Stream Ciphers in Modern Real-time IT Systems: Analysis, Design and Comparative Studies (Studies in Systems, Decision and Control, 375)

Contents
Symbols, Signs, Units, Abbreviations and Terms
1 Introduction
	References
2 Criteria and Indices Substantiation of the Stream Cryptoconversion Efficiency
	2.1 Criteria and Indices of the Stream Cryptoconversions Stability
		2.1.1 Indices Demonstrating the Parameters of Shift-Registers and of Take-Off Points for Non-Linear Functions and Feedbacks
		2.1.2 Indices of Stability of Key Initialization Procedure
		2.1.3 Indices of Stability of a Non-Linear Function (of Non-Linear Conversion Nodes)
		2.1.4 General Stability Indices
	2.2 Software and Hardware-Realization Indices
	2.3 Constructive-Technological Indices
	2.4 Generalization of Indices and Criteria of Stream Cryptoconversion
	2.5 Conclusions and Recommendations
	References
3 Analysis of Stream Cryptoconversion Principles
	3.1 Basic Approaches to Construction and Analysis of SSC and BSC Stream Modes
	3.2 Formalization of Stream Cryptoconversions by Their General Classification
	3.3 Conclusions and Recommendations
	References
4 Analysis of Synchronous Stream Cryptoconversions
	4.1 General Classification of Synchronous Stream Cryptoconversions
	4.2 Stream Encryption Methods Established on Use of Registers with Steady Motion
		4.2.1 Synchronous Stream Cryptoconversions with Steady Motion According to the Scheme of the Filter Generator
		4.2.2 Synchronous Stream Cryptoconversions with Steady Motion According to the Scheme of the Combination Generator
	4.3 Streaming Encryption Methods Established on the Use of Registers with Unsteady Motion
		4.3.1 Generator with Control Register “stop-and-go”
		4.3.2 Generator with Control Register “stop-and-go” with Alternation
		4.3.3 Two-Way stop-and-go Generator
		4.3.4 Cascade Generators with Control Registers (Holmann Cascades)
		4.3.5 Compressor Generator with Control Register
		4.3.6 Self-Priming Generator
		4.3.7 Self-Decimated Generator
		4.3.8 Multi-speed Generator with Internal Product (or with Internal Nonlinear Conversion)
		4.3.9 Majority Generator
	4.4 Conclusions and Recommendations
	References
5 Analysis of Stream Modes for Block Symmetric Ciphers
	5.1 Electronic Codebook Mode—ECB
		5.1.1 General Parameters
		5.1.2 Introducing of Input and Output Data, Internal Modification State
		5.1.3 Enciphering
		5.1.4 Deciphering
		5.1.5 Forming of Cyclic Keys
	5.2 Counter Mode—CTR
		5.2.1 General Parameters
		5.2.2 Enciphering
		5.2.3 Deciphering
	5.3 Cipher Feedback Mode—CFB
		5.3.1 General Parameters
		5.3.2 Enciphering
		5.3.3 Deciphering
	5.4 Cipher Block Chaining—CBC
		5.4.1 General Parameters
		5.4.2 Enciphering
		5.4.3 Deciphering
	5.5 Output Feedback—OFB
