slides04 - Outline CPSC/PMAT 418 Introduction to...

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CPSC/PMAT 418 Introduction to Cryptography Data Encryption Standard, Advanced Encryption Standard Renate Scheidler Department of Mathematics & Statistics Department of Computer Science University of Calgary (Original slides by Mike Jacobson With modifications by Mark Bauer and Renate Scheidler) Week 4 Renate Scheidler (University of Calgary) CPSC/PMAT 418 Week 4 1 / 23 Outline 1 The Data Encryption Standard Overview of DES Multiple DES Encryption 2 History Post-DES 3 Arithmetic on Bytes and 4-Byte Vectors (used in AES) Renate Scheidler (University of Calgary) CPSC/PMAT 418 Week 4 2 / 23 The Data Encryption Standard Overview of DES DES Specifications DES is a block cipher that encrypts 64-bit plaintext blocks to 64-bit ciphertext blocks using 64-bit keys. Note that 8 of the key bits are parity bits, resulting in 56 actual bits of the key. So M = C = { 0 , 1 } 64 and K = { 0 , 1 } 56 . Algorithm: DES Key ( M ) = IP - 1 ( S 16 ( S 15 ( . . . ( S 2 ( S 1 ( IP ( M )))) . . . ))) Consult the FIPS publications and the various DES documents on the “handouts” page for details. Renate Scheidler (University of Calgary) CPSC/PMAT 418 Week 4 3 / 23 The Data Encryption Standard Overview of DES DES Overview 1 The 64 plaintext bits are permuted in a fixed order (transposition cipher). 2 The block is divided into two 32-bit words L 0 and R 0 (for “left” and “right”). 3 The block undergoes 16 substitution rounds . In each round i , the left word L i remains unchanged and the right word R i transformed using XOR and a substitution function f that incorporates a portion of key bits (the round key ) according to a key schedule . Afterwards the two words are swapped (simple transposition). Symbolically: L i = R i - 1 R i = L i - 1 f ( R i - 1 , K i ) i = 1 , 2 . . . , 16 where K i is the round key for round i . 4 In the last round, the two words are not swapped. 5 The original permutation is reversed. Renate Scheidler (University of Calgary) CPSC/PMAT 418 Week 4 4 / 23
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The Data Encryption Standard Overview of DES Diagram of DES INITIAL PERMUTATION f + L 0 L = R 1 0 + R = L 1 0 0 1 f(R , K ) f + L = R 2 1 + R = L 2 1 1 2 f(R , K ) 15 L = R 14 f + + 16 15 R = L 15 16 f(R , K ) L = R 16 15 INVERSE INITIAL PERMUTATION OUTPUT INPUT + R = L f(R , K ) 15 14 14 15 f + K 16 K K K n 2 1 R 0 Renate Scheidler (University of Calgary) CPSC/PMAT 418 Week 4 5 / 23 The Data Encryption Standard Overview of DES DES Decryption Decryption of DES is simply running the DES algorithm on C with the reverse key schedule ( K 16 , K 15 , . . . , K 1 ). Note The invertibility of DES is independent of the function f . Regardless of what function is used for f , decryption works exactly as described above. Works largely because the individual parts of DES are involutions functions that are their own inverses ( g ( g ( x )) = x ) Renate Scheidler (University of Calgary) CPSC/PMAT 418 Week 4 6 / 23 The Data Encryption Standard Overview of DES DES: Assessment DES was a great cipher at the time: highly efficient (for the time) lends itself very well to hardware implementation same encryption and decryption algorithm (only one chip needed for encryption and decryption) withstood all known attacks Renate Scheidler (University of Calgary) CPSC/PMAT 418 Week 4 7 / 23
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