documentatie licenta

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Pseudorandom number generation for cryptographic application

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Table of ContentsTable of contents1 Introduction .............................................................................................................................. 1 1.1 Context .............................................................................................................................. 1 1.2 Project Topics................................................................................................................... 2 1.2.1 Statistical Tests for Random and Pseudo-random Number Generators..................... 2 1.2.2 Statistical Functions................................................................................................... 3 1.3 Project Goals..................................................................................................................... 4 1.3.1 Motivation .................................................................................................................. 4 1.3.2 Objectives................................................................................................................... 4 1.3.3 Project Description..................................................................................................... 5 2 Bibliographical Review ............................................................................................................ 1 3 Theoretical Foundations........................................................................................................... 8 3.1 Statistical Tests for Random and Pseudo-random Number Generators ............................ 8 3.1.1 NIST Statistical Test Suite......................................................................................... 8 3.1.1.1 NIST Test 1 Frequency (Monobit) Test........................................................... 9 3.1.1.2 NIST Test 2 Frequency Test within a Block .................................................. 10 3.1.1.3 NIST Test 3 Runs Test................................................................................... 12 3.1.1.4 NIST Test 4 Test for the Longest Run of Ones in a Block ............................ 14 3.1.1.5 NIST Test 7 Non-overlapping Template Matching Test............................... 17 3.1.1.6 NIST Test 8 Overlapping Template Matching Test....................................... 19 3.1.1.7 NIST Test 9 Maurers Universal Statistical Test....................................... 22 3.1.1.8 NIST Test 9 Maurers Universal Statistical Test (Corons variant)........... 26 3.1.2 CryptoRand Statistical Test Suite ............................................................................ 28 3.1.2.1 The Histogram Test Hl Test........................................................................... 28 3.2 Statistical Functions ........................................................................................................ 32 3.2.1 IBETA Statistical Function ...................................................................................... 32 3.2.2 IGAM and IGAMC Statistical Functions ................................................................ 33 3.2.3 The Chi-square Distribution..................................................................................... 34 3.2.4 The Poison Distribution........................................................................................... 36 3.3 OpenMP .......................................................................................................................... 38 4 Requirements Specifications and System Architecture......................................................... 41 4.1 Block Diagram of the System......................................................................................... 41 4.1.1 SeqTestRand ............................................................................................................ 41 4.1.2 ParTestRand............................................................................................................. 42 4.1.3 SFC........................................................................................................................... 43 4.2 Functional Requirements ................................................................................................ 43 4.3 Non-functional Requirements......................................................................................... 44 4.4 Constraints ...................................................................................................................... 45 4.5 General System Architecture .......................................................................................... 46 5 Design Detail .......................................................................................................................... 48 5.1 Design Policies ................................................................................................................ 48 5.2 Use Cases ........................................................................................................................ 52 5.2.1 SeqTestRand ............................................................................................................ 52 5.2.2 ParTestRand............................................................................................................. 55 5.2.3 SFC........................................................................................................................... 55 5.3 Program Structure........................................................................................................... 60 5.3.1 SeqTestRand ............................................................................................................ 60 5.3.1.1 SeqNIST ............................................................................................................ 60 Table of Contents5.3.1.2 SeqHistograms .................................................................................................. 68 5.3.2 ParTestRand............................................................................................................. 72 5.3.2.1 ParNIST ............................................................................................................ 72 5.3.2.2 ParNIST_blocks ................................................................................................ 74 5.3.3 SFC........................................................................................................................... 74 5.4 User interface .................................................................................................................. 76 5.4.1 SeqTestRand ............................................................................................................ 76 5.4.2 ParTestRand............................................................................................................. 80 5.4.3 SFC........................................................................................................................... 81 6 System Usage......................................................................................................................... 84 6.1 SeqTestRand................................................................................................................... 84 6.2 ParTestRand .................................................................................................................... 89 6.3 SFC .................................................................................................................................. 90 7 Deployment and experimental results .................................................................................... 94 7.1 Used Technology ............................................................................................................ 94 7.2 Running the Applications ................................................................................................ 94 7.2.1 Hardware requirements ............................................................................................ 94 7.2.2 Software requirements............................................................................................. 95 7.3 Encountered Issues and Solutions Found ........................................................................ 95 7.4 Experimental Results ...................................................................................................... 96 7.4.1 NIST Battery ............................................................................................................ 96 7.4.1.1 NIST Test 1 Frequency (Monobit) Test......................................................... 97 7.4.1.2 NIST Test 2 Frequency Test within a Block .................................................. 98 7.4.1.3 NIST Test 3 Runs Test................................................................................... 99 7.4.1.4 NIST Test 4 Test for the Longest Run of Ones in a Block .......................... 100 7.4.1.5 NIST Test 7 Non-overlapping Template Matching Test............................. 101 7.4.1.6 NIST Test 8 Overlapping Template Matching Test..................................... 102 7.4.1.7 NIST Test 9 Maurers Universal Statistical Test ...................................... 103 8 Conclusions .......................................................................................................................... 104 8.1 Results........................................................................................................................... 104 8.2 Comparison with Similar Systems ................................................................................ 105 8.3 Future Development ...................................................................................................... 106 9 References ............................................................................................................................ 107 10 Ann