Differential Cryptanalysis of the Data Encryption Standard

1 Introduction.- 2 Results.- 3 Introduction to Differential Cryptanalysis.- 3.1 Notations and Definitions.- 3.2 Overview.- 3.3 Characteristics.- 3.4 The Signal to Noise Ratio.- 3.5 Known Plaintext Attacks.- 3.6 Structures.- 4 Differential Cryptanalysis of DES Variants.- 4.1 DES Reduced to Four Rounds.- 4.2 DES Reduced to Six Rounds.- 4.3 DES Reduced to Eight Rounds.- 4.3.1 Enhanced Characteristic's Probability.- 4.3.2 Extension to Nine Rounds.- 4.4 DES with an Arbitrary Number of Rounds.- 4.4.1 3R-Attacks.- 4.4.2 2R-Attacks.- 4.4.3 1R-Attacks.- 4.4.4 Summary.- 4.4.5 Enhanced Characteristic's Probability.- 4.5 Modified Variants of DES.- 4.5.1 Modifying the P Permutation.- 4.5.2 Modifying the Order of the S Boxes.- 4.5.3 Replacing XORs by Additions.- 4.5.3.1 Replacing the XORs Within the F Function.- 4.5.3.2 Replacing All the XORs.- 4.5.3.3 Replacing All the XORs in an Equivalent DES Description.- 4.5.4 Random and Modified S Boxes.- 4.5.5 S Boxes with Uniform Difference Distribution Tables.- 4.5.6 Eliminating the E Expansion.- 4.5.7 Replacing the Order of the E Expansion and the XOR with the Subkeys.- 4.6 DES with Independent Keys.- 4.6.1 Eight Rounds.- 4.6.2 Sixteen Rounds.- 4.7 The Generalized DES Scheme (GDES).- 4.7.1 GDES Properties.- 4.7.2 Cryptanalysis of GDES.- 4.7.2.1 A Known Plaintext Attack for n = q.- 4.7.2.2 A Second Known Plaintext Attack for n = q.- 4.7.2.3 A Chosen Plaintext Attack for n = 2q ? 1.- 4.7.2.4 A Chosen Plaintext Attack for n = 3q ? 2.- 4.7.2.5 A Chosen Plaintext Attack for n = lq ? 1.- 4.7.2.6 The Actual Attack on the Recommended Variant.- 4.7.2.7 Summary.- 5 Differential Cryptanalysis of the Full 16-Round DES.- 5.1 Variants of the Attack.- 6 Differential Cryptanalysis of FEAL.- 6.1 Cryptanalysis of FEAL-8.- 6.1.1 Reducing FEAL-8 to Seven Rounds.- 6.1.2 Reducing the Seven-Round Cryptosystem to Six Rounds.- 6.1.3 Reducing the Cryptosystem to 5, 4, 3, 2 and 1 Rounds.- 6.1.4 Calculating the Key Itself.- 6.1.5 Summary.- 6.2 Cryptanalysis of FEAL-N and FEAL-NX with N ? 31 Rounds.- 6.3 Other Properties of FEAL.- 7 Differential Cryptanalysis of Other Cryptosystems.- 7.1 Cryptanalysis of Khafre.- 7.2 Cryptanalysis of REDOC-II.- 7.3 Cryptanalysis of LOKI.- 7.4 Cryptanalysis of Lucifer.- 7.4.1 First Attack.- 7.4.2 Second Attack.- 8 Differential Cryptanalysis of Hash Functions.- 8.1 Cryptanalysis of Snefru.- 8.2 Cryptanalysis of N-Hash.- 9 Non-Differential Cryptanalysis of DES with a Small Number of Rounds.- 9.1 Ciphertext Only Attacks.- 9.1.1 A Three-Round Attack.- 9.1.2 Another Three-Round Attack.- 9.1.3 A Four-Round Attack.- 9.2 Known Plaintext Attacks.- 9.2.1 A Three-Round Attack.- 9.3 Statistical Known Plaintext Attacks.- 9.3.1 A Three-Round Attack.- 9.3.2 A Four-Round Attack.- 9.3.3 A Five-Round Attack.- 9.3.4 A Six-Round Attack.- A Description of DES.- A.1 The Key Scheduling Algorithm.- A.2 DES Modes of Operation.- B The Difference Distribution Tables of DES.