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.

Chapter 13. Symmetry and Satisfiability

2021 ◽  
Author(s):  
Karem A. Sakallah
Keyword(s):  
Group Theory ◽  
Normal Form ◽  
Boolean Functions ◽  
Search Algorithm ◽  
Conjunctive Normal Form ◽  
Search Space ◽  
Decision Problems ◽  
Mathematical Language ◽  
Sat Solvers ◽  
Speed Up

Symmetry is at once a familiar concept (we recognize it when we see it!) and a profoundly deep mathematical subject. At its most basic, a symmetry is some transformation of an object that leaves the object (or some aspect of the object) unchanged. For example, a square can be transformed in eight different ways that leave it looking exactly the same: the identity “do-nothing” transformation, 3 rotations, and 4 mirror images (or reflections). In the context of decision problems, the presence of symmetries in a problem’s search space can frustrate the hunt for a solution by forcing a search algorithm to fruitlessly explore symmetric subspaces that do not contain solutions. Recognizing that such symmetries exist, we can direct a search algorithm to look for solutions only in non-symmetric parts of the search space. In many cases, this can lead to significant pruning of the search space and yield solutions to problems which are otherwise intractable. This chapter explores the symmetries of Boolean functions, particularly the symmetries of their conjunctive normal form (CNF) representations. Specifically, it examines what those symmetries are, how to model them using the mathematical language of group theory, how to derive them from a CNF formula, and how to utilize them to speed up CNF SAT solvers.

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 Accelerating backtrack search with a best-first-search strategy

2014 ◽  
Vol 24 (4) ◽  
pp. 901-916
Author(s):  
Zoltán Ádám Mann ◽  
Tamás Szép
Keyword(s):  
Search Strategy ◽  
Search Algorithm ◽  
Search Space ◽  
New Approach ◽  
Backtrack Search ◽  
Speed Up ◽  
Hard Problems ◽  
Best First Search ◽  
Problem Instances ◽  
Np Hard Problems

Abstract Backtrack-style exhaustive search algorithms for NP-hard problems tend to have large variance in their runtime. This is because “fortunate” branching decisions can lead to finding a solution quickly, whereas “unfortunate” decisions in another run can lead the algorithm to a region of the search space with no solutions. In the literature, frequent restarting has been suggested as a means to overcome this problem. In this paper, we propose a more sophisticated approach: a best-firstsearch heuristic to quickly move between parts of the search space, always concentrating on the most promising region. We describe how this idea can be efficiently incorporated into a backtrack search algorithm, without sacrificing optimality. Moreover, we demonstrate empirically that, for hard solvable problem instances, the new approach provides significantly higher speed-up than frequent restarting.

scholarly journals Optimal Differential Trails in SIMON-like Ciphers

2017 ◽  
pp. 358-379 ◽  
Author(s):  
Zhengbin Liu ◽  
Yongqiang Li ◽  
Mingsheng Wang
Keyword(s):  
Upper Bound ◽  
Efficient Algorithm ◽  
Search Algorithm ◽  
Hamming Weight ◽  
Differential Probability ◽  
Smt Solvers ◽  
Round Function ◽  
Input Size ◽  
Automatic Search ◽  
First Time

In the present paper, we propose an automatic search algorithm for optimal differential trails in SIMON-like ciphers. First, we give a more accurate upper bound on the differential probability of SIMON-like round function. It is shown that when the Hamming weight of the input difference α , which is denoted by wt(α), is less than one half of the input size, the corresponding maximum differential probability of SIMON-like round function is less than or equal to 2−wt(α)−1. Based on this, we adapt Matsui’s algorithm and propose an efficient algorithm for searching for optimal differential trails. With the proposed algorithm, we find the provably optimal differential trails for 12, 16, 19, 28 and 37 rounds of SIMON32/48/64/96/128. To the best of our knowledge, it is the first time that the provably optimal differential trails for SIMON64, SIMON96 and SIMON128 are reported. The provably optimal differential trails for 13, 19 and 25 rounds of SIMECK32/48/64 are also found respectively, which confirm the results given by Kölbl et al. [KR15]. Besides the optimal differential trails, we also find the 14, 17, 23, 31 and 41-round differentials for SIMON32/48/64/96/128, and 14, 21 and 27-round differentials for SIMECK32/48/64, respectively. As far as we know, these are the best differential distinguishers for SIMON and SIMECK so far. Compared with the approach based on SAT/SMT solvers used by K¨olbl et al., our algorithm is more efficient and more practical to evaluate the security against differential cryptanalysis in the design of SIMON-like ciphers.

