Solving Non-Linear Random Sparse Equations over Finite Fields
|
|
- Shauna Hart
- 7 years ago
- Views:
Transcription
1 Solving Non-Linear Random Sparse Equations over Finite Fields Thorsten Schilling UiB May 6, 2009 Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
2 Motivation Algebraic Cryptanalysis Algebraic Cryptanalysis Express cipher as system of equations Well known examples: AES, DES, Trivium etc. Obtaining solution to systems might break cipher Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
3 Motivation Algebraic Cryptanalysis l-sparse Equation System f 1 (X 1 ) = 0, f 2 (X 2 ) = 0,..., f m (X m ) = 0 X i X X i l Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
4 Motivation Example Example Trivium 80 bits IV, 80 bits key 288 bits internal state Output bit is linear combination of state bits Overall very simple design Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
5 Motivation Example Example Trivium (2) Expressed as equation system a i = c i 66 + c i c i 110 c i a i 69 b i = a i 66 + a i 93 + a i 92 a i 91 + b i 78 c i = b i 69 + b i 84 + b i 83 b i 82 + c i 87 Output bit z i z i = c i 66 + c i a i 66 + a i 93 + b i 69 + b i 84 Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
6 Motivation Example Example Trivium (2) Expressed as equation system a i = c i 66 + c i c i 110 c i a i 69 b i = a i 66 + a i 93 + a i 92 a i 91 + b i 78 c i = b i 69 + b i 84 + b i 83 b i 82 + c i 87 Output bit z i z i = c i 66 + c i a i 66 + a i 93 + b i 69 + b i 84 For state recovery solve system: 6-sparse 951 variables 663 quadric equations, 288 linear Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
7 Solving Strategies Introduction Solving Strategies Linearization Gröbner Basis Algorithms Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
8 Solving Strategies Introduction Solving Strategies Linearization Gröbner Basis Algorithms SAT-Solving Is φ = (x i x j... x k )... (x u x v... x w ) SAT? Theoretical worst case bounds [Iwama,04]: sparsity worst case n n n n Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
9 Solving Strategies Introduction Solving Strategies Linearization Gröbner Basis Algorithms SAT-Solving Is φ = (x i x j... x k )... (x u x v... x w ) SAT? Theoretical worst case bounds [Iwama,04]: sparsity worst case n n n n Gluing & Agreeing [Raddum, Semaev] Expected Running Times: sparsity Gluing[Semaev,WCC 07] n n n n Agr.-Gluing[Semaev,ACCT 08] n n n n Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
10 Solving Strategies SAT-solving SAT-solving - DPLL/Davis-Putnam-Logemann-Loveland General structure of the algorithm (input φ in CNF): Extend a partial guess Propagate information Clause Resolution Backtrack if a conflict was detected Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
11 Solving Strategies SAT-solving Past Major Enhancements Algorithmic [Silvia, Sakallah 1996] Non-chronological backtracking Conflict clauses Technical Watched literals [Moskewicz et. al. 2001] Instance specific Guessing heuristics Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
12 Gluing & Agreeing Introduction A New Approach Generalization of a backtracking solving method for sparse non-linear equation systems over finite fields CNF-instances are specialization Exploit sparsity of equations Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
13 Gluing & Agreeing Representation Equation as Symbol f (X i ) = 0 as pair of sets S i = (X i, V i ) X i variables in which the equation is defined V i its satisfying vectors/assignments Random equation over F 2 expected V i = 2 X i 1 Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
14 Gluing & Agreeing Representation Equation as Symbol f (X i ) = 0 as pair of sets S i = (X i, V i ) X i variables in which the equation is defined V i its satisfying vectors/assignments Random equation over F 2 expected V i = 2 X i 1 Example: becomes f e (x 1, x 2, x 3 ) = x 1 x 2 x 3 = 0 S e x 1 x 2 x 3 a a a a Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
15 Gluing & Agreeing Fundamental Operations Gluing Create new symbol S 1 S 2 = (X 1 X 2, U) from two symbols S 1, S 2 where U = {(a 1, b, a 2 ) (a 1, b) V 1 and (b, a 2 ) V 2 } Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
16 Gluing & Agreeing Fundamental Operations Gluing Create new symbol S 1 S 2 = (X 1 X 2, U) from two symbols S 1, S 2 where Example: U = {(a 1, b, a 2 ) (a 1, b) V 1 and (b, a 2 ) V 2 } S a a a a S b b b = S 0 S c c c Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
17 Gluing & Agreeing Fundamental Operations Agreeing Delete from symbols S 1, S 2 vectors whose projections do not match in their common variables X 1 X 2. If symbol gets empty contradiction. Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
