1. 8.1 Chapter 8 Encipherment Using Modern Symmetric-Key Ciphers Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2. 8.2 Objectives ❏ To show how modern standard ciphers, such as DES or AES, can be used to encipher long messages. ❏ To discuss five modes of operation designed to be used with modern block ciphers. ❏ To define which mode of operation creates stream ciphers out of the underlying block ciphers. ❏ To discuss the security issues and the error propagation of different modes of operation. ❏ To discuss two stream ciphers used for real-time processing of data.

3. 8.3 8.1 USE OF MODERN BLOCK CIPHERS Symmetric-key encipherment can be done using modern block ciphers. DES encrypts and decrypts a block of 64 bits; AES encrypts and decrypts a block of 128 bits; In real life applications, the text to be enciphered is of variable size and normally much larger than 64 or 128 bits. Modes of operation have been devised to encipher text of any size employing either DES or AES.

4. 8.4 Figure 8.1 Modes of operation 8.1 USE OF MODERN BLOCK CIPHERS

5. 8.5 The simplest mode of operation is called the electronic codebook ( ECB ) mode. The same key is used to encrypt and decrypt each block. 8.1.1 Electronic Codebook (ECB) Mode Figure 8.2 Electronic codebook (ECB) mode

6. 8.6 It can be proved that each plaintext block at Alice’s site is exactly recovered at Bob’s site. Because encryption and decryption are inverses of each other, Example 8.1 This mode is called electronic codebook because one can precompile 2 K codebooks (one for each key) in which each codebook has 2 n entries in two columns. Each entry can list the plaintext and the corresponding ciphertext blocks. However, if K and n are large, the codebook would be far too large to precompile and maintain. Example 8.2 8.1.1 Electronic Codebook (ECB) Mode

7. 8.7 Following are security issues in ECB mode : 1.Patterns at the block level are preserved. For example, equal blocks in the plaintext become equal blocks in the ciphertext. 2.The block independency creates opportunities for Eve to exchange some ciphertext blocks without knowing the key. For example, if Eve knows that block 8 always convey some specific information, she can replace this block with the corresponding block in the previously intercepted message. Security Issues 8.1.1 Electronic Codebook (ECB) Mode

8. 8.8 Assume that Eve works in a company a few hours per month (her monthly payment is very low). She knows that the company uses several blocks of information for each employee in which the seventh block is the amount of money to be deposited in the employee’s account. Eve can intercept the ciphertext sent to the bank at the end of the month, replace the block with the information about her payment with a copy of the block with the information about the payment of a full-time colleague. Each month Eve can receive more money than she deserves. Example 8.3 8.1.1 Electronic Codebook (ECB) Mode

9. 8.9 A single bit error in transmission can create errors in several (normally half of the bits or all of the bits) in the corresponding block. However, the error does not have any effect on the other blocks. 8.1.1 Electronic Codebook (ECB) Mode Error Propagation

10. 8.10 A technique called ciphertext stealing ( CTS ) can make it possible to use ECB mode without padding. In this technique the last two plaintext blocks, P N−1 and P N, are encrypted differently and out of order, as shown below, assuming that P N−1 has n bits and P N has m bits, where m ≤ n. 8.1.1 Electronic Codebook (ECB) Mode Ciphertext Stealing The head m function selects the leftmost m bits; The tail n-m function selects the rightmost n-m bits.

11. 8.11 The ECB mode of operation is not recommended for encryption of messages of more than one block to be transferred through an insecure channel. Usefulness of the independency of ciphertext block: 1. The area where records need to be encrypted before they are stored in a database or decrypted before they are retrieved, because the order of encryption and decryption of blocks is not important in this mode. 2. We can use parallel processing if we need to create, for example, a very huge encrypted database. 8.1.1 Electronic Codebook (ECB) Mode Application

12. 8.12 In CBC mode, each plaintext block is exclusive-ored with the previous ciphertext block before being encrypted. 8.1.2 Cipher Block Chaining(CBC) Mode Figure 8.3 Cipher block chaining (CBC) mode

13. 8.13 8.1.2 Cipher Block Chaining(CBC) Mode The relation between plaintext and ciphertext blocks is shown below: Example 8.4 It can be proved that each plaintext block at Alice’s site is recovered exactly at Bob’s site. Because encryption and decryption are inverses of each other,

