1. University of Malawi, Chancellor College
Cryptography
Hyunsung Kim, PhD
University of Malawi, Chancellor College
Kyungil University
February, 2016

2. Contents 10. Modern Stream Ciphers 10.1 RC4
10.2 Self-Synchronizing Stream Ciphers
10.3 One-Time Pads
10.4 A5/1

3. Modern Stream Ciphers
They encrypt individual characters (usually binary digits) of a plaintext message one at a time
Stream ciphers are generally faster than block ciphers
Stream ciphers may be advantageous in situations where transmission errors are highly probable because they have limited or no error propagation
Cipher algorithms
RC4
Self synchronizing stream ciphers
One time pads A5

4. Modern Stream Ciphers Stream Cipher Structure state (data) Key
Randomness of stream key completely destroys statistically properties in message
Must never reuse stream key. Otherwise can recover messages
state (data)
Key
next state
function
output
function
KSi
Plaintexti
Ciphertexti

5. Modern Stream Ciphers Plaintext is a stream of bytes : P1, P2, P3, …
Use a key K as the seed to generate a sequence of pseudorandom bytes (keystream) : KS1, KS2, KS3, …
Ciphertext is C1, C2, C3, …, where Ci = Pi  KSi
Various stream ciphers differ in the way they generate keystreams
Key
output
function
state
Plaintexti
Ciphertexti
KSi
next state

6. Security
Used between a Wireless Access Point and Wireless Ethernet Cards
Existing security consists of two subsystems
An authentication algorithm called Shared Key Authentication
A data encapsulation technique called Wired Equivalent Privacy (WEP)
Goals
Create the privacy achieved by a wired network
Simulate physical access control by denying access to unauthenticated stations

7. WEP Encapsulation WEP encapsulation summary 802.11 Hdr Data
Encapsulate
Decapsulate
Hdr IV
Data
ICV
WEP encapsulation summary
A master key shared between the end points
Encryption algorithm = RC4
Per-packet encryption key = 24-bit IV concatenated to a master key
WEP allows IV to be reused with any frame
Data integrity provided by CRC-32 of the plaintext date (the “ICV”)
Data and ICV are encrypted under the per-packet encryption key

8. RC4 The most widely used stream cipher Ron Rivest invented in 1987
The RC stands for Ron’s code
Property
Variable key size
Byte oriented stream cipher
Widely used – web Secure Socket Layer (SSL)/TLS, wireless Wired Equivalent Privacy (WEP)
Normally uses 64 bits and 128 bits key sizes
Consists of 2 parts
Key Scheduling Algorithm (KSA)
Pseudo-Random Generation Algorithm

9. RC4 + Block diagram Secret Key RC4 Key Stream Plaintext Ciphertext … …
...
Plaintext …
...
Ciphertext +

10. RC4

11. RC4 State and Key Initialization Choose n, a positive integer (ex) n=8
Let l=(length of plaintext in bits/n)
Key array K[0], K[1], …, K[2n-1] whose entries are n-bit strings
Enter the key into array K[i] and repeat the key as necessary to fill the array
Permutations are stored in an array S[0], S[1], …, S[2n-1] consisting of integers from 0 to 2n-1, where S[0]=0, S[1]=1, …, S[2n-1]=2n-1

12. RC4 Initial State Permutation
It uses the secret key K[i] to scramble the array S[i]
Algorithm
int i, j = 0;
for(i=0; i<256; i++){
j = ( j + S[i] + K[i] ) % 256;
swap(S[i], S[j]); }

13. RC4 State Permutation for Key Stream Generation
Scrambled S[256] array is used to generate l keystreams
Algorithm
i = j = 0; for(r=0; r<l; r++){
i = ( i + 1) % 256; j = ( j + S[i] ) % 256; swap( S[i], S[j] ); keystream[r] = S[ (S[i] + S[j]) % 256 ] }

14. RC4 (example) Choose n=3 Key is 0110011000011012 Plaintext is “hsk”
Plaintext is “hsk”
h => 6816, s => 7316, k => 6B16
Set l=(length of plaintext in bits/n)
l=(3*8)/3) =8

15. RC4 (example) Key is 314157 Plaintext is “hsk”=320715537
State and Key Initialization
n=3
l=8
Key array K[0], K[1], …, K[23-1]
K[0]=3, K[1]=1, K[2]=4, K[3]=1, K[4]=5
and repeat the key as necessary to fill the array
K[5]=3, K[6]=1, K[7]=4
Permutation array S[0], S[1], …, S[23-1]
S[0]=0, S[1]=1, S[2]=2, S[3]=3, S[4]=4 …, S[7=(23-1)]=7

16. RC4(example)
Key is
Plaintext is “hsk”=
K[0]=3,K[1]=1,K[2]=4,K[3]=1,K[4]=5,K[5]=3,K[6]=1,K[7]=4
S[0]=0,S[1]=1,S[2]=2,S[3]=3,S[4]=4 …, S[7]=7
Initial State Permutation int i, j = 0; for(i=0; i<7; i++){ j=(j+S[i]+K[i])%8; swap(S[i], S[j]); } i j
S[0]
S[1]
S[2]
S[3]
S[4]
S[5]
S[6]
S[7] 3 1 5 2 3 3 6
j=(5+S[2]+K[5])%8
j=(3+S[1]+K[3])%8
j=(0+S[0]+K[0])%8 4 7
j=(5+2+3)%8=2
j=(3+1+1)%8=5
j=(0+0+3)%8=3 7 6