18 Gluing & Agreeing Fundamental Operations Agreeing Delete from symbols S 1, S 2 vectors whose projections do not match in their common variables X 1 X 2. If symbol gets empty contradiction. Example: S a a a a , S b b b become S a , S b b b Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
19 Gluing & Agreeing Fundamental Operations Gluing-Agreeing Algorithm Glue intermediate symbol with another symbol, then agree the intermediate equation system. Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
20 Gluing & Agreeing Agreeing2 Agreeing2 Aim: Reduce number of steps for Agreeing Addresses of common projections stored as tuples S a a a a , S b b b b {a 0, a 1, a 2 ; b 0 }, {a 3 ; b 1, b 2, b 3 } Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
21 Gluing & Agreeing Agreeing2 Mark groups of common projections Example: a 0, a 1, a 3 marked b 1, b 2, b 3 marked {a 0, a 1, a 2 ; b 0 }, {a 3 ; b 1, b 2, b 3 } S a a a a , S b b b b { a 0, a 1, a 2 ; b 0 }, { a 3 ; b 1, b 2, b 3 } S a , S b Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
22 Gluing & Agreeing Agreeing2 Agreeing2 Advantages Information propagation through tuples Asymptotically faster Overhead for reading and writing decreases Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
23 Dynamic Gluing Continuos Implicit Agreeing Continous Implicit Agreeing Tree search through possible Gluings Works only on tuple markings Keep obtained knowledge Persistent marking Flexible in the Gluing order Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
24 Dynamic Gluing Continuos Implicit Agreeing General Algorithm 1 Pick symbol 2 Mark all yet unmarked assignments, except one Guess assignment 3 Run Agreeing2 4 Backtrack on contradiction Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
25 Dynamic Gluing Guessing Heuristics vs. Sorting Guessing Heuristics Which symbol keeps search tree narrow Gluing complexity roughly 2 max i X (i) i sort and keep X (i) i = X 0 X 1... X i i low Better: choose symbol with smallest V i (only unmarked assignments) Other heuristics possible, e.g. maximum X i / V i etc. Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
26 Results Example Result n = m = 150, l = 5 MiniSAT dynglue Decisions 6844 Guesses 1549 Conflicts 5046 Contradictions 280 Propagations Tuple Propagations Time 0.15s Time 0.08s Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
27 Open Questions Open Questions Conflict handling Learning Dynamic Static Heuristics Random systems Equation systems from ciphers Thorsten Schilling (UiB) Solving Equations over Finite Fields May 6, / 21
Satisfiability Checking
Satisfiability Checking SAT-Solving Prof. Dr. Erika Ábrahám Theory of Hybrid Systems Informatik 2 WS 10/11 Prof. Dr. Erika Ábrahám - Satisfiability Checking 1 / 40 A basic SAT algorithm Assume the CNF
More informationAPP INVENTOR. Test Review
APP INVENTOR Test Review Main Concepts App Inventor Lists Creating Random Numbers Variables Searching and Sorting Data Linear Search Binary Search Selection Sort Quick Sort Abstraction Modulus Division
More informationUniversity of Potsdam Faculty of Computer Science. Clause Learning in SAT Seminar Automatic Problem Solving WS 2005/06
University of Potsdam Faculty of Computer Science Clause Learning in SAT Seminar Automatic Problem Solving WS 2005/06 Authors: Richard Tichy, Thomas Glase Date: 25th April 2006 Contents 1 Introduction
More informationDesign of LDPC codes
Design of LDPC codes Codes from finite geometries Random codes: Determine the connections of the bipartite Tanner graph by using a (pseudo)random algorithm observing the degree distribution of the code
More informationCS510 Software Engineering
CS510 Software Engineering Propositional Logic Asst. Prof. Mathias Payer Department of Computer Science Purdue University TA: Scott A. Carr Slides inspired by Xiangyu Zhang http://nebelwelt.net/teaching/15-cs510-se
More informationnpsolver A SAT Based Solver for Optimization Problems
npsolver A SAT Based Solver for Optimization Problems Norbert Manthey and Peter Steinke Knowledge Representation and Reasoning Group Technische Universität Dresden, 01062 Dresden, Germany peter@janeway.inf.tu-dresden.de
More informationHeuristics for Dynamically Adapting Constraint Propagation in Constraint Programming
Heuristics for Dynamically Adapting Constraint Propagation in Constraint Programming Kostas Stergiou AI Lab University of the Aegean Greece CPAIOR 09 Workshop on Bound reduction techniques for CP and MINLP
More informationCOLLEGE ALGEBRA 10 TH EDITION LIAL HORNSBY SCHNEIDER 1.1-1
10 TH EDITION COLLEGE ALGEBRA LIAL HORNSBY SCHNEIDER 1.1-1 1.1 Linear Equations Basic Terminology of Equations Solving Linear Equations Identities 1.1-2 Equations An equation is a statement that two expressions
More informationBlock Ciphers that are Easier to Mask: How Far Can we Go?
