# Lec3 - Symmetric-Key Cryptosystem Sheng Zhong 1...

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1 Symmetric-Key Cryptosystem Sheng Zhong

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2 Cryptosystem: Definition (1) A Cryptosystem is a tuple (M,C, K, G, E, D): M: cleartext (message) space C: ciphertext space K: key space G: key generating algorithm E: encryption algorithm D: decryption algorithm
3 Cryptosystem: Definition (2) G: generate a pair of encryption/decryption keys for a given length must be efficient (polynomial-time) must be “sufficiently random” (so that it is hard to guess) E(ke, m) & D(kd, m): must be efficient We must have: D(kd,E(ke,m))=m When ke=kd, we have a symmetric-key cryptosystem .

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4 Kerchoff’s Principle Knowledge of the algorithm and key size as well as the availability of known plaintext, are standard assumptions in modern cryptoanalysis. Since an adversary may obtain this information eventually, it is preferable not to rely on its secrecy when assessing cryptographic strength.
5 Standard of a Good Cryptosystem G, E, and D should be completely public. E distributes meaningful messages fairly uniformly over the ciphertext space. Without the decryption key, there is no efficient algorithm that can decrypt ciphertexts. In many contexts, more requirements are necessary.

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6 Block Cipher The message is broken into blocks. We can use the block cipher (a type of symmetric-key cryptosystem) to encrypt a block. Tomorrow morning I will go to New York. Block Cipher key
7 Data Encryption Standard (DES) A popular block cipher. Adopted in 1977 by the National Bureau of Standards (now the National Institute of Standards and Technology) M=C= {64-bit strings} K= {56-bit strings}. E is almost identical to D.

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8 DES Encryption Algorithm Generate 16 round keys from the key Each round key is 48 bits. Apply the Initial permutation (IP) to message Apply 16 rounds of operations Apply the final permutation the inverse of IP
9 Initial and Final Permutations Defined by a fixed table. Example: Final Permutation 40 8 48 16 56 24 64 32 39 7 47 15 55 23 63 31 38 6 46 14 54 22 62 30 37 5 45 13 53 21 61 29 36 4 44 12 52 20 60 28 35 3 43 11 51 19 59 27 34 2 42 10 50 18 58 26 33 1 41 9 49 17 57 25

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10 Each Round of Operation Suppose Output of previous round: (L(i-1), R(i-1)). Output of this round: (L(i), R(i)) Then L(i) = R(i-1) R(i) = L(i-1) P(S( E(R(i-1)) K(i) ))
11 E: Expansion Table Expands the 32-bit data to 48 bits 32 1 2 3 4 5 4 5 6 7 8 9 8 9 10 11 12 13 12 13 14 15 16 17 16 17 18 19 20 21 20 21 22 23 24 25 24 25 26 27 28 29 28 29 30 31 32 1

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Lec3 - Symmetric-Key Cryptosystem Sheng Zhong 1...

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