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27
Key Expansion Algorithm
27
keyExpansion(byte key[16], word[44]) {
word temp;
for(i = 0 ; i < 4 ; i++) {
w[i] = (key[4*i], key[4*i+1], key[4*i+2], key[4*i+3]);
}
for(i = 4 ; i < 44 ; i++) {
temp = w[i - 1];
if (i mod 4 == 0)
temp = subWord(rotWord(temp)) Rcon[i/4];
w[i] = w[i - 4] temp;
}
}](https://image.slidesharecdn.com/advancedencryptionstandardugreseacrh-200926183433/75/Advanced-encryption-standard-ug-reseacrh-27-2048.jpg)
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Advanced encryption standard ug reseacrh
- 1. Click to editMaster title style 1 Advanced Encryption Standard B y, A k a s h R a n j a n D a s 5 t h S e m e s t e r B - Te c h , C o m p u t e r S c i e n c e A n d Te c h n o l o g y S i d d a g a n g a I n s t i t u t e O f Te c h n o l o g y, Tu m k u r
- 2. Click to editMaster title style 2 Agenda What is Advanced Encryption Standard (AES)? Why AES? Structure Of AES o Basic Structure Of AES o Detailed Structure Of AES o Data Structure of AES Working of AES encryption and Encryption o AES Transformation Functions o AES Key Expansion Real World Software Application. 2
- 3. Click to editMaster title style 3 What is Advanced Encryption Standard (AES)? 3
- 4. Click to editMaster title style 4 Advanced Encryption Standard (AES) 4 • The Advanced Encryption Standard (AES) is a symmetric block cipher chosen by the US government to protect classified information. • AES is implemented in software and hardware throughout the world to encrypt sensitive data. • The National Institute of Standards and Technology (NIST) started development of AES in 1997 when it announced the need for an alternative to the Data Encryption Standard (DES) , which was starting to become vulnerable to brute force attacks.
- 5. Click to editMaster title style 5 Why AES? 5
- 6. Click to editMaster title style 6 Why AES? 6 Data Encryption Standard (DES) Advanced Encryption Standard (AES) • DES can be broken easily as it has known vulnerabilities. • DES can encrypt 64 bits of plaintext. • Known attacks against DES include : Brute-force, Linear crypt-analysis and Differential crypt-analysis. • AES is more secure than the DES cipher and is the de facto world standard. • AES can encrypt 128 bits of plaintext. • No known crypt-analytical attacks against AES but side channel attacks against AES implementations possible. Biclique attack have better complexity than brute-force but still ineffective.
- 7. Click to editMaster title style 7 Structures Of AES 7
- 8. Click to editMaster title style 8 Simple Structure Of AES 8 AES x y 128 128 128/192/256 k x: plain text (128 bits = 16 bytes) k: secret key y: encrypted text (128 bits = 16 bytes) Key lengths #rounds = nr 128 bits 10 192 bits 12 256 bits 14
- 9. Click to editMaster title style 9 Block Diagram of AES Encryption 9 Plain Text x Key Addition Layer Byte Substitution Layer Shift Rows Mix Column Layer Key Addition Layer Round 1 Diffusion Layer Transform 0 Key k Transform 1 k0 k1 Last Round nr Transform nrknr Cipher Text y= AES(x)
- 10. Click to editMaster title style 10 Block Diagram of AES Decryption 10 Plain Text x = AES-1(y) Key Addition Layer Inverse Substitution Layer Inverse Shift Rows Inverse Mix Column Layer Key Addition Layer Round nr Diffusion Layer Transform 0 Key k Transform 1 k0 k1 Round 1 Transform nr knr Cipher Text Key Addition Layer
- 11. Click to editMaster title style 11 Data Structure of AES In0 In4 In8 In12 In1 In5 In9 In13 In2 In6 In10 In14 In3 In7 In11 in15 s0,0 s0,1 s0,2 s0,3 s1,0 s1,1 s1,2 s1,3 s2,0 s2,1 s2,2 s2,3 s3,0 s3,1 s3,2 s3,3 s0,0 s0,1 s0,2 s0,3 s1,0 s1,1 s1,2 s1,3 s2,0 s2,1 s2,2 s2,3 s3,0 s3,1 s3,2 s3,3 O0 O4 O8 O12 O1 O5 O9 O13 O2 O6 O10 O14 O3 O7 O11 O15 Input State Array Output k0 k4 k8 k12 k1 k5 k9 K13 k2 k6 k10 k14 k3 k7 k11 k15 w0 w1 w2 w42 w43 Key Expanded Key
- 12. Click to editMaster title style 12 Working Of AES 12
- 13. Click to editMaster title style 13 AES Round Function for rounds 1, 2, …. nr-1 A0 A2 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 B0 B2 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 C0 C2 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 s s s s s s s s s s s s s s s s k1 Byte Substitution Shift Rows Mix Columns Key Addition