Block Ciphers that are Easier to Mask: How Far Can we Go? Benoît Gérard 1,2, Vincent Grosso 1, María Naya-Plasencia 3, François-Xavier Standaert 1 1 ICTEAM/ELEN/Crypto Group, Université catholique de Louvain,
More informationCommon Patterns and Pitfalls for Implementing Algorithms in Spark. Hossein Falaki @mhfalaki hossein@databricks.com
Common Patterns and Pitfalls for Implementing Algorithms in Spark Hossein Falaki @mhfalaki hossein@databricks.com Challenges of numerical computation over big data When applying any algorithm to big data
More informationCryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur
Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture No. # 11 Block Cipher Standards (DES) (Refer Slide
More informationA Numerical Study on the Wiretap Network with a Simple Network Topology
A Numerical Study on the Wiretap Network with a Simple Network Topology Fan Cheng and Vincent Tan Department of Electrical and Computer Engineering National University of Singapore Mathematical Tools of
More informationClosest Pair Problem
Closest Pair Problem Given n points in d-dimensions, find two whose mutual distance is smallest. Fundamental problem in many applications as well as a key step in many algorithms. p q A naive algorithm
More informationData Structure [Question Bank]
Unit I (Analysis of Algorithms) 1. What are algorithms and how they are useful? 2. Describe the factor on best algorithms depends on? 3. Differentiate: Correct & Incorrect Algorithms? 4. Write short note:
More informationDiscuss the size of the instance for the minimum spanning tree problem.
3.1 Algorithm complexity The algorithms A, B are given. The former has complexity O(n 2 ), the latter O(2 n ), where n is the size of the instance. Let n A 0 be the size of the largest instance that can
More informationLoad Balancing. Load Balancing 1 / 24
Load Balancing Backtracking, branch & bound and alpha-beta pruning: how to assign work to idle processes without much communication? Additionally for alpha-beta pruning: implementing the young-brothers-wait
More informationInteger Factorization using the Quadratic Sieve
Integer Factorization using the Quadratic Sieve Chad Seibert* Division of Science and Mathematics University of Minnesota, Morris Morris, MN 56567 seib0060@morris.umn.edu March 16, 2011 Abstract We give
More informationImproved Differential Fault Attack on MICKEY 2.0
Noname manuscript No. (will be inserted by the editor) Improved Differential Fault Attack on MICKEY 2.0 Subhadeep Banik Subhamoy Maitra Santanu Sarkar Received: date / Accepted: date Abstract In this paper
More informationLinear (Hull) and Algebraic Cryptanalysis of the Block Cipher PRESENT
Linear (Hull) and Algebraic Cryptanalysis of the Block Cipher PRESENT Jorge Nakahara Jr 1, Pouyan Sepehrdad 1, Bingsheng Zhang 2, Meiqin Wang 3 1 EPFL, Lausanne, Switzerland 2 Cybernetica AS, Estonia and
More informationLogic in general. Inference rules and theorem proving
Logical Agents Knowledge-based agents Logic in general Propositional logic Inference rules and theorem proving First order logic Knowledge-based agents Inference engine Knowledge base Domain-independent
More informationLinear Equations in One Variable
Linear Equations in One Variable MATH 101 College Algebra J. Robert Buchanan Department of Mathematics Summer 2012 Objectives In this section we will learn how to: Recognize and combine like terms. Solve
More informationB-Trees. Algorithms and data structures for external memory as opposed to the main memory B-Trees. B -trees
B-Trees Algorithms and data structures for external memory as opposed to the main memory B-Trees Previous Lectures Height balanced binary search trees: AVL trees, red-black trees. Multiway search trees:
More information11 Multivariate Polynomials
CS 487: Intro. to Symbolic Computation Winter 2009: M. Giesbrecht Script 11 Page 1 (These lecture notes were prepared and presented by Dan Roche.) 11 Multivariate Polynomials References: MC: Section 16.6
More informationChapter 13: Query Processing. Basic Steps in Query Processing
Chapter 13: Query Processing! Overview! Measures of Query Cost! Selection Operation! Sorting! Join Operation! Other Operations! Evaluation of Expressions 13.1 Basic Steps in Query Processing 1. Parsing
