scholarly journals New Techniques for Searching Differential Trails in Keccak

2020 ◽  
pp. 407-437
Author(s):  
Guozhen Liu ◽  
Weidong Qiu ◽  
Yi Tu
Keyword(s):  
Lower Bounds ◽  
Hash Function ◽  
Search Space ◽  
Search Methods ◽  
New Techniques ◽  
New Algorithms

Keccak-f is the permutation used in the NIST SHA-3 hash function standard. Inspired by the previous exhaustive differential trail search methods by Mella et al. at ToSC 2017, we introduce in this paper new algorithms to cover 3-round trail cores with propagation weight at least 53, up from the previous best weight 45. To achieve the goal, the concept of ideal improvement assumption is proposed to construct theoretical representative of subspaces so as to efficiently cover the search space of 3-round trail cores with at least one out-Kernel α state. Of particular note is that the exhaustiveness in 3-round trail core search of at least one out-Kernel α is only experimentally verified. With the knowledge of all 3-round trail cores of weight up to 53, lower bounds on 4/5/6-round trails are tightened to 56/58/108, from the previous 48/50/92, respectively.

scholarly journals Optimal Bounds for the k -cut Problem

2022 ◽  
Vol 69 (1) ◽  
pp. 1-18
Author(s):  
Anupam Gupta ◽  
David G. Harris ◽  
Euiwoong Lee ◽  
Jason Li
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Connected Components ◽  
Small Integer ◽  
Main Ingredient ◽  
Fine Grained ◽  
Optimal Bounds ◽  
Sunflower Lemma ◽  
General Graphs ◽  
New Algorithms

In the k -cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into k connected components. Algorithms of Karger and Stein can solve this in roughly O ( n 2k ) time. However, lower bounds from conjectures about the k -clique problem imply that Ω ( n (1- o (1)) k ) time is likely needed. Recent results of Gupta, Lee, and Li have given new algorithms for general k -cut in n 1.98k + O(1) time, as well as specialized algorithms with better performance for certain classes of graphs (e.g., for small integer edge weights). In this work, we resolve the problem for general graphs. We show that the Contraction Algorithm of Karger outputs any fixed k -cut of weight α λ k with probability Ω k ( n - α k ), where λ k denotes the minimum k -cut weight. This also gives an extremal bound of O k ( n k ) on the number of minimum k -cuts and an algorithm to compute λ k with roughly n k polylog( n ) runtime. Both are tight up to lower-order factors, with the algorithmic lower bound assuming hardness of max-weight k -clique. The first main ingredient in our result is an extremal bound on the number of cuts of weight less than 2 λ k / k , using the Sunflower lemma. The second ingredient is a fine-grained analysis of how the graph shrinks—and how the average degree evolves—in the Karger process.

scholarly journals Bootstrapping Bloch bands

2021 ◽  
Author(s):  
Serguei Tchoumakov ◽  
Serge Florens
Keyword(s):  
Search Space ◽  
Quantum Field Theories ◽  
New Techniques ◽  
Bootstrap Methods ◽  
Quantum Operator ◽  
Canonical Variables ◽  
Distribution Probability ◽  
Anharmonic Potential ◽  
Bloch Band ◽  
Band Spectra

Abstract Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schrödinger equation with an anharmonic potential. The core of bootstrap methods builds on exact recursion relations of arbitrary moments of some quantum operator and the use of an adequate set of positivity criteria. We extend this methodology to models with continuous Bloch band spectra, by considering a single quantum particle in a periodic cosine potential. We find that the band structure can be obtained accurately provided the bootstrap uses moments involving both position and momentum variables. We also introduce several new techniques that can apply generally to other bootstrap studies. First, we devise a trick to reduce by one unit the dimensionality of the search space for the variables parametrizing the bootstrap. Second, we employ statistical techniques to reconstruct the distribution probability allowing to compute observables that are analytic functions of the canonical variables. This method is used to extract the Bloch momentum, a quantity that is not readily available from the bootstrap recursion itself.

Multiwave interaction solutions for the (3+1)-dimensional extended Jimbo–Miwa equation

2020 ◽  
Vol 34 (35) ◽  
pp. 2050405
Author(s):  
Wenying Cui ◽  
Wei Li ◽  
Yinping Liu
Keyword(s):  
Algebraic Method ◽  
Periodic Waves ◽  
New Techniques ◽  
Interaction Solutions ◽  
Long Wave ◽  
Multiwave Interaction ◽  
Different Types ◽  
Wave Limit ◽  
Solving Strategy ◽  
New Algorithms

In this paper, for the (3+1)-dimensional extended Jimbo–Miwa equation, by the direct algebraic method, together with the inheritance solving strategy, we construct its interaction solutions among solitons, rational waves, and periodic waves. Meanwhile, we construct its interaction solutions among solitons, breathers, and lumps of any higher orders by an [Formula: see text]-soliton decomposition algorithm, together with the parameters conjugated assignment and long-wave limit techniques. The highlight of the paper is that by applying new algorithms and new techniques, we obtained different types of new multiwave interaction solutions for the (3+1)-dimensional extended Jimbo–Miwa equation.

