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Tables of Contents for The Twofish Encryption Algorithm
Chapter/Section Title
Page #
Page Count
Preface
iii
AES
iii
This Book
v
Introduction
1
2
Twofish Design Goals
3
2
Twofish Building Blocks
5
4
Feistel Networks
5
1
Whitening
5
1
S-boxes
6
1
MDS Matrices
6
1
Pseudo-Hadamard Transforms
7
1
Key Schedule
7
2
Twofish
9
10
The Function F
11
1
The Function g
11
1
The Key Schedule
12
5
Additional Key Lengths
13
1
The Function h
14
2
The Key-dependent S-boxes
16
1
The Expanded Key Words Kj
16
1
The Permutations q0 and q1
16
1
Round Function Overview
17
2
Performance of Twofish
19
14
Performance on Large Microprocessors
19
7
Keying Options
21
1
Code and Data Size
22
1
Large Memory Implementations
22
1
Total Encryption Times
23
1
Hash Function Performance
23
1
Language, Compiler, and Processor Choice
24
2
Performance on Smart Cards
26
3
RAM Usage
27
1
Encryption Speed and Key Agility
28
1
Code Size
29
1
Performance on the Alpha
29
1
Performance on Future Microprocessors
29
1
Hardware Performance
30
3
Twofish Design Philosophy
33
10
Performance-driven Design
33
2
Performance-Driven Tradeoffs
34
1
Conservative Design
35
1
Simple Design
36
2
Reusing Primitives
37
1
Reversibility
37
1
S-boxes
38
2
Large S-boxes
38
1
Algorithmic S-boxes
39
1
Key-depndent S-boxes
39
1
The Key Schedule
40
3
Performance Issues
42
1
The Design of Twofish
43
20
The Round Structure
43
4
Common Block Cipher Structures
44
3
The Key-dependent S-boxes
47
7
The Fixed Permutations q0 and q1
48
1
The S-boxes
49
1
Exhaustive and Statistical Analysis
50
4
MDS Matrix
54
3
Non-key-dependent Coefficients
54
1
Implementation Issues
54
1
Preserving Diffusion Properties after Rotation
54
2
Rotational Uniqueness of Output Vectors
56
1
Maximizing the Minimal Hamming Distance
56
1
PHT
57
1
Eliminating the PHT
57
1
Diffusion and the Least Significant Bit
57
1
Key Addition
58
1
Feistel Combining Operation
58
1
Use of Different Groups
58
1
Diffusion in the Round Function
59
1
Changes Induced by F
59
1
One-bit Rotation
59
2
Reason for Rotations
60
1
Downsides to Rotations
60
1
Converting to a Pure Feistel Structure
60
1
The Number of Rounds
61
2
Design of the Twofish Key Schedule
63
16
Round Subkeys
64
3
Equivalence of Round Subkeys
64
1
Equivalent keys
65
2
Controlling Changes in Round Subkeys
67
5
XOR Difference Sequences in A and B
68
1
Byte Sequences with Given Difference
68
1
Identical Byte Sequences
69
1
The A and B Sequences
70
1
The Sequence (K2i, K2i+1)
70
1
Difference Sequences in the Subkeys
71
1
The Round Function
72
2
Properties of the Key Schedule and Cipher
74
1
Equivalent Keys
74
1
Self-Inverse Keys
74
1
Pairs of Inverse Keys
74
1
Simple Relations
75
1
Key-dependent Characteristics and Weak Keys
75
1
Reed-Solomon Code
76
3
Cryptanalysis of Twofish
79
40
A Meet-in-the-Middle Attack on Twofish
80
2
Results of the Attack
80
1
Overview of the Attack
80
1
Attacking Twofish with Fixed S and no Whitening
81
1
Attacking Twofish with Fixed S
81
1
Attacking Normal Twofish
81
1
Differential Cryptanalysis
82
8
Results of the Attack
82
1
Overview of the Attack
82
2
Building the Batches
84
3
Mounting the Attack
87
2
Lessons from the Analysis
89
1
Extensions to Differential Cryptanalysis
90
1
Higher-Order Differential Cryptanalysis
90
1
Truncated Differentials
90
1
Search for the Best Differential Characteristic
90
11
Differentials of the S-boxes
91
1
Differentials of F
92
4
Differentials of the Round Function
96
1
Multi-round Patterns
96
1
Results
97
1
Other Problems for the Attacker
97
1
Best S-box Differential
98
1
Other Variants
99
1
Further Work
99
1
Conclusion
100
1
Linear Cryptanalysis
101
2
Multiple Linear Approximations
102
1
Non-linear Cryptanalysis
102
1
Generalized Linear Cryptanalysis
102
1
Partitioning Cryptanalysis
102
1
Differential-linear Cryptanalysis
103
1
Interpolation Attack
103
1
Partial Key Guessing Attacks
104
1
Related-key Cryptanalysis
104
4
Resistance to Related-Key Slide Attacks
104
1
Resistance to Related-key Differential Attacks
105
1
The Zero Difference Case
106
1
Other Difference Sequences
107
1
Probability of a successful Attack with One Related-key Query
107
1
Conclusions
108
1
A Chosen-key Attack
108
3
Overview of the Attack
109
1
Finding a Key Pair
109
1
Choosing the Plaintexts to Request
110
1
Extracting the Key Material
110
1
Side-Channel Cryptanalysis and Fault Analysis
111
1
Attacking Simplified Twofish
112
3
Twofish with Known S-boxes
112
1
Twofish without Round Subkeys
112
2
Twofish with Non-bijective S-boxes
114
1
Trap Doors in Twofish
115
4
Using Twofish
119
6
Chaining Modes
119
1
One-Way Hash Functions
119
1
Message Authentication Codes
120
1
Pseudorandom Number Generators
120
1
Larger Keys
120
1
Additional Block Sizes
120
1
More or Fewer Rounds
120
2
Family Key Variant: Twofish-FK
122
3
Analysis
123
2
Historical Remarks
125
4
Conclusions and Further Work
129
2
References
131
52
A. Overview of Symbols
143
4
B. Twofish Test Vectors
147
10
B.1 Intermediate Values
147
5
B.2 Full Encryptions
152
5
C. Code
157
26
C.1 C Code
157
26
Index
183