More informationCryptography and Network Security. Prof. D. Mukhopadhyay. Department of Computer Science and Engineering. Indian Institute of Technology, Kharagpur
Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 12 Block Cipher Standards
More informationCS 591.03 Introduction to Data Mining Instructor: Abdullah Mueen
CS 591.03 Introduction to Data Mining Instructor: Abdullah Mueen LECTURE 3: DATA TRANSFORMATION AND DIMENSIONALITY REDUCTION Chapter 3: Data Preprocessing Data Preprocessing: An Overview Data Quality Major
More informationPrevious Lectures. B-Trees. External storage. Two types of memory. B-trees. Main principles
B-Trees Algorithms and data structures for external memory as opposed to the main memory B-Trees Previous Lectures Height balanced binary search trees: AVL trees, red-black trees. Multiway search trees:
More informationMPBO A Distributed Pseudo-Boolean Optimization Solver
MPBO A Distributed Pseudo-Boolean Optimization Solver Nuno Miguel Coelho Santos Thesis to obtain the Master of Science Degree in Information Systems and Computer Engineering Examination Committee Chairperson:
More informationOptimizing Description Logic Subsumption
Topics in Knowledge Representation and Reasoning Optimizing Description Logic Subsumption Maryam Fazel-Zarandi Company Department of Computer Science University of Toronto Outline Introduction Optimization
More informationPhysical Data Organization
Physical Data Organization Database design using logical model of the database - appropriate level for users to focus on - user independence from implementation details Performance - other major factor
More informationCpt S 223. School of EECS, WSU
Priority Queues (Heaps) 1 Motivation Queues are a standard mechanism for ordering tasks on a first-come, first-served basis However, some tasks may be more important or timely than others (higher priority)
More informationQuestions 1 through 25 are worth 2 points each. Choose one best answer for each.
Questions 1 through 25 are worth 2 points each. Choose one best answer for each. 1. For the singly linked list implementation of the queue, where are the enqueues and dequeues performed? c a. Enqueue in
More informationY. Xiang, Constraint Satisfaction Problems
Constraint Satisfaction Problems Objectives Constraint satisfaction problems Backtracking Iterative improvement Constraint propagation Reference Russell & Norvig: Chapter 5. 1 Constraints Constraints are
More informationPractical Survey on Hash Tables. Aurelian Țuțuianu
Practical Survey on Hash Tables Aurelian Țuțuianu In memoriam Mihai Pătraşcu (17 July 1982 5 June 2012) I have no intention to ever teach computer science. I want to teach the love for computer science,
More informationBetween Restarts and Backjumps
Between Restarts and Backjumps Antonio Ramos, Peter van der Tak, and Marijn Heule Department of Software Technology, Delft University of Technology, The Netherlands Abstract. This paper introduces a novel
More informationRegression Verification: Status Report
Regression Verification: Status Report Presentation by Dennis Felsing within the Projektgruppe Formale Methoden der Softwareentwicklung 2013-12-11 1/22 Introduction How to prevent regressions in software
More informationLecture 2: Universality
CS 710: Complexity Theory 1/21/2010 Lecture 2: Universality Instructor: Dieter van Melkebeek Scribe: Tyson Williams In this lecture, we introduce the notion of a universal machine, develop efficient universal
More informationDATA ANALYSIS II. Matrix Algorithms
DATA ANALYSIS II Matrix Algorithms Similarity Matrix Given a dataset D = {x i }, i=1,..,n consisting of n points in R d, let A denote the n n symmetric similarity matrix between the points, given as where
More informationShort Programs for functions on Curves
Short Programs for functions on Curves Victor S. Miller Exploratory Computer Science IBM, Thomas J. Watson Research Center Yorktown Heights, NY 10598 May 6, 1986 Abstract The problem of deducing a function
More informationSearch Taxonomy. Web Search. Search Engine Optimization. Information Retrieval
Information Retrieval INFO 4300 / CS 4300! Retrieval models Older models» Boolean retrieval» Vector Space model Probabilistic Models» BM25» Language models Web search» Learning to Rank Search Taxonomy!