Improving Matsui’s Search Algorithm For The Best Differential/Linear Trails And Its Applications For DES, DESL And GIFT

2020 ◽  
Author(s):  
Fulei Ji ◽  
Wentao Zhang ◽  
Tianyou Ding
Keyword(s):  
Search Algorithm ◽  
Search Space ◽  
Search Methods ◽  
New Methods ◽  
Linear Layer ◽  
Speed Up ◽  
Automatic Search ◽  
The Cost ◽  
First Time ◽  
Improved Algorithm

Abstract Automatic search methods have been widely used for cryptanalysis of block ciphers, especially for the most classic cryptanalysis methods—differential and linear cryptanalysis. However, the automatic search methods, no matter based on MILP, SMT/SAT or CP techniques, can be inefficient when the search space is too large. In this paper, we propose three new methods to improve Matsui’s branch-and-bound search algorithm, which is known as the first generic algorithm for finding the best differential and linear trails. The three methods, named reconstructing DDT and LAT according to weight, executing linear layer operations in minimal cost and merging two 4-bit S-boxes into one 8-bit S-box, respectively, can efficiently speed up the search process by reducing the search space as much as possible and reducing the cost of executing linear layer operations. We apply our improved algorithm to DESL and GIFT, which are still the hard instances for the automatic search methods. As a result, we find the best differential trails for DESL (up to 14-round) and GIFT-128 (up to 19-round). The best linear trails for DESL (up to 16-round), GIFT-128 (up to 10-round) and GIFT-64 (up to 15-round) are also found. To the best of our knowledge, these security bounds for DESL and GIFT under single-key scenario are given for the first time. Meanwhile, it is the longest exploitable (differential or linear) trails for DESL and GIFT. Furthermore, benefiting from the efficiency of the improved algorithm, we do experiments to demonstrate that the clustering effect of differential trails for 13-round DES and DESL are both weak.

A Mixed-Integer Memetic Algorithm Applied to Batch Process Optimization

2013 ◽  
Vol 300-301 ◽  
pp. 645-648 ◽  
Author(s):  
Yung Chien Lin
Keyword(s):  
Memetic Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Space ◽  
Memetic Algorithms ◽  
Batch Processes ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Genetic Operators ◽  
Search Methods

Evolutionary algorithms (EAs) are population-based global search methods. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators with local search methods. With global exploration and local exploitation in search space, MAs are capable of obtaining more high-quality solutions. On the other hand, mixed-integer hybrid differential evolution (MIHDE), as an EA-based search algorithm, has been successfully applied to many mixed-integer optimization problems. In this paper, a mixed-integer memetic algorithm based on MIHDE is developed for solving mixed-integer constrained optimization problems. The proposed algorithm is implemented and applied to the optimal design of batch processes. Experimental results show that the proposed algorithm can find a better optimal solution compared with some other search algorithms.

scholarly journals Constrained Novelty Search: A Study on Game Content Generation

2015 ◽  
Vol 23 (1) ◽  
pp. 101-129 ◽  
Author(s):  
Antonios Liapis ◽  
Georgios N. Yannakakis ◽  
Julian Togelius
Keyword(s):  
Genetic Algorithm ◽  
Search Space ◽  
Selection Method ◽  
Search Algorithms ◽  
Genetic Operators ◽  
Search Methods ◽  
Search Spaces ◽  
Novelty Search ◽  
Feasible Space ◽  
Content Generation

Novelty search is a recent algorithm geared toward exploring search spaces without regard to objectives. When the presence of constraints divides a search space into feasible space and infeasible space, interesting implications arise regarding how novelty search explores such spaces. This paper elaborates on the problem of constrained novelty search and proposes two novelty search algorithms which search within both the feasible and the infeasible space. Inspired by the FI-2pop genetic algorithm, both algorithms maintain and evolve two separate populations, one with feasible and one with infeasible individuals, while each population can use its own selection method. The proposed algorithms are applied to the problem of generating diverse but playable game levels, which is representative of the larger problem of procedural game content generation. Results show that the two-population constrained novelty search methods can create, under certain conditions, larger and more diverse sets of feasible game levels than current methods of novelty search, whether constrained or unconstrained. However, the best algorithm is contingent on the particularities of the search space and the genetic operators used. Additionally, the proposed enhancement of offspring boosting is shown to enhance performance in all cases of two-population novelty search.

scholarly journals Particle swarm optimisation representations for simultaneous clustering and feature selection

2020 ◽  
Author(s):  
Andrew Lensen ◽  
Bing Xue ◽  
Mengjie Zhang
Keyword(s):  
Feature Selection ◽  
Data Analysis ◽  
Real World ◽  
Particle Swarm ◽  
Search Space ◽  
Particle Swarm Optimisation ◽  
New Techniques ◽  
Unlabelled Data ◽  
Synthetic Datasets ◽  
Work Done

© 2016 IEEE. Clustering, the process of grouping unlabelled data, is an important task in data analysis. It is regarded as one of the most difficult tasks due to the large search space that must be explored. Feature selection is commonly used to reduce the size of a search space, and evolutionary computation (EC) is a group of techniques which are known to give good solutions to difficult problems such as clustering or feature selection. However, there has been relatively little work done on simultaneous clustering and feature selection using EC methods. In this paper we compare medoid and centroid representations that allow particle swarm optimisation (PSO) to perform simultaneous clustering and feature selection. We propose several new techniques which improve clustering performance and ensure valid solutions are generated. Experiments are conducted on a variety of real-world and synthetic datasets in order to analyse the effectiveness of the PSO representations across several different criteria. We show that a medoid representation can achieve superior results compared to the widely used centroid representation.

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