1. 1 Chapter 3 Ciphers Mechanism that decides the process of encryption/decryption Stream Cipher: Bit-by-bit encryption / decryption Block Cipher: Block-by-block encryption / decryption

2. 2 Chapter 3 Types of Cipher Fig 3.1 Algorithm Types Stream Ciphers Block Ciphers

3. 3 Chapter 3 Basic operations upon string of 0/1 Coded Word –XOR ( ⊕ ) –Transposition –Logical Operations (A ∩B,…) Block Number –+,-,*,/ –Finite Field (under Modular) –Exponentiation (under Modular) –…

4. 4 Chapter 3 XOR operation ⊕ XOR operation ⊕ : –Encrypted: M ⊕ K= C –Decrypted: C ⊕ K= M –Math. Notation: Encryption: M ⊕ K  C Decryption: C ⊕ K  M MKC 000 011 100 110

5. 5 Chapter 3 Basic of stream cipher Message M comes in bit strings Key bit strings are generated from a key K Encryption: –Cipher C are basically an bit XOR operation between message bit strings and key bit strings (generated from key K) Decryption: –Message M comes from an bit XOR operation between Cipher C strings and key bit strings (generated from key K)

6. 6 Chapter 3 Encrypt/Decrypt with XOR Plain text Sender (A) Networ k Receive r (B) Cipher text …01101 10011… …10100 10011… …01101 Cipher text

7. 7 Chapter 3 How to generate the key bit sequence by a key Pseudo random generator Key A serial of bit sequence LFSR, Linear Feedback shift register + 100 output Concept

8. 8 Chapter 3 Program for LFSR Parameter: –Unsigned long shiftRegister –shiftRegister = input_key Procedure: –Output shiftRegister&0x0000001 ; –shiftRegister = ( (shiftRegister >>2) ^ (shiftRegister >>1) & 0x00000001) >1);

9. 9 Chapter 3 Stream Cipher basic (XOR Blockbit level) F4 0100011000110100 0001010100001111 S; + 0101001100111011 Plain text Cipher text the key In normal format In binary format

10. 10 Chapter 3 Block Cipher Message are chocked into numbers of block Each block are encrypted with block ciphers Block between block are operated with one of the four modes (ECB,CBC,OFB, OCB). Known Block Ciphers: –DES, triple DES,IDEA, RC5, Blowfish, AES

11. 11 Chapter 3 Symmetric Key Cryptography Fig 3.15 Plain text Encrypt with symmetric key Plain text Decrypt with symmetric key Sender (A) Net wor k Receive r (B) Cipher text

12. 12 Chapter 3 Data Encryption Standard (DES) History –1977 published by National Institute of Standard and Technology, USA –Based on IBM Lucifer cipher and NSA Specification: –Uses a 56-bit key (among 64-bit), and map a 64-bit input block into a 64-bit output block. Theory basics: –Input permutation, key introduce bit string (s-box), XOR Comment: –DES is efficient to implement in hardware but relative slow in software. For example, a 500-MIPS CPU can encrypt at 30 Koctets per second.

13. 13 Chapter 3 Conceptual View of DES Fig 3.16 64-bit Plain text 56-bit Key DES 64-bit Cipher text Block 1 64-bit Plain text 56-bit Key DES 64-bit Cipher text Block 2 64-bit Plain text 56-bit Key DES 64-bit Cipher text Block n 

14. 14 Chapter 3 Broad Level Steps in DES Fig 3.19 Initial Permutation (IP) LPTRPT 16 rounds Key Key i Final Permutation (FP) Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Plain text (64 bits) Cipher text (64 bits)

15. 15 Chapter 3 Initial permutation (IP) Input 64-bit after bit position change (IP) produces 64-bit output 585042342618102605244362820124 625446383022146645648403224168 57494133251791595143352719113 615345372921135635547393123157 Means: Output bit 1 from bit 58, bit 2 from bit 50, bit 3 from 42,…

16. 16 Chapter 3 Board level include the master Key 64-bit input Round 1 Round 2 64-bit output Round 16 56-bit key Generate 16 per-round keys Initial Permutation Final Permutation Swap left and right halves 48-bit K 1 48-bit K 2 48-bit K 16

17. 17 Chapter 3 A DES Round

18. 18 Chapter 3 The Mangler Function Two inputs: 32-bit plus 48-bit subkey Output: 32-bit Operations: –Step 1: 32-bit are expanded into 48-bit –Step 2: the expanded 48-bit are XORed with the 48-bit subkey –Step 3: the 48-bit result are divide into 8 blocks with 6 bits. –Step 4: each block are lookup into the S-box to generate the 4 bit –Step 5: the result 32-bit are then permutated to generate the 32 output.