scholarly journals Parallel AND/OR Search for Marginal MAP

2020 ◽  
Vol 34 (06) ◽  
pp. 10226-10234
Author(s):  
Radu Marinescu ◽  
Akihiro Kishimoto ◽  
Adi Botea
Keyword(s):  
Graphical Models ◽  
State Of The Art ◽  
Search Algorithm ◽  
Search Space ◽  
Parallel Search ◽  
Sequential Search ◽  
Limited Memory ◽  
Mixed Inference ◽  
First Time ◽  
Inference Task

Marginal MAP is a difficult mixed inference task for graphical models. Existing state-of-the-art algorithms for solving exactly this task are based on either depth-first or best-first sequential search over an AND/OR search space. In this paper, we explore and evaluate for the first time the power of parallel search for exact Marginal MAP inference. We introduce a new parallel shared-memory recursive best-first AND/OR search algorithm that explores the search space in a best-first manner while operating with limited memory. Subsequently, we develop a complete parallel search scheme that only parallelizes the conditional likelihood computations. We also extend the proposed algorithms into depth-first parallel search schemes. Our experiments on difficult benchmarks demonstrate the effectiveness of the parallel search algorithms against current sequential methods for solving Marginal MAP exactly.

scholarly journals Automatic Search for the Linear (Hull) Characteristics of ARX Ciphers: Applied to SPECK, SPARX, Chaskey, and CHAM-64

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Mingjiang Huang ◽  
Liming Wang
Keyword(s):  
Evaluation Method ◽  
Search Algorithm ◽  
Search Space ◽  
Linear Potential ◽  
Linear Hull ◽  
Key Recovery ◽  
Large Correlation ◽  
Optimal Linear ◽  
Automatic Search ◽  
Key Recovery Attack

Linear cryptanalysis is an important evaluation method for cryptographic primitives against key recovery attack. In this paper, we revisit the Walsh transformation for linear correlation calculation of modular addition, and an efficient algorithm is proposed to construct the input-output mask space of specified correlation weight. By filtering out the impossible large correlation weights in the first round, the search space of the first round can be substantially reduced. We introduce a concept of combinational linear approximation table (cLAT) for modular addition with two inputs. When one input mask is fixed, another input mask and the output mask can be obtained by the Splitting-Lookup-Recombination approach. We first split the n-bit fixed input mask into several subvectors and then find the corresponding bits of other masks, and in the recombination phase, pruning conditions can be used. By this approach, a large number of search branches in the middle rounds can be pruned. With the combination of the optimization strategies and the branch-and-bound search algorithm, we can improve the search efficiency for linear characteristics on ARX ciphers. The linear hulls for SPECK32/48/64 with a higher average linear potential (ALP) than existing results have been obtained. For SPARX variants, an 11-round linear trail and a 10-round linear hull have been found for SPARX-64 and a 10-round linear trail and a 9-round linear hull are obtained for SPARX-128. For Chaskey, a 5-round linear trail with a correlation of 2−61 has been obtained. For CHAM-64, 34/35-round optimal linear characteristics with a correlation of 2−31/2−33 are found.

scholarly journals An Information-Motivated Exploration Agent to Locate Stationary Persons with Wireless Transmitters in Unknown Environments

Sensors ◽  
2021 ◽  
Vol 21 (22) ◽  
pp. 7695
Author(s):  
Daniel Barry ◽  
Andreas Willig ◽  
Graeme Woodward
Keyword(s):  
Information Gain ◽  
Search Algorithm ◽  
A Priori ◽  
Search Space ◽  
Wireless Transmitters ◽  
Multiple Sensors ◽  
Single Target ◽  
Information Exploration ◽  
Speed Up ◽  
Priori Information

Unmanned Aerial Vehicles (UAVs) show promise in a variety of applications and recently were explored in the area of Search and Rescue (SAR) for finding victims. In this paper we consider the problem of finding multiple unknown stationary transmitters in a discrete simulated unknown environment, where the goal is to locate all transmitters in as short a time as possible. Existing solutions in the UAV search space typically search for a single target, assume a simple environment, assume target properties are known or have other unrealistic assumptions. We simulate large, complex environments with limited a priori information about the environment and transmitter properties. We propose a Bayesian search algorithm, Information Exploration Behaviour (IEB), that maximizes predicted information gain at each search step, incorporating information from multiple sensors whilst making minimal assumptions about the scenario. This search method is inspired by the information theory concept of empowerment. Our algorithm shows significant speed-up compared to baseline algorithms, being orders of magnitude faster than a random agent and 10 times faster than a lawnmower strategy, even in complex scenarios. The IEB agent is able to make use of received transmitter signals from unknown sources and incorporate both an exploration and search strategy.

