Lecture 3: Symmetric Key Encryption

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1 Lecture 3: Symmetric Key Encryption CS996: Modern Cryptography Spring 2007 Nitesh Saxena

2 Outline Symmetric Key Encryption Continued Discussion of Potential Project Topics Project proposal due 02/22/07 in class 1-2 page long What you want to do; possible references 2/22/2007 Lecture 1 - Introduction 2

3 Grading 50% - Homeworks (probably 6 in #) 10% - Notes Scribing 40% - Project (and presentation) 2/22/2007 Lecture 1 - Introduction 3

4 Let s use the board, please take notes 2/22/2007 Lecture 1 - Introduction 4

5 DES Data Encryption Standard Encrypts by series of substitution and transpositions. Based on Feistel Structure Worldwide standard for more than 20 years. Has a history of controversy. Designed by IBM (Lucifer) with later help (interference?) from NSA. No longer considered secure for highly sensitive applications. Replacement standard AES (advanced encryption standard) recently completed. 2/22/2007 Lecture 1 - Introduction 5

6 DES - Overview 2/22/2007 Lecture 1 - Introduction 6

7 DES Each iteration. 2/22/2007 Lecture 1 - Introduction 7

8 DES Function F 2/22/2007 Lecture 1 - Introduction 8

9 2/22/2007 Lecture 1 - Introduction 9

10 Operation Tables of DES (Key Schedule, PC-1, PC-2) 2/22/2007 Lecture 1 - Introduction 10

11 Operation Tables (IP, IP -1, E and P) 2/22/2007 Lecture 1 - Introduction 11

12 S-boxes: S Sj Is the table entry from S( b1b 2b3b4b5b6) row : b 1 b 2 column : b 3 b 4 b 5 b 6 S( ) = 6d = /22/2007 Lecture 1 - Introduction 12

13 DES Decryption Same as the encryption algorithm with the reversed key schedule NEXT! 2/22/2007 Lecture 1 - Introduction 13

14 x L0 R0 R 0 L0 F( R0, K 1) Plain text Initial permutation (IP) Round-1 (key K 1 ) Rounds 2-15 L15 R15 L15 F( R15, K 16) L15 F( R15, K 16) R15 y R15 Round-16 (key K 16 ) swap IP inverse Cipher text 2/22/2007 Lecture 1 - Introduction 14

15 L15 F( R15, K 16) R15 y L15 F( R15, K 16) R15 R15 = L IP inverse Cipher text IP Round-1 (K 16 ) F( R15, K 16) F( R15, 16) 15 K encrypt decrypt R15 L15 Since b b = 0 b 0 = b 2/22/2007 Lecture 1 - Introduction 15

16 DES Security S-Box design not well understood (secret). Has survived some recent sophisticated attacks (differential cryptanalysis) We ll talk about such attacks in the crypto class next semster (not here!) Key is too short. Hence is vulnerable to brute force attack distributed attack took 3 months. $1,000,000 machine will crack DES in 35 minutes 1997 estimate. $10, days. 2/22/2007 Lecture 1 - Introduction 16

17 DES Cracking machine 2/22/2007 Lecture 1 - Introduction 17

18 Super-encryption. If key length is a concern, then instead of encrypting once, encrypt twice!! C = E K2 (E K1 (P)) P = D K2 (D K1 (C)) Does this result in a larger key space? Encrypting with multiple keys is known as super-encryption. May not always be a good idea. 2/22/2007 Lecture 1 - Introduction 18

19 Double DES K 1 K 2 P E X E C Encryption K 2 K 1 C D X D P Decryption Double DES is almost as easy to break as single DES (Needs more memory though)! 2/22/2007 Lecture 1 - Introduction 19

20 Double DES Meet-in-the-middle Attack (due to Diffie-Hellman) Based on the observation that, if C = E K2 (E K1 (P)) Then X = E K1 (P) = D K2 (C). Given a known (P, C) pair, encrypt P with all possible values of K and store result in table T. Next, decrypt C with all possible keys K and check result. If match occurs then check key pair with new known (P, C) pair. If match occurs, you have found the keys. Else continue as before. Process will terminate successfully. 2/22/2007 Lecture 1 - Introduction 20

21 Meet-in-the-middle Explanation. The first match does not say anything as we have 2 64 ciphertexts and keys. On the average / 2 64 = 2 48 keys will produce same ciphertext. So there could be 2 48 possible candidates We can use a second pair (P,C ) So, probability that false alarm will survive two known (P, C) pairs is 2 48 / 2 64 = One can always check a third pair to further reduce the chance of a false alarm. 2/22/2007 Lecture 1 - Introduction 21

22 Triple DES K 1 K 2 K 1 P A B E D E Encryption C K 1 K 2 K 1 C B A D E D Decryption P Triple DES (2 keys) requires search. Is reasonably secure. 3 keys requires /22/2007 Lecture 1 - Introduction 22

23 DES Encryption modes Electronic Code Book (ECB) Cipher Block Chain (CBC) 2/22/2007 Lecture 1 - Introduction 23

24 Electronic Code Book (ECB) Mode Although DES encrypts 64 bits (a block) at a time, it can encrypt a long message (file) in Electronic Code Book (ECB) mode. Time = 1 Time = 2 Time = N P1 P2 PN K DES Encrypt K DES Encrypt K DES Encrypt C1 C2 CN C1 C2 CN K DES Decrypt K DES Decrypt K DES Decrypt P1 P2 PN If same key is used then identical plaintext blocks map to identical ciphertext. 2/22/2007 Lecture 1 - Introduction 24

25 Cipher Block Chain (CBC) Mode. IV Time = 1 P1 Time = 2 P2 Time = N PN + + CN-1 + K DES Encrypt K DES Encrypt K DES Encrypt C1 C2 CN C1 C2 CN K DES Decrypt K DES Decrypt K DES Decrypt IV + + CN-1 + P1 P2 PN 2/22/2007 Lecture 1 - Introduction 25

26 Let s use the board again, please take notes 2/22/2007 Lecture 1 - Introduction 26

27 Today s Reading 2/22/2007 Lecture 1 - Introduction 27

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