		5.5.1 General Parameters
		5.5.2 Enciphering
		5.5.3 Deciphering
	5.6 Conclusions and Recommendations
	References
6 Comparison of Stream Modes in Block Symmetric Ciphers
	6.1 Statistical Researches of the BSC «Kalyna»
		6.1.1 Statistical Researches of BSC «Kalyna» in the ECB-Mode
		6.1.2 Statistical Researches of the BSC «Kalyna» in the CTR-Mode
		6.1.3 Statistical Researches of the BSC «Kalyna» in the CFB-Mode
		6.1.4 Statistical Researches of the BSC «Kalyna» in the CBC-Mode
		6.1.5 Statistical Researches of the BSC «Kalyna» in the OFB-Mode
	6.2 Statistical Researches of BSC AES (FIPS-197) and GOST 28147-89 (DSTU GOST 28147:2009) in Different Using Modes
	6.3 Comparison of Statistical Security Indices of BSC
	6.4 Substantiation of Recommendations Concerning BSC-Usage in Various Cryptographic Appliances
	6.5 Conclusions and Recommendations
	References
7 Analysis of Standardized Algorithms for Streaming Cryptographic Convention, Defined in ISO/IEC 18033-4
	7.1 General Models of Stream Codes, Defined in ISO/IEC 18033-4
		7.1.1 Models of Key Stream Generators
		7.1.2 Output Function Models
	7.2 Specialized Key Stream Generators
		7.2.1 MUGI Key Stream Generator
		7.2.2 SNOW 2.0 Key Stream Generator
		7.2.3 Rabbit Streaming Code
		7.2.4 Decim Key Stream Generator
		7.2.5 Key Stream Generator KCipher-2
	7.3 Fluid Code Security Levels with ISO/IEC 18033-4
	7.4 Conclusions and Recommendations
	References
8 Comparative Analysis of Determined Generators for Random Bits, Defined in the Nist Special Publication 800-90A
	8.1 Analysis and Research of the Main Conversions in DGRB with Using of the Hashing Funcions
	8.2 Analysis and Research of the Main Conversions in DGRB with Using of Symmetric Ciphering
	8.3 Analysis and Researches of Main Conversions in DRGB, Based on Numeric-Theoretical Problems
	8.4 Comparative DGRB-Researches, Defined in the Standard NIST Special Publication 800-90A
	8.5 Conclusions and Recommendations
	References
9 Analysis of Bitstreamed Cryptographic Conversion Algorithms from the International Project eSTREAM
	9.1 Analysis of Software-Oriented Stream Ciphers, Recognized as Winners of the International Project eSTREAM
		9.1.1 Stream Cipher HC-128
		9.1.2 Stream Cipher Salsa20
		9.1.3 Stream Cipher SOSEMANUK
	9.2 Analysis of Hardware-Oriented Stream Ciphers, Recognised as Winners of the International Project eSTREAM
		9.2.1 Stream Cipher Grain
		9.2.2 Stream Cipher MICKEY
		9.2.3 Stream Cipher Trivium
	9.3 Stream Cipher CryptMT Version 3
		9.3.1 Specification of the Cipher
		9.3.2 CryptMT Cipher Security
		9.3.3 Comparison of Productivity
	9.4 Conclusions and Recommendations
	References
10 Analysis of Stream Cryptographic Transfer Algorithms for Light (Less-Resource) Cryptographies Defined in ISO/IEC 29192
