Customizing FFT with FMA for China Accelerator

Contact Info

Product

Resources

About