s-bc - BLOCK CIPHERS 1 / 44 Permutations and Inverses A...

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Unformatted text preview: BLOCK CIPHERS 1 / 44 Permutations and Inverses A function f : { , 1 } { , 1 } is a permutation if there is an inverse function f 1 : { , 1 } { , 1 } satisfying x { , 1 } : f 1 ( f ( x )) = x This means f must be one-to-one and onto, meaning for every y { , 1 } there is a unique x { , 1 } such that f ( x ) = y . 2 / 44 Permutations and Inverses x 00 01 10 11 f ( x ) 01 11 00 10 A permutation x 00 01 10 11 f ( x ) 01 11 11 10 Not a permutation 3 / 44 Permutations and Inverses x 00 01 10 11 f ( x ) 01 11 00 10 A permutation x 00 01 10 11 f 1 ( x ) 10 00 11 01 Its inverse 4 / 44 Block Ciphers Let E : { , 1 } k { , 1 } { , 1 } be a function taking a key K and input x to return output E ( K , x ) . For each key K we let E K : { , 1 } { , 1 } be the function defined by E K ( x ) = E ( K , x ) . We say that E is a block cipher if E K : { , 1 } { , 1 } is a permutation for every K , meaning has an inverse E 1 K , E , E 1 are efficiently computable, where E 1 ( K , x ) = E 1 K ( x ) . 5 / 44 Example The table entry corresponding to the key in row K and input in column x is E K ( x ). 00 01 10 11 00 00 01 10 11 01 01 00 11 10 10 10 11 00 01 11 11 10 01 00 In this case, the inverse cipher E 1 is given by the same table: the table entry corresponding to the key in row K and output in column y is E 1 K ( y ). 6 / 44 Block Ciphers: Example Let = k and define E : { , 1 } k { , 1 } { , 1 } by E K ( x ) = E ( K , x ) = K x Then E K has inverse E 1 K where E 1 K ( y ) = K y Why? Because E 1 K ( E K ( x )) = E 1 K ( K x ) = K K x = x The inverse of block cipher E is the block cipher E 1 defined by E 1 ( K , y ) = E 1 K ( y ) = K y 7 / 44 Block cipher usage K $ { , 1 } k K (magically) given to parties S, R, but not to A. S,R use E K Algorithm E is public! Think of E K as encryption under key K . Leads to security requirements like: Hard to get K from y 1 , y 2 , . . . Hard to get x i from y i 8 / 44 DES History 1972 NBS (now NIST) asked for a block cipher for standardization 1974 IBM designs Lucifer Lucifer eventually evolved into DES. Widely adopted as a standard including by ANSI and American Bankers association Used in ATM machines Replaced (by AES) only a few years ago 9 / 44 DES parameters Key Length k = 56 Block length = 64 So, DES: { , 1 } 56 { , 1 } 64 { , 1 } 64 DES 1 : { , 1 } 56 { , 1 } 64 { , 1 } 64 10 / 44 DES Construction function DES K ( M ) // | K | = 56 and | M | = 64 ( K 1 , . . . , K 16 ) KeySchedule ( K ) // | K i | = 48 for 1 i 16 M IP ( M ) Parse M as L bardbl R // | L | = | R | = 32 for i = 1 to 16 do L i R i 1 ; R i f ( K i , R i 1 ) L i 1 C IP 1 ( L 16 bardbl R 16 ) return C Round i: Invertible given K i : 11 / 44 DES Construction function DES...
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This note was uploaded on 08/31/2011 for the course CSE 207 taught by Professor Daniele during the Winter '08 term at UCSD.

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s-bc - BLOCK CIPHERS 1 / 44 Permutations and Inverses A...

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