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Slide 1 - Advanced Cryptanalysis Part 1  Cryptography 1
Slide 2 - Advanced Cryptanalysis Modern cryptanalysis Differential cryptanalysis Linear cryptanalysis Side channel attack on RSA Lattice reduction attack on knapsack Hellman’s TMTO attack on DES Part 1  Cryptography 2
Slide 3 - Linear and Differential Cryptanalysis Part 1  Cryptography 3
Slide 4 - Introduction Both linear and differential cryptanalysis developed to attack DES Applicable to other block ciphers Differential --- Biham and Shamir, 1990 Apparently known to NSA in 1970’s For analyzing ciphers, not a practical attack A chosen plaintext attack Linear cryptanalysis --- Matsui, 1993 Perhaps not know to NSA in 1970’s Slightly more feasible than differential cryptanalysis A known plaintext attack Part 1  Cryptography 4
Slide 5 - DES Overview 8 S-boxes Each S-box maps 6 bits to 4 bits Example: S-box 1 Part 1  Cryptography 5 L R S-boxes XOR Ki subkey L R Linear stuff Linear stuff input bits (0,5)  input bits (1,2,3,4) | 0 1 2 3 4 5 6 7 8 9 A B C D E F ----------------------------------- 0 | E 4 D 1 2 F B 8 3 A 6 C 5 9 0 7 1 | 0 F 7 4 E 2 D 1 A 6 C B 9 5 3 4 2 | 4 1 E 8 D 6 2 B F C 9 7 3 A 5 0 3 | F C 8 2 4 9 1 7 5 B 3 E A 0 6 D
Slide 6 - Overview of Differential Cryptanalysis Part 1  Cryptography 6
Slide 7 - Differential Cryptanalysis Consider DES All of DES is linear except S-boxes Differential attack focuses on nonlinearity Idea is to compare input and output differences For simplicity, first consider one round and one S-box Part 1  Cryptography 7
Slide 8 - Differential Cryptanalysis Spse DES-like cipher has 3 to 2 bit S-box Part 1  Cryptography 8 column row 00 01 10 11 0 10 01 11 00 1 00 10 01 11 Sbox(abc) is element in row a column bc Example: Sbox(010) = 11
Slide 9 - Differential Cryptanalysis Part 1  Cryptography 9 column row 00 01 10 11 0 10 01 11 00 1 00 10 01 11 Suppose X1 = 110, X2 = 010, K = 011 Then X1  K = 101 and X2  K = 001 Sbox(X1  K) = 10 and Sbox(X2  K) = 01
Slide 10 - Differential Cryptanalysis Part 1  Cryptography 10 column row 00 01 10 11 0 10 01 11 00 1 00 10 01 11 Suppose Unknown: K Known: X = 110, X = 010 Known: Sbox(X  K) = 10, Sbox(X  K) = 01 Know X  K  {000,101}, X  K  {001,110} Then K  {110,011}  {011,100}  K = 011 Like a known plaintext attack on S-box
Slide 11 - Differential Cryptanalysis Attacking one S-box not very useful! Attacker cannot always see input and output To make this work we must do 2 things Extend the attack to one round Must account for all S-boxes Choose input so only one S-box “active” Then extend attack to (almost) all rounds Note that output is input to next round Choose input so output is “good” for next round Part 1  Cryptography 11
Slide 12 - Differential Cryptanalysis We deal with input and output differences Suppose we know inputs X and X For input X input to S-box is X  K and for input X the input to S-box is X  K Key K is unknown Input difference: (X  K)  (X  K) = X  X Input difference is independent of key K Output difference: Y  Y is (almost) input difference to next round Goal is to “chain” differences thru rounds Part 1  Cryptography 12
Slide 13 - Differential Cryptanalysis If we obtain known output difference from known input difference… May be able to chain differences thru rounds It’s OK if this only occurs with some probability If input difference is 0… …output difference is 0 Allows us to make some S-boxes “inactive” with respect to differences Part 1  Cryptography 13
Slide 14 - S-box Differential Analysis Part 1  Cryptography 14 column row 00 01 10 11 0 10 01 11 00 1 00 10 01 11 Sbox(X)Sbox(X) 00 01 10 11 000 8 0 0 0 001 0 0 4 4 X 010 0 8 0 0  011 0 0 4 4 X 100 0 0 4 4 101 4 4 0 0 110 0 0 4 4 111 4 4 0 0 Input diff 000 not interesting Input diff 010 always gives output diff 01 More biased, the better (for the attacker)