In recent years, it has become a popular trend to propose quantum versions of classical attacks. The rectangle attack as a differential attack is widely used in symmetric cryptanalysis and applied on many block ciphers. To improve its efficiency, we propose a new quantum rectangle attack firstly. In rectangle attack, it counts the number of valid quartets for each guessed subkeys and filters out subkey candidates according to the counter. To speed up this procedure, we propose a quantum key counting algorithm based on parallel amplitude estimation algorithm and amplitude amplification algorithm. Then, we complete with the remaining key bits and search the right full key by nested Grover search. Besides, we give a strategy to find a more suitable distinguisher to make the complexity lower. Finally, to evaluate post-quantum security of the tweakable block cipher Deoxys-BC, we perform automatic search for good distinguishers of Deoxys-BC according to the strategy, and then apply our attack on 9/10-round Deoxys-BC-256 and 12/13/14-round Deoxys-BC-384. The results show that our attack has some improvements than classical attacks and Grover search.
Incompressible Euler flows in narrow domains, in which the horizontal length scale is much larger than other scales, play an important role in many different applications, and their leading-order behavior can be described by the hydrostatic Euler equations. In this paper, we show that steady solutions of the hydrostatic Euler equations in an infinite strip strictly away from stagnation must be shear flows. Furthermore, we prove the existence, uniqueness, and asymptotic behavior of global steady solutions to the hydrostatic Euler equations in general nozzles. In terms of stream function formulation, the hydrostatic Euler equations can be written as a degenerate elliptic equation, for which the Liouville type theorem in a strip is a consequence of the analysis for the second order ordinary differential equation (ODE). The analysis on the associated ODE also helps determine the far field behavior of solutions in general nozzles, which plays an important role in guaranteeing the equivalence of stream function formulation. One of the key ingredients for the analysis on flows in a general nozzle is a new transformation, which combines a change of variable and an Euler–Lagrange transformation. With the aid of this new transformation, the solutions in the new coordinates enjoy explicit representations so that the regularity with respect to the horizontal variable can be gained in a clear way.
In this paper, we consider the complex Ginzburg-Landau equation
The study focuses on investigating the finite-time blow-up phenomenon, which remains an open question for a broad range of parameters, particularly for (beta ) and (delta ). Specifically, for a fixed (beta in {mathbb {R}}), the existence of finite-time blow-up solutions for arbitrarily large values of ( |delta | ) is still unknown. According to a conjecture made by Popp et al. (Physica D Nonlinear Phenom 114:81–107 1998), when (beta = 0) and (delta ) is large, blow-up does not occur for generic initial data. In this paper, we show that their conjecture is not valid for all types of initial data, by presenting the existence of blow-up solutions for (beta = 0) and any (delta in {mathbb {R}}) with different types of blowup.
The paper establishes the nonlinear (orbital) stability of static 180-degree Néel walls in ferromagnetic films under the reduced wave-type dynamics for the in-plane magnetization proposed by Capella et al. (Nonlinearity 20:2519–2537, 2007). The result follows from the spectral analysis of the linearized operator around the Néel wall’s phase, which features a challenging non-local operator. As part of the proof, we show that the non-local linearized operator is a compact perturbation of a suitable non-local linear operator at infinity, a result that is interesting in itself.
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