17. RC4(example)
Key is
Plaintext is “hsk”=
K[0]=3,K[1]=1,K[2]=4,K[3]=1,K[4]=5,K[5]=3,K[6]=1,K[7]=4
S[0]=3,S[1]=5,S[2]=0,S[3]=1,S[4]=7,S[5]=6,S[6]=4,S[7]=2
State Permutation for Key Stream Generation i=j=0; for(r=0; r<8; r++){ i=(i+1)%8; j=(j+S[i])%8; swap(S[i], S[j]); t=(S[i]+S[j])%8; keystream[r]=S[t] } i j t ks
S[0]
S[1]
S[2]
S[3]
S[4]
S[5]
S[6]
S[7] 1 5 3 1 2 5 5 3 6 5 4 5 7 2 5 4 7 2
j=(0+S[1])%8 6 5 1 6
j=(0+5)%8=5 7 7 4 7
t=(S[1]+S[5])%8 2 5
t=(6+5)%8=3

18. RC4(example) Key is 314157 Plaintext is “hsk”=320715537
K[0]=3,K[1]=1,K[2]=4,K[3]=1,K[4]=5,K[5]=3,K[6]=1,K[7]=4
S[0]=3,S[1]=5,S[2]=0,S[3]=1,S[4]=7,S[5]=6,S[6]=4,S[7]=2
Key is
Plaintext is “hsk”=
Ciphertext Ci = Pi  Keystreami
C0 = P0Keystream0 =
C1 = P1Keystream1
C2 = P2Keystream2 = 00 = 000000 = 000 = 0
C3 = P3Keystream3 = 72 = 111010 = 101 = 5
C4 = P4Keystream4 = 12 = 001010 = 011 = 3
C5 = P5Keystream5 = 56 = 101110 = 011 = 3
C6 = P6Keystream6 = 57 = 101111 = 010 = 2
C7 = P7Keystream7 = 35 = 011101 = 110 = 6 i j t ks
S[0]
S[1]
S[2]
S[3]
S[4]
S[5]
S[6]
S[7] = 1 5 3 1
31 =
011001 = 010
= 2 2 5 5
= 20 =
010000 = 010
= 2 3 6 5 4 5 7 2 5 4 7 2 6 5 1 6 7 7 4 7 2 5

19. RC4 Show Block Diagram for Decryption
Decrypt by using Key with

20. Self-synchronizing Stream Cipher
When you simply XOR the plaintext with the keystream to get the ciphertext, that is called a synchronous stream cipher
Eve might get a hold of a matched plaintext/ciphertext pair and find part of the keystream and somehow find the whole keystream IV IV
Key
Key
Ciphertext
Plaintext
Plaintext

21. Self-synchronizing Stream Cipher
Self-synchronizing stream cipher uses old plaintext to encrypt also
ci = pi  ki  pi-2 if pi-1 = 0
pi-3 if pi-1 = 1
Initially p-1 = p0 = 0 IV IV
Key
Key
Plaintext
Ciphertext
Plaintext
pi-1
pi-1
pi-2
pi-2
pi-3
pi-3

22. Self-synchronizing Stream Cipher
Example
Plaintext : Go
Keystream :
=47 6F16 = IV IV
Key
Ciphertext
Plaintext
pi-1
pi-1
pi-2 if pi-1 = 0
pi-3 if pi-1 = 1
pi-2
pi-2
pi-3
pi-3

23. One-time Pads
Fix the vulnerability of the mono-alphabetical substitution cipher by encrypting letters in different locations differently
Key is a random string that is at least as long as the plaintext
Encryption is similar to shift cipher
Invented by Vernam in the 1920s
Requires the following to be added to a message
A truly random number string
As long as the message
Pad is used once and destroyed

24. One-time Pads

25. One-time Pads Let Zm={0,1,…,m-1} be the alphabet
Plaintext P = (p1 p2 … pn)
Key K = (k1 k2 … kn)
Ciphertext C = (c1 c2 … cn)
Encryption
C = (p1k1 p2k2 … pnkn) mod m
Decryption
P = (c1k1 c2k2 … cnkn) mod m

26. A5/1 Used in Global System for Mobil Communications (GSM)
Example of a cipher manufacturers tried to keep secret, it was leaked and also reversed engineered within 5 years
A5/1 produces 228 bits to XOR with the frame
One 228 bit frame is sent every 4.6 milliseconds: 114 bits for the communication in each direction
Initialized using a 64-bit key combined with a publicly-known 22-bit frame number
A5/1 is based around a combination of three LFSRs with irregular clocking

27. A5/1 Block Diagram x19 + x5 + x2 + x + 1 (clock bit 8 )

28. A5/1 Initialization Registers set to all 0’s
Incorporate the key and frame number:
For 64 cycles, the key is mixed in by XORing the ith key bit with the least significant bit of each register
For 22 cycles, the 22 bit frame value is mixed in – same as with key value
Normal clocking used
100 cycles are run using the majority clocking, the output is discarded
End result is the initial state