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The Advanced Encryption Standard ( AES ) Simplified

The Advanced Encryption Standard ( AES ) Simplified. Cryptosystems and Secrecy. With cryptosystems, we desire perfect secrecy : the probability that the contents of some intercepted data corresponds to some plaintext message is unaltered by knowledge of the ciphertext for that message.

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The Advanced Encryption Standard ( AES ) Simplified

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  1. The Advanced Encryption Standard (AES) Simplified

  2. Cryptosystems and Secrecy • With cryptosystems, we desire perfect secrecy: • the probability that the contents of some intercepted data corresponds to some plaintext message is unaltered by knowledge of the ciphertext for that message. • Measuring the strength for cryptosystem by what is known as its work factor: • the amount of time needed to decipher a message without knowledge of the key. • A cryptosystem is considered secure when its workfactor is exponential in the length of the key: 2.

  3. Cryptosystem Design • General goals for designing secure encryption algorithms: • Confusion • Diffusion • A good encryption algorithm would satisfy the following two criteria: • No output bit should be a linear function of the input bits. In other words, the algorithm must induce non-linearity. This ensures confusion. • Avalanche Criteria: the probability of changing a given bit in the output is ½ when any subset of the input bits are complemented

  4. Advanced Encryption Standard (AES) • the US "standard" secret key cryptosystem, replacing DES (Data Encryption Standard, adopted in 1977) • AES is the result of a three year competition. This competition was announced in September 1997 and had entries from 12 different countries • The one submission that eventually won was called "Rijndael" and was invented by two Belgians, Joan Daemen and Vincent Rijmen.

  5. A Brief History of DES • In 1974, IBM proposed "Lucifer", an encryption algorithm that uses 64-bit keys. Two years later, NBS (in consultation with NSA) made a modified version of that algorithm into a standard. • DES takes in 64 bits of data, employs a 56-bit key, and executes 16 cycles of substitution and permutation before outputting 64 bits of encrypted data.

  6. A Brief History of DES

  7. A Brief History of DES • In the summer of 1998, the Electronic Frontier Foundation (EFF) built a DES cracker machine at a cost of $250,000 • It had 1536 chips, worked at a rate of 88 billion keys per second, and was able to break a DES encrypted message in 56 hours • One year later, with the cracker working in tandem with 100,000 PCs over the Internet, a DES encrypted message was cracked in only 22 hours. • One common way to make DES more secure today is to encrypt three times using DES. • triple-DES (3DES). • 3DES is extremely slow, so a better algorithm was needed.

  8. Requirements for AES • AES had to be a private key algorithm. It had to use a shared secret key. • It had to support the following key sizes: • 128 bits ( = 3.4 x 10 keys, equivalent to 2560-bit RSA) • 192 bits ( = 6.2 x 10 keys) • 256 bits ( = 1.1 x 10 keys) • DES uses only 56-bit keys, giving a key space of 7.2 x 10 keys • If you were able to search half the DES key space in 1 second, then on average, it would take 149 trillion years to crack a 128-bit AES key. 38 57 77 16

  9. Requirements for AES • It had to satisfy certain engineering criteria: • performance, efficiency, implementability, and flexibility. • Rijndael can be implemented easily in both hardware and software, • has realizations that require little memory (so the algorithm can be used in smartcards).

  10. Requirements for AES • It had to be a block cipher • an encryption algorithm structured in terms of an internal function and runs that function repeatedly on the input. • Each iteration is called a round; • AES uses 10 rounds.

  11. Requirements for AES • AES is also an instance of a Feistel cipher, a special case of a block cipher. • The input to such a cipher consists of 2t bits. • The input is first divided into 2 parts: • L and R • The cipher then proceeds in rounds. • In the i-th round, Li := Ri-1 Ri := Li-1 XOR f(Ri-1, ki), • where f is some function, and k is some number derived from the key, to be used in round i. 0 0 i i

  12. The AES Cipher • Block length is limited to 128 bit • The key size can be independently specified to 128, 192 or 256 bits

  13. The AES Cipher • Key received as input array of 4 rows and Nk columns • Nk = 4,6, or 8, parameter which depends key size • Input key is expanded into an array of 44/52/60 words of 32 bits each • 4 different words serve as a key for each round k0 k4 k8 k12 …… k1 k5 k9 k13 w0 w1 w2 w42 w43 k2 k6 k10 k14 k3 k7 k11 k15

  14. The AES Cipher • Single 128 bit block as input • Copied to a State array with Nb columns (Nb=4) Input State array Output in0 in4 in8 in12 S00 S01 S02 S03 o0 o4 o8 o12 in1 in5 in9 in13 S10 S11 S12 S13 o1 o5 o9 o13 in2 in6 in10 in14 S20 S21 S22 S23 o2 o6 o10 o14 in3 in7 in11 in15 S30 S31 S32 S33 o3 o7 o11 o15

  15. The AES Cipher • Number of rounds, Nr, depends on key size • Each round is a repetition of functions that perform a transformation over State array • Consists of 4 main functions: one permutation and three substitutions Substitute bytes, Shift rows, Mix columns, Add round key

  16. The AES Cipher • AddRoundKey() – round key is added to the State using XOR operation • MixColumns() – takes all the columns of the State and mixes their data, independently of one another, making use of arithmetic over GF(2^8) • ShiftRows() – processes the State by cyclically shifting the last three rows of the State by different offsets • SubBytes() – uses S-box to perform a byte-by-byte substitution of State

  17. The AES Cipher plaintext Add round key Substitute bytes Substitute bytes Substitute bytes Shift rows Shift rows Shift rows Round 1 Round 9 Mix columns Mix columns Add round key Add Round key Add round key Cipher text W[4,7] W[36,39] W[40,43] key

  18. The AES Cipher Cipher(byte in[4*Nb], byte out[4*Nb], word w[Nb*(Nr+1)]) Begin byte state[4,Nb] state = in AddRoundKey(state, w[0, Nb-1]) for round=1 to Nr-1 SubBytes(state) ShiftRows(state) MixColumns(state) AddRoundKey(state, w[round*Nb, round+1)*Nb-1]) end for SubBytes(state) ShiftRows(state) AddRoundKey(state, w[Nr*Nb, (Nr+1)*Nb-1) Out = state end

  19. The AES Cipher • Only Add round key makes use of the key • Other three functions are used for diffusion and confusion • Final round consists of only three stages

  20. The AES Inverse Cipher ciphertext Add round key Inv. Shift rows Inv. Shift rows Inv. Shift rows Inv. Sub bytes Inv. Sub bytes Inv. Sub bytes Round 1 Round 9 Add round key Add round key Add round key Inv. Mix Columns Inv. Mix columns plaintext W[36,39] W[4,7] W[0,3] key

  21. The AES Inverse Cipher InvCipher(byte in[4*Nb], byte out[4*Nb], word w[Nb*(Nr+1)]) Begin byte state[4,Nb] state = in AddRoundKey(state, w[Nr*Nb, (Nr+1)*Nb-1) for round=1 to Nr-1 InvShiftRows(state) InvSubBytes(state) AddRoundKey(state, w[round*Nb, round+1)*Nb-1]) InvMixColumns(state) end for InvShiftRows(state) InvSubBytes(state) AddRoundKey(state, w[0, Nb-1]) Out = state end

  22. The AES Inverse Cipher • Decryption algorithm uses the expanded key in reverse order • All functions are easily reversible and their inverse form is used in decryption • Decryption algorithm is not identical to the encryption algorithm • Again, final round consists of only three stages

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