More informationA hybrid approach for solving real-world nurse rostering problems
Presentation at CP 2011: A hybrid approach for solving real-world nurse rostering problems Martin Stølevik (martin.stolevik@sintef.no) Tomas Eric Nordlander (tomas.nordlander@sintef.no) Atle Riise (atle.riise@sintef.no)
More informationArithmetic Coding: Introduction
Data Compression Arithmetic coding Arithmetic Coding: Introduction Allows using fractional parts of bits!! Used in PPM, JPEG/MPEG (as option), Bzip More time costly than Huffman, but integer implementation
More information1. The memory address of the first element of an array is called A. floor address B. foundation addressc. first address D.
1. The memory address of the first element of an array is called A. floor address B. foundation addressc. first address D. base address 2. The memory address of fifth element of an array can be calculated
More informationAdaptive Tolerance Algorithm for Distributed Top-K Monitoring with Bandwidth Constraints
Adaptive Tolerance Algorithm for Distributed Top-K Monitoring with Bandwidth Constraints Michael Bauer, Srinivasan Ravichandran University of Wisconsin-Madison Department of Computer Sciences {bauer, srini}@cs.wisc.edu
More informationComputer Science MS Course Descriptions
Computer Science MS Course Descriptions CSc I0400: Operating Systems Underlying theoretical structure of operating systems; input-output and storage systems, data management and processing; assembly and
More informationCryptography and Network Security Department of Computer Science and Engineering Indian Institute of Technology Kharagpur
Cryptography and Network Security Department of Computer Science and Engineering Indian Institute of Technology Kharagpur Module No. # 01 Lecture No. # 05 Classic Cryptosystems (Refer Slide Time: 00:42)
More informationBounded Treewidth in Knowledge Representation and Reasoning 1
Bounded Treewidth in Knowledge Representation and Reasoning 1 Reinhard Pichler Institut für Informationssysteme Arbeitsbereich DBAI Technische Universität Wien Luminy, October 2010 1 Joint work with G.
More informationTable of Contents. Bibliografische Informationen http://d-nb.info/996514864. digitalisiert durch
1 Introduction to Cryptography and Data Security 1 1.1 Overview of Cryptology (and This Book) 2 1.2 Symmetric Cryptography 4 1.2.1 Basics 4 1.2.2 Simple Symmetric Encryption: The Substitution Cipher...
More information7. LU factorization. factor-solve method. LU factorization. solving Ax = b with A nonsingular. the inverse of a nonsingular matrix
7. LU factorization EE103 (Fall 2011-12) factor-solve method LU factorization solving Ax = b with A nonsingular the inverse of a nonsingular matrix LU factorization algorithm effect of rounding error sparse
More informationLecture 3: Finding integer solutions to systems of linear equations
Lecture 3: Finding integer solutions to systems of linear equations Algorithmic Number Theory (Fall 2014) Rutgers University Swastik Kopparty Scribe: Abhishek Bhrushundi 1 Overview The goal of this lecture
More informationSolutions to Problem Set 1
YALE UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE CPSC 467b: Cryptography and Computer Security Handout #8 Zheng Ma February 21, 2005 Solutions to Problem Set 1 Problem 1: Cracking the Hill cipher Suppose
More informationNonlinear Iterative Partial Least Squares Method
Numerical Methods for Determining Principal Component Analysis Abstract Factors Béchu, S., Richard-Plouet, M., Fernandez, V., Walton, J., and Fairley, N. (2016) Developments in numerical treatments for
More informationRethinking SIMD Vectorization for In-Memory Databases
SIGMOD 215, Melbourne, Victoria, Australia Rethinking SIMD Vectorization for In-Memory Databases Orestis Polychroniou Columbia University Arun Raghavan Oracle Labs Kenneth A. Ross Columbia University Latest
More informationMAC. SKE in Practice. Lecture 5
MAC. SKE in Practice. Lecture 5 Active Adversary Active Adversary An active adversary can inject messages into the channel Active Adversary An active adversary can inject messages into the channel Eve
More informationSkyRecon Cryptographic Module (SCM)
SkyRecon Cryptographic Module (SCM) FIPS 140-2 Documentation: Security Policy Abstract This document specifies the security policy for the SkyRecon Cryptographic Module (SCM) as described in FIPS PUB 140-2.