	10.1 Stream Cipher Enocoro
		10.1.1 Data Structure
		10.1.2 The General Specification of Enocoro V2
		10.1.3 Enocoro-128v2 Stream Encryption Specification
		10.1.4 Data Encryption Using Enocoro-128v2
		10.1.5 Key Stream Statistics Tests
		10.1.6 Attacks Based on a Compromise of Time-Memory-Data
		10.1.7 Initialization Vector Recovery Attacks
		10.1.8 The Maximum Degree of Monomials Test
	10.2 RC4 Stream Cipher
		10.2.1 Specification of the Algorithm
		10.2.2 RS4 SSC Security
		10.2.3 Realization
	10.3 Conclusions and Recommendations
	References
11 Comparative Research of Fluid Cryptographic Transformation Algorithms
	11.1 Comparative Studies of Statistical Security of Stream Cryptographic Transformation Algorithms
		11.1.1 Methods of Analysis of Passing Statistical Tests
		11.1.2 NIST STS Statistical Test Package
		11.1.3 Results of Experimental Studies of SSC Statistical Properties Using the NIST STS Statistical Testing Package
		11.1.4 Characteristics of DIEHARD Statistical Tests
		11.1.5 Results of Experimental Statistical Studies SSC Properties Using the DIEHARD Package
	11.2 Comparative Researches of Computing Complexity of the FLOW-Cryptographic Transformation Algorithms
		11.2.1 The Essence of the Method of Testing Speed Characteristics Stream Ciphers
		11.2.2 Investigation of the Characteristics of Ciphers on Different Processors
	11.3 Conclusions and Recommendations
	References
12 Areas of Application for Nonlinear Shift Registers in PRS Generators
	12.1 Key Issues During the Design of Streaming Encryption Algorithms
	12.2 General Second-Order NLFSR Model
	12.3 Research of the Basic Methods of Construction of NLFSR
		12.3.1 De Bruijn’s Sequence
		12.3.2 Algorithms for Generating De Bruijn Sequences
	12.4 Problems of SPS Synthesis and Analysis on the Basis of NLFSR
	12.5 Cryptographic Stability of NLFSR
		12.5.1 System of Criteria and Indicators of Cryptographic Evaluation Stability of NLFSR
		12.5.2 Unconditional Criteria of Cryptographic Stability
		12.5.3 Conditional Criteria of Cryptographic Stability
		12.5.4 Estimation of Cryptographic Stability of NLFSR as Filtering or Combining Function
	12.6 Conclusions
	References
13 Requirements for Feedback Coefficients, What Should the M-Nlfsr Respond to?
	13.1 Requirements 1–4
		13.1.1 Formulation and Substantiation of Requirements 1–4
		13.1.2 Calculation of the Number of NLFSR that Meet the Requirements 1–4. Empirical Expression for the Calculation of M-NLFSR
		13.1.3 Conclusions on the Application of Requirements 1–4
	13.2 Requirements 5–6
		13.2.1 Formulation and Substantiation of Requirements 5–6
		13.2.2 Calculation of the Set of NLFSR that Do not Meet the Requirements 1–6
		13.2.3 Quantitative Evaluation of the Obtained Results
	13.3 Requirements 7–8
		13.3.1 Formulation and Substantiation of Requirements 7–8
		13.3.2 The Method of Calculating the Set of Combinations, that Do not Meet the Requirement 8
		13.3.3 Inclusion and Exclusion Formula
		13.3.4 Solve the Problem of Computing a Non-intersecting Set for Small Values of L
		13.3.5 Calculating the Complete Set of Feedback Combinations that Do not Meet Requirement 8
	13.4 Requirement 9
		13.4.1 Description Requirements 9
		13.4.2 Joint Application of Requirement 9 with Other Requirements
		13.4.3 Quantitative Assessment of the Application of the Requirements
		13.4.4 Conditions of the Zero Set Truncated by Requirement 9
		13.4.5 Estimation of Spent Resources (RAM)
		13.4.6 Estimation of Time Costs
		13.4.7 Optimization of Pattern Construction
		13.4.8 Conclusions on the Application of the Requirement 9
	13.5 Conclusions
14 Method of Synthesis M-NLFSR. Hardware and Software Search M-NLFSR Second Order. List M-NLFSR
	14.1 Development of Mathematical Apparatus Based on Solutions of the System of Linear Equations for Optimization of M-NLFSR Search
		14.1.1 Restoration of NLFSR in a Known Sequence Using the SLAE Solution
		14.1.2 Selection of Forming Sequences for Assembly of SLAE
		14.1.3 Search M-NLFSR Using SLAE
	14.2 Model with Simplified Formalized Description of Second-Order Nonlinear Feedback
		14.2.1 Finding M-NLFSR for Large Registers
		14.2.2 Search Results for M-NLFSR—List of M-NLFSR Dimension from L = 19 to L = 25
	14.3 Search for M-NLFSR with the Use of Hardware Implemented on FPGA
