# Modern Symmetric-Key Ciphers

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Modern Symmetric-Key Ciphers
Chapter 8 Encipherment Using Modern Symmetric-Key Ciphers

8-1 USE OF MODERN BLOCK CIPHERS
Symmetric-key encipherment can be done using modern block ciphers. Modes of operation have been devised to encipher text of any size employing either DES or AES.

8-1 Continued Figure 8.1 Modes of operation

8.1.1 Electronic Codebook (ECB) Mode
The simplest mode of operation is called the electronic codebook (ECB) mode. Figure 8.2 Electronic codebook (ECB) mode

Continued Example 8.1 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 8.2 This mode is called electronic codebook because one can precompile 2K codebooks (one for each key) in which each codebook has 2n 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.

Continued Example 8.3 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.

8.1.1 Continued Security Issues
1- Patterns at the block level are preserved 2- The block independency creates opportunities for Eve to exchange some ciphertext blocks without knowing the key. Error Propagation A single bit error in transmission can create errors in several in the corresponding block. However, the error does not have any effect on the other blocks.

8.1.1 Continued Ciphertext Stealing
A technique called ciphertext stealing (CTS) can make it possible to use ECB mode without padding. In this technique the last two plaintext blocks, PN−1 and PN , are encrypted differently and out of order, as shown below, assuming that PN−1 has n bits and PN has m bits, where m ≤ n .

8.1.1 Continued Applications
The ECB mode is not recommended for encryption of messages more than one block. One area where the independency of the ciphertext block is useful is where records need to be encrypted before they are stored in a database or decrypted before they are retrieved….Access to the database can be random. Another advantage of this mode is that we can use parallel processing if we need to create a very huge encrypted database.

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

Continued Figure 8.3 Cipher block chaining (CBC) mode

8.1.2 Continued Initialization Vector (IV)
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, Initialization Vector (IV) The initialization vector (IV) should be known by the sender and the receiver.

8.1.2 Continued Security Issues
Patterns at the block level are not preserved. However, if the first M blocks in two different messages are equal, they are enciphered into equal blocks unless different Ivs are used. Hence, recommend the use of timestamp as an IV. Eve can add some ciphertext blocks to the end of the ciphertext stream. Error Propagation In CBC mode, a single bit error in ciphertext block Cj during transmission may create error in most bits in plaintext block Pj during decryption.

8.1.2 Continued Applications Parallel processing is not possible.
CBC mode is not used to encrypt and decrypt random-access files records because of the need to access the previous records. CBC mode is used for authentication.

8.1.2 Continued Ciphertext Stealing
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.

8.1.3 Cipher Feedback (CFB) Mode
In some situations, we need to use DES or AES as secure ciphers, but the plaintext or ciphertext block sizes are to be smaller. Figure 8.4 Encryption in cipher feedback (CFB) mode

Continued Note In CFB mode, encipherment and decipherment use the encryption function of the underlying block cipher. The relation between plaintext and ciphertext blocks is shown below:

size of the block r, is normally chosen to fit the data unit to be encrypted ( a character for example). The system does not have to wait until It has received a large block of data (64 or 128 bits) before starting the encryption. Disadvantages CFB is less efficient than CBC and ECB because it needs to apply the encryption function for each small block of size r.

8.1.3 Continued CFB as a Stream Cipher
Figure 8.5 Cipher feedback (CFB) mode as a stream cipher

8.1.3 Continued Security Issues The patterns are not preserved.
The IV should be changed for each message Eve can add some ciphertext block to the end of the ciphertext stream. Error Propagation A single bit error in ciphertext block Ci during transmission creates a single bit eror in plaintext block Pi. However most of the bits in the following plaintext blocks are in error. Application This mode can be used to encipher blocks of small size such as characters or bit at a time.

18.1.4 Output Feedback (OFB) Mode
In this mode each bit in the ciphertext is independent of the previous bit or bits. This avoids error propagation. Figure 8.6 Encryption in output feedback (OFB) mode

8.1.4 Continued OFB as a Stream Cipher
Figure 8.7 Output feedback (OFB) mode as a stream cipher

Continued Security Issues The patterns are not preserved. Error Propagation A single bit error in the ciphertext affects only the corresponding bit in the plaintext.

Counter (CTR) Mode In the counter (CTR) mode, there is no feedback. The pseudorandomness in the key stream is achieved using a counter. Figure 8.8 Encryption in counter (CTR) mode

Continued Figure 8.9 Counter (CTR) mode as a stream cipher

8.1.5 Continued Notes CTR creates n-bit blocks that are independent
from each other; they depend only on the value of the counter. CTR, like ECB mode, cannot be used for real- time processing. CTR, like ECB mode, 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.