More informationConjugating data mood and tenses: Simple past, infinite present, fast continuous, simpler imperative, conditional future perfect
Matteo Migliavacca (mm53@kent) School of Computing Conjugating data mood and tenses: Simple past, infinite present, fast continuous, simpler imperative, conditional future perfect Simple past - Traditional
More informationRandomized algorithms
Randomized algorithms March 10, 2005 1 What are randomized algorithms? Algorithms which use random numbers to make decisions during the executions of the algorithm. Why would we want to do this?? Deterministic
More informationMemory Efficient All-Solutions SAT Solver and Its Application for Reachability Analysis
Memory Efficient All-Solutions SAT Solver and Its Application for Reachability Analysis Orna Grumberg, Assaf Schuster, and Avi Yadgar Computer Science Department, Technion, Haifa, Israel Abstract. This
More informationLinear Codes. Chapter 3. 3.1 Basics
Chapter 3 Linear Codes In order to define codes that we can encode and decode efficiently, we add more structure to the codespace. We shall be mainly interested in linear codes. A linear code of length
More informationChapter 6: Episode discovery process
Chapter 6: Episode discovery process Algorithmic Methods of Data Mining, Fall 2005, Chapter 6: Episode discovery process 1 6. Episode discovery process The knowledge discovery process KDD process of analyzing
More information5. A full binary tree with n leaves contains [A] n nodes. [B] log n 2 nodes. [C] 2n 1 nodes. [D] n 2 nodes.
1. The advantage of.. is that they solve the problem if sequential storage representation. But disadvantage in that is they are sequential lists. [A] Lists [B] Linked Lists [A] Trees [A] Queues 2. The
More informationProgramming Exercise 3: Multi-class Classification and Neural Networks
Programming Exercise 3: Multi-class Classification and Neural Networks Machine Learning November 4, 2011 Introduction In this exercise, you will implement one-vs-all logistic regression and neural networks
More informationOn Boolean Ideals and Varieties with Application to Algebraic Attacks
Nonlinear Phenomena in Complex Systems, vol. 17, no. 3 (2014), pp. 242-252 On Boolean Ideals and Varieties with Application to Algebraic Attacks A. G. Rostovtsev and A. A. Mizyukin Saint-Petersburg State
More informationTheoretical Computer Science (Bridging Course) Complexity
Theoretical Computer Science (Bridging Course) Complexity Gian Diego Tipaldi A scenario You are a programmer working for a logistics company Your boss asks you to implement a program that optimizes the
More informationThe Geometry of Polynomial Division and Elimination
The Geometry of Polynomial Division and Elimination Kim Batselier, Philippe Dreesen Bart De Moor Katholieke Universiteit Leuven Department of Electrical Engineering ESAT/SCD/SISTA/SMC May 2012 1 / 26 Outline
More informationEfficient Recovery of Secrets
Efficient Recovery of Secrets Marcel Fernandez Miguel Soriano, IEEE Senior Member Department of Telematics Engineering. Universitat Politècnica de Catalunya. C/ Jordi Girona 1 i 3. Campus Nord, Mod C3,
More informationChapter 6 Quantum Computing Based Software Testing Strategy (QCSTS)
Chapter 6 Quantum Computing Based Software Testing Strategy (QCSTS) 6.1 Introduction Software testing is a dual purpose process that reveals defects and is used to evaluate quality attributes of the software,
More informationDr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010
CS 494/594 Computer and Network Security Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010 1 Introduction to Cryptography What is cryptography?