		14.3.1 M-NLFSR Search Method
		14.3.2 The Structure of the Hardware and Software
		14.3.3 Implementation of NLFSR on FPGA
		14.3.4 FPGA Performance
		14.3.5 Search Results for M-NLFSR—List of M-NLFSR Dimension from L = 26 to L = 30
		14.3.6 Conclusions on the Use of FPGA in the Search for M-NLFSR
	14.4 Search for MRZNZZ with the Application of Parallel Calculation at GPU
		14.4.1 Use of Parallel Computing Technologies in GPUs
		14.4.2 GPU Application for Streaming Encryption Systems
		14.4.3 GPU Application in the Second Stage of M-NLFSR Search Obtained M-NLFSR Dimension L = 31, 32
	14.5 Conclusions
	References
15 Research of Second-Order Properties of NLFSR. Comparative Analysis of M-NLFSR and M-LFSR
	15.1 Assessment of Linear Complexity
	15.2 Assessment of Quadratic Complexity
	15.3 Estimation of the Amount of the Amount of Two or More Sequences Generated by M-NLFSR
	15.4 Assessment of Linear and Quadratic Complexity Sum of Sequences
	15.5 Analysis of the Applicability of Decimation and Properties of Group Addition to M-NLFSR
	15.6 Study of Statistical Characteristics of prs, Which are Generated M-NLFSR
		15.6.1 Setting up a Computational Experiment
		15.6.2 Analysis of Results
	15.7 Comparison of the Volume of the M-LFSR and M-NLFSR Ensembles for GF(2) and in Field Extensions GF(22)
	15.8 Quantitative Calculation of the set of NLFSR Third and More High Order
	15.9 Evaluation of M-NLFSR and M-LFSR Productivity in the Software Implementation of the Algorithm
	15.10 Distribution of Number of Nonlinears Feedback in M-NLFSR
	15.11 Research of NLFSR as a Filter or Combining Functions
		15.11.1 Balance
		15.11.2 The Presence of Prohibitions
		15.11.3 Correlation Immunity
		15.11.4 Nonlinearity
	15.12 Cryptographic Resistance Assessment Model as a Basic Element of Current Symmetric Encryption Schemes. Comparisons by Developed Model of NLFSR and LFSR Assessments
	15.13 Conclusions on Chap. 15
	References
16 Stream Symmetric Cipher “Strumok”
	16.1 Justification of the Mathematical Structure of the Cipher
		16.1.1 Justification of General Requirements for the Key System Perspective Symmetric Stream Cipher for Post-Quantum Application
		16.1.2 General Cipher Parameters
		16.1.3 Substantiation of the Mathematical Structure of the Stream Symmetric Cipher “Strumok”
		16.1.4 Init Internal State Initialization Function
		16.1.5 Next State Function Next
		16.1.6 Key Stream Function Strm
		16.1.7 Function of Finite Automaton FSM
		16.1.8 Nonlinear Substitution Function T
	16.2 Substantiation of the Main Cryptographic Elements of the Stream Symmetric Cipher “STRUMOK”
		16.2.1 Rationale for Fast Execution of Nonlinear Substitution Operation
		16.2.2 Substantiation of Fast Execution of Multiplication Operation on α−1 in Arithmetic of Field GF (264)
		16.2.3 Algorithm for Fast Execution of Multiplication Operation by α−1 in Arithmetic of the GF Field (264)
		16.2.4 Substantiation of Fast Execution of Multiplication Operation by α−1 in Arithmetic of the GF Field (264)
		16.2.5 Algorithm for Fast Execution of Multiplication Operation by α - 1 in Arithmetic of Field GF(264)
	16.3 Evaluation of «STRUMOK» Cipher Speed
		16.3.1 Substantiation of the Method of Research of the Speed of Streaming Cryptoconversion
		16.3.2 Comparative Studies of the Speed of Streaming Cryptoconversion
		16.3.3 Comparison with AMD FX6300 SixCoreProcessor 3.50 GHz
	16.4 Substantiation of Flow Characteristics Symmetric Encryption by Stability/Complexity Ratio
		16.4.1 Estimate the Number of Operations and the Minimum Amount of Memory, Required for the Implementation of the Cipher “Strumok”
		16.4.2 Substantiation of the Characteristics of the Cipher “Strumok” in Terms of Stability/Complexity
	16.5 Conclusions in this Chapter
	References
17 Conclusions
	References
Appendix A
Appendix B
B.1 Substitution 0
B.2 Substitution 1
B.3 Substitution 2
B.4 Substitution 3
Appendix C
C.1 Table T0
C.2 Table T1
C.3 Table T2
C.4 Table T3
C.5 Table T4
C.6 Table T5
C.7 Table T6
C.8 Table T7
Appendix D
D.1 Table Mulα [a]
D.2 Table Mulα - 1  [a]1
Appendix E
E.1 256-Bit Key
E.1.1 Key Initialization Vector and Key Sequence
E.1.2 Sample of Internal States
E.2 512-Bit Key
E.2.1 Key Initialization Vector and Key Sequence
E.2.2 Sample of Internal States