14. 8.14 The initialization vector ( IV ) should be known by the sender and the receiver. Although keeping the IV secret is not necessary, the integrity of the vector plays an important role in the security of CBC mode; IV should be kept safe from change. Several methods have been recommended for using IV : A pseudorandom number can be selected by the sender and transmitted through secure channel (e.g., using ECB mode). A fixed value can be agreed upon IV by Alice and Bob when the secret key is established. 8.1.2 Cipher Block Chaining(CBC) Mode Initialization Vector (IV)

15. 8.15 Following are two of the security issues in CBC mode : 1.Equal plaintext blocks belonging to the same message are enciphered into different ciphertext blocks. However, if two messages are equal, their encipherment is the same if they use the same IV. For this reason, some people recommend the use of a timestamp as an IV. 2.Eve can add some ciphertext blocks to the end of the ciphertext stream. 8.1.2 Cipher Block Chaining(CBC) Mode Security Issues

16. 8.16 In CBC mode, a single bit error in ciphertext block C j during transmission may create error in most bits in plaintext block P j during decryption. However, this single error toggles only one bit in the plaintext block P j+1 (the bit in the same location). Plaintext blocks P j+2 to P N are not affected by this single bit error. A single bit error in ciphertext is self-recovered. 8.1.2 Cipher Block Chaining(CBC) Mode Error Propagation

17. 8.17 8.1.2 Cipher Block Chaining(CBC) Mode Algorithm

18. 8.18 The ciphertext stealing technique described for ECB mode can also be applied to CBC mode, as shown below. The head function is the same as described in ECB mode; the pad function inserts 0’s. 8.1.2 Cipher Block Chaining(CBC) Mode Ciphertext Stealing

19. 8.19 The CBC mode of operation can be used to encipher messages. However, because of chaining mechanism, parallel processing is not possible. CBC mode is not used to encrypt and decrypt random-access files records because encryption and decryption require access to the previous records. CBC mode is also used for authentication (Chapter 11). 8.1.2 Cipher Block Chaining(CBC) Mode Application

20. 8.20 In some situations, we need to use DES or AES as secure ciphers, but the plaintext or ciphertext block sizes are to be smaller. In this mode the size of the block used in DES or AES is n, but the size of the plaintext or ciphertext block is r, where r≤ n. 8.1.3 Cipher Feedback (CFB) Mode The idea is to use DES or AES, not for encrypting the plaintext or decrypting the ciphertext, but for encrypting or decrypting the contents of a shift register, S, of size n.

21. 8.21 Encryption is done by XORing an r- bit plaintext block with r bits of S. Decryption is done by XORing an r- bit ciphertext block with r bits of S. For each block, the shift register S i is made by shifting S i-1 r bits to the left and filling the rightmost r bits with C i-1. S i is then encrypted to T i. Only the rightmost r bits of T i are XORed with P i to make C i. 8.1.3 Cipher Feedback (CFB) Mode

22. 8.22 8.1.3 Cipher Feedback (CFB) Mode Figure 8.4 Encryption in cipher feedback (CFB) mode

23. 8.23 The relation between plaintext and ciphertext blocks is shown below: In CFB mode, encipherment and decipherment use the encryption function of the underlying block cipher. 8.1.3 Cipher Feedback (CFB) Mode

24. 8.24 CFB as a Stream Cipher Figure 8.5 Cipher feedback (CFB) mode as a stream cipher 8.1.3 Cipher Feedback (CFB) Mode

25. 8.25 8.1.3 Cipher Feedback (CFB) Mode

26. 8.26 There are three security issues in CFB mode : 1.Just like CBC, the pattern at block level are not preserved. 2.More than one message can be encrypted with the same key, but the value IV should be changed for each message. 3.Eve can add some ciphertext block to the end of the ciphertext stream. Security Issues 8.1.3 Cipher Feedback (CFB) Mode

27. 8.27 In CFB mode, a single bit error in ciphertext block C j during transmission creates a single bit error (at the same position) in plaintext block P j. However, most of the bits in the following plaintext blocks are in error (with 50 percent probability) as long as some bits of C j are still in the register. After the shift register is totally refreshed, the system recovers from the error. Error Propagation 8.1.3 Cipher Feedback (CFB) Mode

