Analysis on the MinRank Attack using Kipnis-Shamir Method Against Rainbow

Minrank problem is investigated as a problem related to a rank attack in multivariate cryptography and decoding of a rank code in coding theory. Recently, the Kipnis-Shamir method for solving this problem has been made significant progress due to Verbel et al. As this method reduces the problem to the MQ problem that asks for a solution of a system of quadratic equations, its complexity depends on the solving degree of a quadratic system deduced from the method. A theoretical value introduced by Verbel et al. approximates the minimal solving degree of the quadratic systems in the method although their value is defined under a certain limit for a considering system. A quadratic system outside their limitation often has the larger solving degree, but its solving complexity is not necessary larger since it has a smaller number of variables and equations. Thus, in order to discuss the best complexity of the Kipnis-Shamir method, we need a theoretical value approximating the solving degree of each deduced quadratic system. A quadratic system deduced from the Kipnis-Shamir method has a multi-degree always, and its solving complexity is influenced by this property. In this paper, we introduce a theoretical value defined by such a multi-degree and show it approximates the solving degree of each quadratic system. Thus we are able to compare the systems in the method and to discuss the best complexity. As its application, in the Minrank problem from the rank attack using the Kipnis-Shamir method against Rainbow, we show a case that a quadratic system outside Verbel et al.\u27s limitation is the best. Consequently, by using our estimation, the complexities of the attack against Rainbow parameter sets Ia, IIIc and Vc are improved as $2^{160.6}, 2^{327.9}$ and $2^{437.0}$, respectively

Instability and stability properties of traveling waves for the double dispersion equation

In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation $~u_{tt} -u_{xx}+a u_{xxxx}-bu_{xxtt} = - (|u|^{p-1}u)_{xx}~$ for $~p>1$, $~a\geq b>0$. The main characteristic of this equation is the existence of two sources of dispersion, characterized by the terms $u_{xxxx}$ and $u_{xxtt}$. We obtain an explicit condition in terms of $a$, $b$ and $p$ on wave velocities ensuring that traveling wave solutions of the double dispersion equation are strongly unstable by blow up. In the special case of the Boussinesq equation ($b=0$), our condition reduces to the one given in the literature. For the double dispersion equation, we also investigate orbital stability of traveling waves by considering the convexity of a scalar function. We provide both analytical and numerical results on the variation of the stability region of wave velocities with $a$, $b$ and $p$ and then state explicitly the conditions under which the traveling waves are orbitally stable.Comment: 16 pages, 4 figure

New Complexity Estimation on the Rainbow-Band-Separation Attack

Multivariate public key cryptography is a candidate for post-quantum cryptography, and it allows generating particularly short signatures and fast verification. The Rainbow signature scheme proposed by J. Ding and D. Schmidt is such a multivariate cryptosystem and is considered secure against all known attacks. The Rainbow-Band-Separation attack recovers a secret key of Rainbow by solving certain systems of quadratic equations, and its complexity is estimated by the well-known indicator called the degree of regularity. However, the degree of regularity generally is larger than the solving degree in experiments, and an accurate estimation cannot be obtained. In this paper, we propose a new indicator for the complexity of the Rainbow-Band-Separation attack using the $F_4$ algorithm, which gives a more precise estimation compared to one using the degree of regularity. This indicator is deduced by the two-variable power series $$\frac{\prod _{i=1}^m(1-t_1^{d_{i1}}t_2^{d_{i2}})}{(1-t_1)^{n_1}(1-t_2)^{n_2}},$$ which coincides with the one-variable power series at $t_1=t_2$ deriving the degree of regularity. Moreover, we show a relation between the Rainbow-Band-Separation attack using the hybrid approach and the HighRank attack. By considering this relation and our indicator, we obtain a new complexity estimation for the Rainbow-Band-Separation attack. Consequently, we are able to understand the precise security of Rainbow against the Rainbow-Band-Separation attack using the $F_4$ algorithm