More informationA Tool for Generating Partition Schedules of Multiprocessor Systems
A Tool for Generating Partition Schedules of Multiprocessor Systems Hans-Joachim Goltz and Norbert Pieth Fraunhofer FIRST, Berlin, Germany {hans-joachim.goltz,nobert.pieth}@first.fraunhofer.de Abstract.
More information1 Data Encryption Algorithm
Date: Monday, September 23, 2002 Prof.: Dr Jean-Yves Chouinard Design of Secure Computer Systems CSI4138/CEG4394 Notes on the Data Encryption Standard (DES) The Data Encryption Standard (DES) has been
More information10/27/14. Streaming & Sampling. Tackling the Challenges of Big Data Big Data Analytics. Piotr Indyk
Introduction Streaming & Sampling Two approaches to dealing with massive data using limited resources Sampling: pick a random sample of the data, and perform the computation on the sample 8 2 1 9 1 9 2
More informationHow To Model A System
Web Applications Engineering: Performance Analysis: Operational Laws Service Oriented Computing Group, CSE, UNSW Week 11 Material in these Lecture Notes is derived from: Performance by Design: Computer
More informationUnit 7 Quadratic Relations of the Form y = ax 2 + bx + c
Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics
More informationSolving simultaneous equations using the inverse matrix
Solving simultaneous equations using the inverse matrix 8.2 Introduction The power of matrix algebra is seen in the representation of a system of simultaneous linear equations as a matrix equation. Matrix
More informationThe Bi-Objective Pareto Constraint
The Bi-Objective Pareto Constraint Renaud Hartert and Pierre Schaus UCLouvain, ICTEAM, Place Sainte Barbe 2, 1348 Louvain-la-Neuve, Belgium {renaud.hartert,pierre.schaus}@uclouvain.be Abstract. Multi-Objective
More informationComplexity Theory. IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar
Complexity Theory IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar Outline Goals Computation of Problems Concepts and Definitions Complexity Classes and Problems Polynomial Time Reductions Examples
More informationGuessing Game: NP-Complete?
Guessing Game: NP-Complete? 1. LONGEST-PATH: Given a graph G = (V, E), does there exists a simple path of length at least k edges? YES 2. SHORTEST-PATH: Given a graph G = (V, E), does there exists a simple
More informationGenetic Algorithms commonly used selection, replacement, and variation operators Fernando Lobo University of Algarve
Genetic Algorithms commonly used selection, replacement, and variation operators Fernando Lobo University of Algarve Outline Selection methods Replacement methods Variation operators Selection Methods
More informationProbability Using Dice
Using Dice One Page Overview By Robert B. Brown, The Ohio State University Topics: Levels:, Statistics Grades 5 8 Problem: What are the probabilities of rolling various sums with two dice? How can you
More informationHealthcare data analytics. Da-Wei Wang Institute of Information Science wdw@iis.sinica.edu.tw
Healthcare data analytics Da-Wei Wang Institute of Information Science wdw@iis.sinica.edu.tw Outline Data Science Enabling technologies Grand goals Issues Google flu trend Privacy Conclusion Analytics
More informationApplication of cube attack to block and stream ciphers
Application of cube attack to block and stream ciphers Janusz Szmidt joint work with Piotr Mroczkowski Military University of Technology Military Telecommunication Institute Poland 23 czerwca 2009 1. Papers
More informationInformation, Entropy, and Coding
Chapter 8 Information, Entropy, and Coding 8. The Need for Data Compression To motivate the material in this chapter, we first consider various data sources and some estimates for the amount of data associated
More informationDATABASE DESIGN - 1DL400
DATABASE DESIGN - 1DL400 Spring 2015 A course on modern database systems!! http://www.it.uu.se/research/group/udbl/kurser/dbii_vt15/ Kjell Orsborn! Uppsala Database Laboratory! Department of Information
More informationIMPROVING PERFORMANCE OF RANDOMIZED SIGNATURE SORT USING HASHING AND BITWISE OPERATORS
Volume 2, No. 3, March 2011 Journal of Global Research in Computer Science RESEARCH PAPER Available Online at www.jgrcs.info IMPROVING PERFORMANCE OF RANDOMIZED SIGNATURE SORT USING HASHING AND BITWISE