28. 8.28 The CFB mode of operation can be used to encipher blocks of small size such as one character or bit at a time. There is no need for padding because the size of the plaintext block is normally fixed (8 for a character or 1 for a bit). Application 8.1.3 Cipher Feedback (CFB) Mode If the blocks in the text and in the underlying cipher are the same size ( n=r ), the encryption/decryption becomes simpler. Special Case

29. 8.29 Output feedback mode ( OFB ) is very similar to CFB mode, with one difference: each bit in the ciphertext is independent of the previous bit or bits. This avoids error propagation. If an error occurs in transmission, it does not affect the bits that follow. 8.1.4 Output Feedback (OFB) Mode

30. 8.30 8.1.4 Output Feedback (OFB) Mode Figure 8.6 Encryption in output feedback (OFB) mode

31. 8.31 OFB as a Stream Cipher Figure 8.7 Output feedback (OFB) mode as a stream cipher 8.1.4 Output Feedback (OFB) Mode

32. 8.32 8.1.4 Output Feedback (OFB) Mode

33. 8.33 There are two security issues in OFB mode : 1.Just like CFB, the pattern at block level are not preserved. 2.Any change in the ciphertext affects the plaintext encrypted at the receiver side. Security Issues 8.1.4 Output Feedback (OFB) Mode Error Propagation A single bit error in ciphertext affects only the corresponding bit in the plaintext. Special Case If the blocks in the text and in the underlying cipher are the same size ( n=r ), the encryption/decryption becomes simpler.

34. 8.34 In the counter (CTR) mode, there is no feedback. The pseudorandomness in the key stream is achieved using a counter. To provide a better randomness, the increment value can depend on the block number to be incremented. 8.1.5 Counter (CTR) Mode

35. 8.35 8.1.5 Counter (CTR) Mode Figure 8.8 Encryption in counter (CTR) mode

36. 8.36 The relation between plaintext and ciphertext blocks is shown below. Like OFB, CTR creates a key stream that is independent from the previous ciphertext block, but CTR does not use feedback. Like ECB, CTR creates n -bit ciphertext blocks that is independent from each other; they depend only on the value of the counter. 8.1.5 Counter (CTR) Mode

37. 8.37 Like ECB, CTR cannot be used for real-time processing, since it need to wait to get a complete n -bit block of data. CTR can be used to encrypt and decrypt random-access files as long as the value of the counter can be related to the record number in the file. 8.1.5 Counter (CTR) Mode

38. 8.38 Figure 8.9 Counter (CTR) mode as a stream cipher 8.1.5 Counter (CTR) Mode CTR as a Stream Cipher

39. 8.39 8.1.5 Counter (CTR) Mode

40. 8.40 A single error in the ciphertext affects only the corresponding bit in the plaintext. Security Issues 8.1.5 Counter (CTR) Mode Error Propagation The security issues for the CTR mode are the same as those for OFB mode.

41. 8.41 Comparison of Different Modes 8.1.5 Counter (CTR) Mode

42. 8.42 8.2 USE OF STREAM CIPHERS Although the five modes of operations enable the use of block ciphers for encipherment of messages or files in large units and small units, sometimes pure stream are needed for enciphering small units of data such as characters or bits. Stream ciphers are more efficient for real-time processing. Several stream ciphers have been used in different protocols during the last few decades. We will discuss here only two : RC4 and A5/1.

43. 8.43 8.2.1 RC4 RC4 is a stream cipher that was designed in 1984 by Ronald Rivest and used in many data communication and networking protocols, including SSL/TLS and the IEEE802.11 wireless LAN standard. RC4 is a byte-oriented stream cipher in which a byte of a plaintext is exclusive-ored with a byte of key to produce a byte of a ciphertext.

44. 8.44 8.2.1 RC4 RC4 is based on the concept of a state. At each moment, a state of 256 bytes is active, from which one of the bytes is randomly selected to serve as the key for encryption. The idea can be shown as an array of bytes : State

45. 8.45 Figure 8.10 The idea of RC4 stream cipher 8.2.1 RC4 The Idea

46. 8.46 Initialization Initialization is done in two steps: 8.2.1 RC4 The first step The second step

47. 8.47 Encryption or Decryption After k has been created, the plaintext byte is encrypted with k to create the ciphertext byte. Decryption is the reverse process. Key Stream Generation The keys in the key stream are generated, one by one. i and j are initialized to 0. 8.2.1 RC4