Continued Comparison of Different Modes

Topics discussed in this section:
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. Topics discussed in this section: 8.2.1 RC A5/1

RC4 Developed by RSA Labs, RC4 is a symmetric, byte-oriented stream cipher with a variable length key size, in which a byte (8 bits) of a plaintext is exclusive-ored with a byte of key to produce a byte of a ciphertext KEY RC4 HAS two main parts: KSA (Key Scheduling Algorithm) PRGA (Pseudo Random Generation Algorithm) ksa PRGA K State RC4 is based on the concept of a state. P C +

Continued Figure The idea of RC4 stream cipher KSA PRGA

RC4 Key Schedule KSA Starts with an array S of numbers: 0..255
􀁺 Use key to truly shuffle S 􀁺 S forms internal state of the cipher 􀁺 Given a key k of length L bytes Scrambling Pseudocode : for i = 0 to 255 do S[i] = i j = 0 j = (j + S[i] + k[i ]) (mod 256) swap (S[i], S[j])

RC4 PRGA and Encryption Encryption involves XORing data bytes with output of the PRGA 􀁺 The PRGA initializes i and j to 0 and then loops over 4 basic operations: increase j, increase j using s[i], swap and output s[i]+s[j] 􀁺PRGA Pseudocode is: i = j = 0 for each message byte Mi i = (i + 1) (mod 256) j = (j + S[i]) (mod 256) swap(S[i], S[j]) t = (S[i] + S[j]) (mod 256) ; Ki = S[t] Encryption : Ci = Mi XOR S[t]

RC4 Encryption Example Lets consider the stream cipher RC4, but instead of the full 256 bytes, we will use 8 x 3-bits. That is, the state vector S is 8 x 3-bits. We will operate on 3-bits of plaintext at a time since S can take the values 0 to 7, which can be represented as 3 bits. Assume we use a 4 x 3-bit key of K = [ ]. And a plaintext P = [ ]

RC4 PRGA and Encryption The first step is to generate the stream.
Initialise the state vector S and temporary vector T. S is initialised so the S[i] = i, and T is initialised so it is the key K (repeated as necessary). S = [ ] T = [ ] Now perform the initial permutation on S. j = 0; for i = 0 to 7 do j = (j + S[i] + T[i]) mod 8 Swap(S[i],S[j]); end For i = 0: j = ( ) mod 8 = 1 Swap(S[0],S[1]); S = [ ]

RC4 PRGA and Encryption For i = 1: j = 3 Swap(S[1],S[3])

RC4 PRGA and Encryption For i = 4: j = 3 Swap(S[4],S[3])
Hence, our initial permutation of S = [ ];

RC4 PRGA and Encryption Now we generate 3-bits at a time, k, that we XOR with each 3-bits of plaintext to produce the ciphertext. The 3-bits k is generated by: i, j = 0; while (true) { i = (i + 1) mod 8; j = (j + S[i]) mod 8; Swap (S[i], S[j]); t = (S[i] + S[j]) mod 8; k = S[t]; } The first iteration: S = [ ] i = (0 + 1) mod 8 = 1 j = (0 + S[1]) mod 8 = 3 Swap(S[1],S[3]) S = [ ] t = (S[1] + S[3]) mod 8 = 7 k = S[7] = 5 Remember, P = [ ]

RC4 PRGA and Encryption Remember, P = [1 2 2 2]
So our first 3-bits of ciphertext is obtained by: k XOR P 5 XOR 1 = 101 XOR 001 = 100 = 4 The second iteration: S = [ ] i = (1 + 1 ) mod 8 = 2 j = (2 + S[2]) mod 8 = 1 Swap(S[2],S[1]) S = [ ] t = (S[2] + S[1]) mod 8 = 3 k = S[3] = 3 Second 3-bits of ciphertext are: 3 XOR 2 = 011 XOR 010 = 001 = 1

RC4 PRGA and Encryption After 4 iterations: To encrypt the plaintext stream P = [ ] with key K = [ ] using our simplified RC4 stream cipher we get C = [ ]. (or in binary: P = , K = and C = ) Simplified

A5/1 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.. Figure General outline of A5/1

8.2.2 Continued Key Generator
A5/1 uses three LFSRs with 19, 22, and 23 bits. Figure Three LFSR’s in A5/1

Continued Example 8.7 At a point of time the clocking bits are 1, 0, and 1. Which LFSR is clocked (shifted)? Solution The result of Majority (1, 0, 1) = 1. LFSR1 and LAFS3 are shifted, but LFSR2 is not.

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

Topics discussed in this section:
8-3 OTHER ISSUES Encipherment using symmetric-key block or stream ciphers requires discussion of other issues. Topics discussed in this section: 8.3.1 Key Management Key Generation

Key management is discussed in Chapter 15.
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. Note Key management is discussed in Chapter 15.

Random number generators are discussed in Appendix K.
Key Generation 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. Note Random number generators are discussed in Appendix K.