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Slide 1 - Symmetric Key Crypto Part 1  Cryptography 1
Slide 2 - Symmetric Key Crypto Stream cipher --- like a one-time pad Key is relatively short Key is stretched into a long keystream Keystream is then used like a one-time pad Block cipher --- based on codebook concept Block cipher key determines a codebook Each key yields a different codebook Employ both “confusion” and “diffusion” Part 1  Cryptography 2
Slide 3 - Stream Ciphers Part 1  Cryptography 3
Slide 4 - Stream Ciphers Not as popular today as block ciphers We’ll discuss two examples A5/1 Based on shift registers Used in GSM mobile phone system RC4 Based on a changing lookup table Used many places Part 1  Cryptography 4
Slide 5 - A5/1 A5/1 consists of 3 shift registers X: 19 bits (x0,x1,x2, …,x18) Y: 22 bits (y0,y1,y2, …,y21) Z: 23 bits (z0,z1,z2, …,z22) Part 1  Cryptography 5
Slide 6 - A5/1 At each step: m = maj(x8, y10, z10) Examples: maj(0,1,0) = 0 and maj(1,1,0) = 1 If x8 = m then X steps t = x18  x17  x16  x13 xi = xi1 for i = 18,17,…,1 and x0 = t If y10 = m then Y steps t = y21  y20 yi = yi1 for i = 21,20,…,1 and y0 = t If z10 = m then Z steps t = z22  z21  z20  z7 zi = zi1 for i = 22,21,…,1 and z0 = t Keystream bit is x18  y21  z22 Part 1  Cryptography 6
Slide 7 - A5/1 Each value is a single bit Key is used as initial fill of registers Each register steps or not, based on (x8, y10, z10) Keystream bit is XOR of right bits of registers Part 1  Cryptography 7 X Y Z    
Slide 8 - A5/1 In this example, m = maj(x8, y10, z10) = maj(1,0,1) = 1 Register X steps, Y does not step, and Z steps Keystream bit is XOR of right bits of registers Here, keystream bit will be 0  1  0 = 1 Part 1  Cryptography 8 X Y Z    
Slide 9 - Shift Register Crypto Shift register-based crypto is efficient in hardware Harder to implement in software In the past, very popular Today, more is done in software due to faster processors Shift register crypto still used some Part 1  Cryptography 9
Slide 10 - RC4 A self-modifying lookup table Table always contains some permutation of 0,1,…,255 Initialize the permutation using key At each step, RC4 Swaps elements in current lookup table Selects a keystream byte from table Each step of RC4 produces a byte Efficient in software Each step of A5/1 produces only a bit Efficient in hardware Part 1  Cryptography 10
Slide 11 - RC4 Initialization S[] is permutation of 0,1,…,255 key[] contains N bytes of key for i = 0 to 255 S[i] = i K[i] = key[i (mod N)] next i j = 0 for i = 0 to 255 j = (j + S[i] + K[i]) mod 256 swap(S[i], S[j]) next j i = j = 0 Part 1  Cryptography 11
Slide 12 - RC4 Keystream For each keystream byte, swap table elements and select byte i = (i + 1) mod 256 j = (j + S[i]) mod 256 swap(S[i], S[j]) t = (S[i] + S[j]) mod 256 keystreamByte = S[t] Use keystream bytes like a one-time pad Note: first 256 bytes must be discarded Otherwise attacker can recover key Part 1  Cryptography 12
Slide 13 - Stream Ciphers Stream ciphers were big in the past Efficient in hardware Speed needed to keep up with voice, etc. Today, processors are fast, so software-based crypto is fast enough Future of stream ciphers? Shamir: “the death of stream ciphers” May be exaggerated… Part 1  Cryptography 13