More informationRemoving Partial Inconsistency in Valuation- Based Systems*
Removing Partial Inconsistency in Valuation- Based Systems* Luis M. de Campos and Serafín Moral Departamento de Ciencias de la Computación e I.A., Universidad de Granada, 18071 Granada, Spain This paper
More informationLDPC Codes: An Introduction
LDPC Codes: An Introduction Amin Shokrollahi Digital Fountain, Inc. 39141 Civic Center Drive, Fremont, CA 94538 amin@digitalfountain.com April 2, 2003 Abstract LDPC codes are one of the hottest topics
More informationAbstract Data Type. EECS 281: Data Structures and Algorithms. The Foundation: Data Structures and Abstract Data Types
EECS 281: Data Structures and Algorithms The Foundation: Data Structures and Abstract Data Types Computer science is the science of abstraction. Abstract Data Type Abstraction of a data structure on that
More informationHow to make the computer understand? Lecture 15: Putting it all together. Example (Output assembly code) Example (input program) Anatomy of a Computer
How to make the computer understand? Fall 2005 Lecture 15: Putting it all together From parsing to code generation Write a program using a programming language Microprocessors talk in assembly language
More informationBOĞAZİÇİ UNIVERSITY COMPUTER ENGINEERING
Parallel l Tetrahedral Mesh Refinement Mehmet Balman Computer Engineering, Boğaziçi University Adaptive Mesh Refinement (AMR) A computation ti technique used to improve the efficiency i of numerical systems
More informationPerformance Test of Local Search Algorithms Using New Types of
Performance Test of Local Search Algorithms Using New Types of Random CNF Formulas Byungki Cha and Kazuo Iwama Department of Computer Science and Communication Engineering Kyushu University, Fukuoka 812,
More informationChapter 7: Functional Programming Languages
Chapter 7: Functional Programming Languages Aarne Ranta Slides for the book Implementing Programming Languages. An Introduction to Compilers and Interpreters, College Publications, 2012. Fun: a language
More informationCSE 326: Data Structures B-Trees and B+ Trees
Announcements (4//08) CSE 26: Data Structures B-Trees and B+ Trees Brian Curless Spring 2008 Midterm on Friday Special office hour: 4:-5: Thursday in Jaech Gallery (6 th floor of CSE building) This is
More informationSearching Algorithms
Searching Algorithms The Search Problem Problem Statement: Given a set of data e.g., int [] arr = {10, 2, 7, 9, 7, 4}; and a particular value, e.g., int val = 7; Find the first index of the value in the
More informationImproving SAT-Based Weighted MaxSAT Solvers CP 2012 (Quebec)
CP 2012 (Quebec) Carlos Ansótegui 1 María Luisa Bonet 2 Joel Gabàs 1 Jordi Levy 3 Universitat de Lleida (DIEI, UdL) 1. Universitat Politècnica de Catalunya (LSI, UPC) 2. Artificial Intelligence Research
More information1 Review of Newton Polynomials
cs: introduction to numerical analysis 0/0/0 Lecture 8: Polynomial Interpolation: Using Newton Polynomials and Error Analysis Instructor: Professor Amos Ron Scribes: Giordano Fusco, Mark Cowlishaw, Nathanael
More informationGRASP: A Search Algorithm for Propositional Satisfiability
506 IEEE TRANSACTIONS ON COMPUTERS, VOL. 48, NO. 5, MAY 1999 GRASP: A Search Algorithm for Propositional Satisfiability JoaÄo P. Marques-Silva, Member, IEEE, and Karem A. Sakallah, Fellow, IEEE AbstractÐThis
More informationNetwork coding for security and robustness
Network coding for security and robustness 1 Outline Network coding for detecting attacks Network management requirements for robustness Centralized versus distributed network management 2 Byzantine security
More informationFast Contextual Preference Scoring of Database Tuples
Fast Contextual Preference Scoring of Database Tuples Kostas Stefanidis Department of Computer Science, University of Ioannina, Greece Joint work with Evaggelia Pitoura http://dmod.cs.uoi.gr 2 Motivation
More informationLecture Note 8 ATTACKS ON CRYPTOSYSTEMS I. Sourav Mukhopadhyay
Lecture Note 8 ATTACKS ON CRYPTOSYSTEMS I Sourav Mukhopadhyay Cryptography and Network Security - MA61027 Attacks on Cryptosystems Up to this point, we have mainly seen how ciphers are implemented. We
More information