Lecture3

Lecture3 - Lecture 3 Block Ciphers and Modes of Operation...

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1 Lecture 3 Block Ciphers and Modes of Operation CNT 5412 Network Security
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Block Cipher • A block cipher E π ( ) is a (parametrized) deterministic function mapping n -bit plaintext blocks to n -bit ciphertext blocks. The value n is called the blocklength . – It is essentially a simple substitution cipher with character set = {0, 1} n . – Example for a 64 bit block: M i C i 01011100 … 10101……. (64 bits) (64 bits) Are there any restrictions on this function for it to be a cipher?
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3 Counting the number of functions Consider a mapping f: N N, N a finite set Let |N| be the size of the set N. Then there are |N| |N| such functions If one considers only 1-1 functions, (injective), then there are |N|! such functions If |N| is 2 64 then there are 2 64 ! one-one (injective) functions. Note: Since N is a finite set, an injective function over N to itself is also bijective
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4 Specifying the functions • Specifying an arbitrary function on 64-bit blocks (or even just an arbitrary bijective function) takes too many bits. – For an arbitrary function of k bits, it takes k2 k bits to specify it directly. For 64 bit blocks, this is 64·2 64 or 2 70 . – Even specifying a 1-1 function of k bits takes about the same number of bits. (text claims one can do it in 2 69 bits) • Note that we can use Stirling’s approximation to estimate n! if needed: n e n n n ≈ π 2 !
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5 The Key to the Cipher • The parameter key is a k -bit binary string. – It may be that the set of all keys, the keyspace K, is a proper subset of all k -bit binary strings. In that case, we say that the effective key size, or security parameter , provided by the cipher is log 2 |K| • The keyed block cipher E κ ( ) is a bijection, and has a unique inverse: the decryption function D ( ). – Alternative notation: K{ } and K -1 { }
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6 Using simple transformations on block subcomponents: substitution • Substitution: changing each input subblock to some output subblock. • Example 8 bit block: xor with 11101011 = y” Let an input block be m = 01100100 Then, the output of the “substitution” is m y = 10001111 = c Note: is this mapping 1-1 onto?
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7 Using simple transformations on block subcomponents: permutation • A permutation in this context is simply a shuffling of the bits of the subblock. • Example 8-bit block
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Lecture3 - Lecture 3 Block Ciphers and Modes of Operation...

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