CS283 Lecture 2 - Part 1 - Stream Ciphers - 20090915

# CS283 Lecture 2 - Part 1 - Stream Ciphers - 20090915 -...

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ecture 2 art 1 - tream Ciphers Lecture 2 Part 1 Stream Ciphers GWU CS 172/283 Autumn 2009

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Math Break - Binary Arithmetic in Modern Cryptography GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 2
Math Break - Mod 2 Arithmetic odern cryptography is based on digital (binary) logic Modern cryptography is based on digital (binary) logic • Everything is represented by two symbols: “0” and “1”. • The basic (mod (2)) bit operations are – Addition (mod 2): 1 + 1 = 0 0+ 0 = 0 1 + 0 = 1 0 + 1 =1 – Multiplication (mod 2): 1*1=1 0*0 = 0 1*0 = 0 0*1 = 0 GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 3

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Math Break - Logic Equivalents Binary Addition mod(2) is equivalent to the logical Excusive OR operation p q p q FFF TFT F T T TTF Binary Multiplication mod(2) is equivalent to logical AND Some systems also use Inclusive OR operation – 1 OR 1 = 1 OR 0 = 0 OR 1 = 1. GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 4 – 0 OR 0 = 0.
Math Break - Shift Registers hift register starting position (22 symbols (bits) wide) 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 Shift register starting position (22 symbols (bits) wide) A Right Circular Shift ( ) by 1 Symbol (bit) gives 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 A Left Circular Shift ( ) by 1 Symbol (bit) gives 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 5

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efinition: Synchronous Stream Cipher Definition: Synchronous Stream Cipher P : plaintext C : ciphertext K : keyspace o far this is the same as what we have with a block cipher) (so far this is the same as what we have with a block cipher) L : keystream alphabet g: keystream generator k 1 ,k 2 ,… = g(K) where K K , and k i L e k i : P C d k i : C P d (e (x)) = x GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 6 k i k i
efinition: Synchronous Stream Cipher Definition: Synchronous Stream Cipher (From Bishop (10.2 new text)) Let E be an encipherment algorithm, and let E k (b) be the encipherment of message b with key k. Let a message m = b 1 b 2 …. , where each b i is of a fixed length and let k = k 1 k 2 …. Then a stream cipher is a cipher for which E k (m) = E k1 (b 1 )E k2 (b 2 )…… If the key stream k of a stream cipher repeats itself, y pp , then such a cipher is defined as a periodic cipher GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 7

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Stream Ciphers • The cleartext or ciphertext message is processed by the cipher algorithm as a stream of symbols. ey stream ot a single key) encrypts and A key stream (not a single key) encrypts and decrypts the stream of symbols = e y 1 y 2 e k 1 (x 1 )e k 2 (x 2 )… GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 8
Periodic Stream Cipher Characteristics • Binary addition as XOR which is easy to implement in hardware. Encryption and decryption are the same operations: modulo 2 addition on 1 bit (XOR) GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 9

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Synchronous Stream Cipher • A stream cipher is Synchronous when the keystream is generated by a key generator, g, that is independent of the plaintext (K) =>k g(K) > k 1 ,k 2 ,… GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 10
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CS283 Lecture 2 - Part 1 - Stream Ciphers - 20090915 -...

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