48. 8.48 Algorithm 8.2.1 RC4

49. 8.49 Algorithm (Continued) 8.2.1 RC4

50. 8.50 To show the randomness of the stream key, we use a secret key with all bytes set to 0. The key stream for 20 values of k is (222, 24, 137, 65, 163, 55, 93, 58, 138, 6, 30, 103, 87, 110, 146, 109, 199, 26, 127, 163). Example 8.5 Repeat Example 8.5, but let the secret key be five bytes of (15, 202, 33, 6, 8). The key stream is (248, 184, 102, 54, 212, 237, 186, 133, 51, 238, 108, 106, 103, 214, 39, 242, 30, 34, 144, 49). Again the randomness in the key stream is obvious. Example 8.6 8.2.1 RC4

51. 8.51 It is believed that the cipher is secure if the key size is at least 128 bits (16 bytes). There are some reported attacks for smallest key sizes (less than 5 bytes), but the protocols that use RC4 today all use key size that make RC4 secure. However, to protect against differential cryptanalysis, it is recommended the different keys be used for different sessions. Security Issues 8.2.1 RC4

52. 8.52 A5/1 (a member of the A5 family of ciphers) is used in the Global System for Mobile Communication ( GSM ), a network for mobile telephone communication. Phone communication in GSM is done as a sequence of 228-bit frames in which each frame lasts 4.6 milliseconds. 8.2.2 A5/1

53. 8.53 8.2.2 A5/1 Figure 8.11 General outline of A5/1

54. 8.54 Key Generator A5/1 uses three LFSR s with 19, 22, and 23 bits. 1-bit output is fed to 228-bit buffer to be used for encryption (or decryption). Figure 8.12 Three LFSR’s in A5/1 8.2.2 A5/1

55. 8.55 Initialization is done for each frame of encryption (or decryption). The initialization uses a 64-bit secret key and 22 bits of corresponding frame number. 2.2. 8.2.2 A5/1 1. First, set all bits in three LFSR s to 0. Initialization

56. 8.56 4. 8.2.2 A5/1 3.3.

57. 8.57 The majority function, Majority(b 1, b 2, b 3 ), has a value before each click of time; the three input bits are called clocking bits : LFSR1[10], LFSR2[11], and LFSR3[11] if the rightmost bit is 0. (Bit positions are counted from the right.) Majority Function 8.2.2 A5/1 Key Stream Bits The key generator creates the key stream one bit at each click of time. Before the key is created the majority function is calculated. Then each LFSR is clocked if its clocking bit matches with the result of the majority function; otherwise, it is not clocked.

58. 8.58 At a point of time the clocking bits are 1, 0, and 1. Which LFSR is clocked (shifted)? Example 8.7 Solution The result of Majority(1, 0, 1) = 1. LFSR1 and LFSR3 are shifted, but LFSR2 is not. 8.2.2 A5/1

59. 8.59 Encryption/Decryption The bit streams created from the key generator are buffered to form a 228-bit key that is exclusive-or ed with the plaintext frame to create the ciphertext frame. Encryption/decryption is done one frame at a time. 8.2.2 A5/1

60. 8.60 Although GSM continues to use A5/1, several attacks on GSM have been recorded. Two have been mentioned. In 2000, Alex Biryukov, Adi Shamir, and David Wagner showed that a real-time attack that finds the key in minutes from small known plaintexts, but it needs a preprocessing stage with 2 48 steps. In 2003, Ekdahl and Johnson published an attack that broke A5/1 in a few minutes using 2 to 5 minutes of plaintext. With some new attack on the horizon, GSM may need to replace or fortify A5/1 in the future. 8.2.2 A5/1 Security Issues

61. 8.61 8.3 OTHER ISSUES Encipherment using symmetric-key block or stream ciphers requires discussion of other issues.

62. 8.62 Alice and Bob need to share a secret key between themselves to securely communicate using a symmetric-key cipher. If there are n entities in the community, n(n − 1)/2 keys are needed. 8.3.1 Key Management Key management is discussed in Chapter 15.

63. 8.63 Different symmetric-key ciphers need keys of different sizes. The selection of the key must be based on a systematic approach to avoid a security leak. The keys need to be chosen randomly. This implies that there is a need for random (or pseudorandom) number generator. 8.3.2 Key Generation Random number generators are discussed in Appendix K.