An Evaluation of Provincial Macroeconomic Performance in Vietnam

2017 ◽  
pp. 34-47
Author(s):  
Hoi Le Quoc ◽  
Nam Pham Xuan ◽  
Tuan Nguyen Anh
Keyword(s):  
Development Strategy ◽  
Institutional Transformation ◽  
Economic Indicators ◽  
Macroeconomic Performance ◽  
Economic Development Strategy ◽  
Socio Economic Development ◽  
The Cost ◽  
Development Objectives ◽  
First Time

The study was targeted at developing a methodology for constructing a macroeconomic performance index at a provincial level for the first time in Vietnam based on 4 groups of measurements: (i) Economic indicators; (ii) oriented economic indicators; (iii) socio-economic indicators; and (iv) economic - social – institutional indicators. Applying the methodology to the 2011 - 2015 empirical data of all provinces in Vietnam, the research shows that the socio-economic development strategy implemented by those provinces did not provide balanced outcomes between growth and social objectives, sustainability and inclusiveness. Many provinces focused on economic growth at the cost of structural change, equality and institutional transformation. In contrast, many provinces were successful in improving equality but not growth. Those facts threaten the long-term development objectives of the provinces.

Localization of WSN using Distributed Particle Swarm Optimization algorithm with precise references

2016 ◽  
Vol 7 ◽  
pp. 1
Author(s):  
Ravichander Janapati ◽  
Ch. Balaswamy ◽  
K. Soundararajan
Keyword(s):  
Particle Swarm Optimization ◽  
Search Algorithm ◽  
Particle Swarm ◽  
Search Space ◽  
Research Area ◽  
Population Based ◽  
Wireless Sensor ◽  
Cooperative Localization ◽  
Localization Algorithm ◽  
Swarm Optimization

Localization is the key research area in wireless sensor networks. Finding the exact position of the node is known as localization. Different algorithms have been proposed. Here we consider a cooperative localization algorithm with censoring schemes using Crammer Rao bound (CRB). This censoring scheme  can improve the positioning accuracy and reduces computation complexity, traffic and latency. Particle swarm optimization (PSO) is a population based search algorithm based on the swarm intelligence like social behavior of birds, bees or a school of fishes. To improve the algorithm efficiency and localization precision, this paper presents an objective function based on the normal distribution of ranging error and a method of obtaining the search space of particles. In this paper  Distributed localization of wireless sensor networksis proposed using PSO with best censoring technique using CRB. Proposed method shows better results in terms of position accuracy, latency and complexity.  

Automatic Mining of Quantitative Association Rules with Gravitational Search Algorithm

2017 ◽  
Vol 27 (03) ◽  
pp. 343-372 ◽  
Author(s):  
Umit Can ◽  
Bilal Alatas
Keyword(s):  
Association Rules ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Fitness Function ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Search Space ◽  
Search Method ◽  
Quantitative Association Rules ◽  
Gravitational Search

The classical optimization algorithms are not efficient in solving complex search and optimization problems. Thus, some heuristic optimization algorithms have been proposed. In this paper, exploration of association rules within numerical databases with Gravitational Search Algorithm (GSA) has been firstly performed. GSA has been designed as search method for quantitative association rules from the databases which can be regarded as search space. Furthermore, determining the minimum values of confidence and support for every database which is a hard job has been eliminated by GSA. Apart from this, the fitness function used for GSA is very flexible. According to the interested problem, some parameters can be removed from or added to the fitness function. The range values of the attributes have been automatically adjusted during the time of mining of the rules. That is why there is not any requirements for the pre-processing of the data. Attributes interaction problem has also been eliminated with the designed GSA. GSA has been tested with four real databases and promising results have been obtained. GSA seems an effective search method for complex numerical sequential patterns mining, numerical classification rules mining, and clustering rules mining tasks of data mining.

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