Structural behavior analysis of high strength steel-concrete composite girders

In order to study structural behaviors of high strength steel-concrete composite girders, 14 group-components models with different geometry parameters and material properties were built by using ANSYS software under deuce symmetrical loads at mid-span. The analysis result indicates that steel girder bears about 77. 0% of whole vertical shear strength in plastic state, and the ratios of maximum and minimum values of mid-span deflections for different material strength girders in elastic and plastic states are 79. 5% and 28. 0% respectively; the ratios of maximum and minimum values of mid-span deflections for different transverse bar ratios and widthes of concrete slab girders in plastic state are 62. 1% and 53. 3% respectively; the ratios of maximum and minimum values of longitudinal slips for different material strengthes, widthes of concrete slab, transverse bar ratios and thicknesses of concrete deck girders in plastic state are 25. 0%, 41. 9%, 63. 2% and 70. 7% respectively. Therefore, increasing the strength and section size of steel is economic and reasonable method to increase the vertical shear strength of the girders; the steel and concrete strengthes affect little on the mid-span deflection of the girders in elastic state, and the transverse bar ratio and the width of concrete slab have larger effect on the mid-span deflection in plastic state; the geometry parameters and material properties of the girders have little effect on the longitudinal slip in elastic state, but the material strength, width of concrete slab, transverse bar ratio and thickness of concrete deck have obvious effects on the longitudinal slip in plastic state

Optimization of Urban Block Form by Adding New Volumes for Capacity Improvement and Solar Performance Using A Multi-Objective Genetic Algorithm: A Case Study of Nanjing

During urban renewal, multi-story residential blocks face a contradiction of balancing residential capacity improvement and solar constraint. This paper constructed a set of automatic workflows for adding new volumes to existing buildings, and a multi-objective optimization was applied with a Wallacei plug-in in Grasshopper to optimize the solar radiation, solar hours, and block capacity. First, this study established three building addition modes of existing blocks in the horizontal direction, vertical direction, and mixed direction, respectively. Three optimization objectives—maximum floor area ratio, maximum average radiation amount, and minimum solar shade—were defined. Second, the net increase in the floor area ratio of the block was calculated to balance capacity improvement and solar constraint. Third, the advantages of the three addition modes under different orientations were discussed. Among all three modes, the mixed addition mode had the best capacity improvement effect, with a 70% increase in floor area ratio. The vertical addition mode had the least impact on the solar shade of existing buildings. The horizontal addition mode could further improve the floor area ratio in areas where building height was strictly limited. The results can provide insights and inspiring guidelines for the renewal of the existing residential blocks to solve the floor area ratio constraint from solar radiation, as well as achieve urban function reconstruction and vitality regeneration

Study on the Microstructure and Properties of Welded Joints of Laser Shock Peening on HC420LA Low-Alloy High-Tensile Steel

Laser shock peening is a promising surface strengthening technology that can effectively improve the mechanical properties of materials. This paper is based on the laser shock peening process for HC420LA low-alloy high-strength steel weldments. Contrast analysis of the evolution of the microstructure, residual stress distribution and mechanical properties of the welded joints before and after the laser shock peening on each region is carried out; a combination of tensile fracture and impact toughness fracture morphology analyses of laser shock peening on the welded joint strength and toughness regulation mechanism are also completed. The results show that the laser shock peening can refine the microstructure of the welded joint effectively, the microhardness of all areas of the joint increases and the weld residual tensile stresses are transformed into beneficial residual compressive stresses, affecting a layer depth of 600 μm. In addition, the strength and impact toughness of welded joints of HC420LA low-alloy high-strength steel are improved

Modeling of Laser Melting Deposition Equipment Based on Digital Twin

With the rapid development of new-generation information technologies such as big data, cloud computing, Internet of Things, and mobile internet in traditional manufacturing, the development of intelligent manufacturing (IM) is accelerating. Digital twin is an important method to achieve the goal of IM, and provides an effective means for the integrated development of design and manufacturing (R & M). In view of the problems of long installation and debugging cycles, and process parameters requiring multiple trial and error in the research and development (R & D) process of laser melting deposition (LMD) equipment, this paper focuses on building an LMD equipment model based on digital twin technology. It involves performing virtual assembly, motion setting, collision inspection, and PLC debugging, thereby providing an innovative method and insights for improving the R & D efficiency of the IM of LMD equipment

Modeling of Laser Melting Deposition Equipment Based on Digital Twin

With the rapid development of new-generation information technologies such as big data, cloud computing, Internet of Things, and mobile internet in traditional manufacturing, the development of intelligent manufacturing (IM) is accelerating. Digital twin is an important method to achieve the goal of IM, and provides an effective means for the integrated development of design and manufacturing (R & M). In view of the problems of long installation and debugging cycles, and process parameters requiring multiple trial and error in the research and development (R & D) process of laser melting deposition (LMD) equipment, this paper focuses on building an LMD equipment model based on digital twin technology. It involves performing virtual assembly, motion setting, collision inspection, and PLC debugging, thereby providing an innovative method and insights for improving the R & D efficiency of the IM of LMD equipment