CS283 Lecture 2 - Part 1 - Stream Ciphers - 200909155

# CS283 Lecture 2 - Part 1 - Stream Ciphers - 200909155 -...

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GWU CS 172/283 Autumn 2009 Lecture 2 – Part 1 - Stream Ciphers

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GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 2 Math Break - Binary Arithmetic in Modern Cryptography
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 3 Math Break - Mod 2 Arithmetic 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

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GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 4 Math Break - Logic Equivalents Binary Addition mod(2) is equivalent to the logical Excusive OR operation 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. 0 OR 0 = 0. p q p q F F F T F T F T T T T F
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 5 Math Break - Shift Registers 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 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) 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 A Right Circular Shift ( ) by 1 Symbol (bit) gives

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GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 6 Definition: Synchronous Stream Cipher P : plaintext C : ciphertext K : keyspace (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 k i (e k i (x)) = x
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 7 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, then such a cipher is defined as a periodic cipher

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GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 8 Stream Ciphers The cleartext or ciphertext message is processed by the cipher algorithm as a stream of symbols. A key stream (not a single key) encrypts and decrypts the stream of symbols 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 9 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)

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GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 10 Synchronous Stream Cipher A stream cipher is Synchronous when the keystream is generated by a key generator, g, that is independent of the plaintext g(K) => k 1 ,k 2 ,…
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 02 – Part 1 - Rev 20090915 11 Asynchronous Stream Cipher (from Wikipedia) Asynchronous stream cipher patented in 1946, has the advantage that the receiver will automatically synchronize with the keystream generator after receiving N

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