A NONLINEAR DECOMPOSITION METHOD IN ANALYSIS OF SOME ENCRYPTION SCHEMES USING GROUP AUTOMORPHISMS

2018 ◽  
pp. 38-45
Author(s):  
V. A. Roman’kov ◽  
◽  
A. A. Obzor ◽  
Keyword(s):  
Decomposition Method ◽  
Encryption Schemes ◽  
Nonlinear Decomposition ◽  
Group Automorphisms

Two general schemes of algebraic cryptography

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Vitaly Roman’kov
Keyword(s):  
Algebraic System ◽  
Decomposition Method ◽  
General Scheme ◽  
Search Problem ◽  
Algebraic Cryptanalysis ◽  
Algebraic Setting ◽  
Diffie Hellman ◽  
Algebraic Cryptography ◽  
Algorithmic Problems ◽  
Nonlinear Decomposition

AbstractIn this paper, we introduce two general schemes of algebraic cryptography. We show that many of the systems and protocols considered in literature that use two-sided multiplications are specific cases of the first general scheme. In a similar way, we introduce the second general scheme that joins systems and protocols based on automorphisms or endomorphisms of algebraic systems. Also, we discuss possible applications of the membership search problem in algebraic cryptanalysis. We show how an efficient decidability of the underlined membership search problem for an algebraic system chosen as the platform can be applied to show a vulnerability of both schemes. Our attacks are based on the linear or on the nonlinear decomposition method, which complete each other. We give a couple of examples of systems and protocols known in the literature that use one of the two introduced schemes with their cryptanalysis. Mostly, these protocols simulate classical cryptographic schemes, such as Diffie–Hellman, Massey–Omura and ElGamal in algebraic setting. Furthermore, we show that, in many cases, one can break the schemes without solving the algorithmic problems on which the assumptions are based.

A decomposition method in non-linear programmm

Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér
Keyword(s):  
Decomposition Method ◽  
Non Linear

DECOMPOSITION METHOD FOR DETERMINING THE HIGH REFLECTED SECTIONS OF A COMPLEX OBJECT SURFACE

2018 ◽  
Vol 77 (11) ◽  
pp. 945-956 ◽  
Author(s):  
N. N. Kolchigin ◽  
M. N. Legenkiy ◽  
A. A. Maslovskiy ◽  
А. Demchenko ◽  
S. Vinnichenko ◽  
...  
Keyword(s):  
Decomposition Method ◽  
Complex Object ◽  
Object Surface

A Spectrum-Adaptive Decomposition Method for Effective Atomic Number Estimation Using Dual Energy CT

2020 ◽  
Vol 2020 (14) ◽  
pp. 293-1-293-7
Author(s):  
Ankit Manerikar ◽  
Fangda Li ◽  
Avinash C. Kak
Keyword(s):  
Atomic Number ◽  
Decomposition Method ◽  
Traditional Approach ◽  
Effective Atomic Number ◽  
Dual Energy ◽  
Performance Comparison ◽  
Estimation Methods ◽  
Dual Energy Ct ◽  
Projection Data ◽  
X Ray

Dual Energy Computed Tomography (DECT) is expected to become a significant tool for voxel-based detection of hazardous materials in airport baggage screening. The traditional approach to DECT imaging involves collecting the projection data using two different X-ray spectra and then decomposing the data thus collected into line integrals of two independent characterizations of the material properties. Typically, one of these characterizations involves the effective atomic number (Zeff) of the materials. However, with the X-ray spectral energies typically used for DECT imaging, the current best-practice approaches for dualenergy decomposition yield Zeff values whose accuracy range is limited to only a subset of the periodic-table elements, more specifically to (Z < 30). Although this estimation can be improved by using a system-independent ρe — Ze (SIRZ) space, the SIRZ transformation does not efficiently model the polychromatic nature of the X-ray spectra typically used in physical CT scanners. In this paper, we present a new decomposition method, AdaSIRZ, that corrects this shortcoming by adapting the SIRZ decomposition to the entire spectrum of an X-ray source. The method reformulates the X-ray attenuation equations as direct functions of (ρe, Ze) and solves for the coefficients using bounded nonlinear least-squares optimization. Performance comparison of AdaSIRZ with other Zeff estimation methods on different sets of real DECT images shows that AdaSIRZ provides a higher output accuracy for Zeff image reconstructions for a wider range of object materials.

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