19. 19 Chapter 3 32-bit(RPT) 48-bit(subkey) Expansion permutation XOR 48-bit 48-bit divide into 8 6-bit blocks S-box 1S-box 8S-box 2 32-bit P-Box permutation 32-bit

20. 20 Chapter 3 Expansion permutation 3212345456789 8910111213121314151617 161718192021202122232425 24252627282928293031321 P-box permutation 16720212912281711523265183110 28241432273919133062211425

21. 21 Chapter 3 S-box(1~8) S-box 1 1441312151183106125907 0157414213110612119538 4114813621115129731050 1512824917511314100613 For example: bit 101101, table look up 11 0110 00000001001000110100010101101111 00 01 10 11

22. 22 Chapter 3 How Sub key generate from Key Input : 64 bits Output: 48 bits x 16 (round 1~16) Steps: –1) 64 bits to 56 bits, and the 56 bits is divide into 2 halves, each of 28 bits, called C and D. (through a discard permutation) –2) each of 28 bits are rotated (round 1,2,9,1nd 16 are 1bit, and other are 2-bit) –3) from the 2 halves, among the 56 bits only 48 bits are got through compression permutation

23. 23 Chapter 3 Discard permutation compression permutation 14171124153281562110 23191242681672720132 415231374755304051453348 444939563453464250362932

24. 24 Chapter 3 Mathematics‘ notation on Block cipher Like DES For plain text m, encrypted with key K1, is denoted as: E k1 [m] (m) k1 if encrypt / decrypt operation is obvious. For a cipher text c, decrypted with key K1, is denoted as: D k1 [c] (c) k1 if encrypt / decrypt operation is obvious. i.e., D k1 [E k1 [m] ] = m ((m) k1 ) k1 = m

25. 25 Chapter 3 DES operation mode Operation modes: –Block between block operation –Four modes: ECS (Electronic Code Book) CBC (Cipher Block Chaining) CFB (Cipher Feedback) OFB (Output Feedback)

26. 26 Chapter 3 Encryption in ECB Mode Fig 3.6 Encrypt Plain text block 1 Key Cipher text block 1 Step 1 Encrypt Plain text block 2 Key Cipher text block 2 Step 2 Encrypt Plain text block n Key Cipher text block n Step n

27. 27 Chapter 3 Decryption in ECB Mode Fig 3.7 Decrypt Cipher text block 1 Key Plain text block 1 Step 1 Decrypt Cipher text block 2 Key Plain text block 2 Step 2 Decrypt Cipher text block n Key Plain text block n Step n

28. 28 Chapter 3 ECB Example Fig 3.4 FOUR_AND_FOUR Plain text Encrypt VFa% *yT1x Cipher text (a) The Encryption Process at the sender’s end VFa% *yT1x Cipher text Decrypt FOUR_AND_FOUR Plain text (b) The Decryption Process at the receiver’s end

29. 29 Chapter 3 Encryption in CBC Mode Fig 3.8 Encrypt Plain text block 1 IV Cipher text block 1 Step 1 Encrypt Plain text block 2 Cipher text block 2 Step 2 Encrypt Plain text block n Cipher text block n Step n Key XOR Key XOR

30. 30 Chapter 3 Decryption in CBC Mode Fig 3.9 Decrypt Cipher text block 1 IV Plain text block 1 Step 1 Decrypt Cipher text block 2 Plain text block 2 Step 2 Decrypt Cipher text block n Plain text block n Step n Key XOR Key XOR

31. 31 Chapter 3 Encryption in CFB Mode Fig 3.13 IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits Cipher text j bits IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits Cipher text j bits

32. 32 Chapter 3 Algorithm Modes Fig 3.5 Algorithm Modes Electronic Code Book (ECB) Cipher Block Chaining (CBC) Cipher Feedback (CFB) Output Feedback (OFB) These two modes work on block ciphers. These two modes work on block ciphers acting as stream ciphers.

33. 33 Chapter 3 Encryption in OFB Mode Fig 3.14 IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits Cipher text j bits IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits Cipher text j bits

34. 34 Chapter 3 Modified Versions of DES Double DES: Perform DES twice with two different keys Triple DES with Three Different Keys Triple DES with Two Different Keys

35. 35 Chapter 3 Double DES Encryption Fig 3.36 Original Plain Text Encrypt K1 Cipher Text Encrypt K2 Cipher Text

36. 36 Chapter 3 Double DES Decryption Fig 3.37 Original Plain Text Decrypt K2 Decrypt K1 Cipher Text

37. 37 Chapter 3 Double DES Expressed P Encrypt K1 Temporary result (T) Encrypt K2 C E K1 (P) E K2 (E K1 (P)) T = E K1 (P) C = E K2 (E K1 (P)) Subject to: meet-in-the-middle attack Step 1: store all possible E K1 (P) Step 2: decrypt c with all possible key value D K2 (C) Step 3: find a match value at step 1 and 2.

38. 38 Chapter 3 Triple DES Fig 3.41 Original Plain Text Encrypt K1 Cipher Text 1 Encrypt K2 Cipher Text 2 Encrypt K3 Final Cipher Text

39. 39 Chapter 3 Triple DES with Two Keys Fig 3.42 Original Plain Text Encrypt K1 Cipher Text 1 Decrypt K2 Cipher Text 2 Encrypt K1 Final Cipher Text

40. 40 Chapter 3 RC5 Developed by Ron Rivest Quite fast, flexibility (security vs speed) Almost no memory for execution: –Suitable for PDA, smart card,..

41. 41 Chapter 3 Basic principles Variable lengths –Block size (word bits and 2-word blocks), number of rounds and number of 8-bit bytes (octets) of the key Particular RC5 instance should be assigned, denoted as RC5-w/r/b, e.g., RC5-32/12/16 means 64-bit block, 12 round, and 16x8 bits key

42. 42 Chapter 3 Encryption using RC5 Fig 3.54 First, divide the original plain text into two blocks of equal size. Call them as A and B. Add A and S[0] to produce C. Add B and S[1] to produce D. 1. XOR C and D to produce E. 4. XOR D and F to produce G. 2. Circular-left shift E by D bits. 3. Add E and S[2i] to produce F. 5. Circular-left shift G by F bits. 6. Add G and S[2i + 1] to produce H. Increment i by 1. Check: Is i > r? Stop Yes No Note: First perform all the left-hand side steps, and then come to the right hand side steps, as indicated by the step numbers. Call F as C (i.e. C = F) Call H as D (i.e. D = H)

43. 43 Chapter 3 RC5 Encryption Fig 3.63 A = A + S[0] B = B + S[1] For i = 1 to r A = ((A XOR B) <<< B) + S[2i] B = ((B XOR A) <<< A) + S[2i + 1] Next i

44. 44 Chapter 3 RC5 Decryption Fig 3.64 For i = r to 1 step –1 (i.e. decrement i each time by 1) B = ((B – S[2i + 1]) >>> A) XOR A A = ((A – S[2i]) >>> B) XOR B Next i B = B – S[1] A = A – S[0]

45. 45 Chapter 3 Sub-key creation in RC5 8-bit as a unit First, the key is put to array L, denoted as, L[0], L[1],…, L[b-1] Second, generate the array S, by using two constant P (0xb7e15163)and Q (0x9e3779b9), up to 2 times round plus 1, S[0], S[1],…S[2r+1] Third, Mixing array L and S, to produce the final subkey array S

46. 46 Chapter 3 s[0]=p For i=1 to 2r+1 s[i]=(s[i-1]+Q) mod 2^32 Next i i=j=0 A=B=0 Do 3n times (n =max(2r+1, b)) A=s[i]=(s[i]+A+B)<<<3 B=L[j]=(L[j]+A+B)<<<(A+B) i = (i+1) mod 2(r+1) j= (j+1) mod b end-do Array S generated Mix Array S and L to generate S

47. 47 Chapter 3 Advanced Encryption Standard (AES) 1990s, US want to the next generation cipher, and among many 15 proposals, Rijndael was accepted. Features: –Fast, variable in block size and key size. –Security Application: –Triple DES and AES.

48. 48 Chapter 3