- 14. Click to editMaster title style 14 Byte Substitution Layer 14 • The first layer in each round. • S(Ai) = Bi • Ai : each byte in the state matrix. • Bi : substituted byte. • S : substitution function. • S- Box is the only non-linear element of AES i.e. it holds that ByteSub(A) + ByteSub(B) ≠ ByteSub(A+B) for two states A and B. • S-Box substitution is bijective mapping. • Each of 28 = 256 possible inputs elements is one-to-one mapped to one output element. • Allows us to uniquely reverse the S-Box for decryption. • S-Box is usually realized as a 256-by-8 bit look up table with fixed entries. A0 A4 A8 A12 A1 A5 A9 A13 A2 A6 A10 A14 A3 A7 A11 A15 B0 B4 B8 B12 B1 B5 B9 B13 B2 B6 B10 B14 B3 B7 B11 B15
- 15. Click to editMaster title style 15 AES S – Box for Encryption 15
- 16. Click to editMaster title style 16 Inverse AES S – Box for Decryption 16
- 17. Click to editMaster title style 17 Computation of sub byte transformation 17 • Ex 1 : Let’s assume the input byte to the S-BOX is Ai = (C2)hex , then the substituted value is S((C2)hex) = (25)hex On a bit level: S(11000010) = (00100101) • Even though the S-Box is bijective, it does not have any fixed points i.e. there aren’t inputs values Ai such that S(Ai) = Ai. • Even the zero input is not a fixed point: S(00000000) = S(01100011) • Ex 2 : Let’s assume that the input to the byte substitution layer is: (C2,C2,C2,C2,….,C2)hex The output state is then (25,25,25,25,…..,25)hex
- 18. Click to editMaster title style 18 18 s0,0 s0,1 s0,2 s0,3 s1,0 s1,1 s1,2 s1,3 s2,0 s2,1 s2,2 s2,3 s3,0 s3,1 s3,2 s3,3 x y s'0,0 s'0,1 s'0,2 s'0,3 s'1,0 s'1,1 s'1,2 s'1,3 s'2,0 s'2,1 s'2,2 s'2,3 s'3,0 s'3,1 s'3,2 s'3,3 Input State matrix S-Box Output State matrix
- 19. Click to editMaster title style 19 Mathematical description of the S-BOX 19 GF(28) inverse Affine mapping Ai B’i Bi • GF(28): Galois Field • The function used here is Galois Field Inversion. • B’i = Ai -1, where Ai and B’i are considered elements in the galois field GF(28) with fixed polynomial P(x) = x8+x4+x3+x+1. • The inverse is obtained from a look up table of the multiplicative inverse in GF(28). • In Affine mapping each byte B’i is multiplied by a constant bit-matrix followed by the addition of a constant 8-bit vector.
- 20. Click to editMaster title style 20 Multiplicative inverse table in GF(28) 20
- 21. Click to editMaster title style 21 Affine Mapping 21
- 22. Click to editMaster title style 22 Example: S-BOX computation 22 • Ex: We assume the S-BOX input Ai = (11000010)2 = (C2)hex . Solution: Step 1: From look-up table (Multiplicative inverse table in GF(28)) we can see that the inverse Ai -1 = B’i = (2F)hex = (00101111)2 Step 2 : We now apply the B’i bit vector as input to the affine transformation. Bi = (00100101)2 = (25)hex Thus, S((C2)hex) = (25)hex • If one computes both steps for all 256 possible input elements of the S-BOX and stores the results, one obtains the Multiplicative inverse table in GF(28).
- 23. Click to editMaster title style 23 Shift-Rows Sub Layer 23 • From Byte substitution layer we get the substituted byte matrix. • Shift Rows transformation shifts: • The second row of the state matrix by three bytes to the right. • The third row by two bytes to the right. • The fourth row by one byte to the right. • The first row remains as it is. • The purpose of the shift rows transformation is to increase diffusion properties of AES. B0 B4 B8 B12 B1 B5 B9 B13 B2 B6 B10 B14 B3 B7 B11 B15 B0 B4 B8 B12 B5 B9 B13 B1 B10 B14 B2 B6 B15 B7 B3 B11 No shift One position left shift Two positions left shift Three positions left shift
- 24. Click to editMaster title style 24 Mix-Column Sub Layer 24 • Linear Transformation which mixes each column of the state matrix. • Let B be the 16 byte input state matrix and C be the 16 byte output state matrix, Mix-Column(B) = C • Each four byte column is considered as a vector and multiplied by a fixed 4x4 matrix.
- 25. Click to editMaster title style 25 Key Addition Layer 25 • The key schedule takes the original input key (of length 128, 192, or 256 bit) and derives the sub-keys used in AES. • XOR addition of a sub-key is used both at the input and output of AES. This process is referred to as key whitening. • The number of sub-keys is equal to the number of rounds plus one, due to the key needed for key whitening in the first key addition layer. • AES sub-keys are computed recursively, i.e. , in order to derive sub-key ki , sub-key ki-1 must be known.
- 26. Click to editMaster title style 26 AES Key Schedule for 128-bit key size 26
- 27. Click to editMaster title style 27 Key Expansion Algorithm 27 keyExpansion(byte key[16], word[44]) { word temp; for(i = 0 ; i < 4 ; i++) { w[i] = (key[4*i], key[4*i+1], key[4*i+2], key[4*i+3]); } for(i = 4 ; i < 44 ; i++) { temp = w[i - 1]; if (i mod 4 == 0) temp = subWord(rotWord(temp)) Rcon[i/4]; w[i] = w[i - 4] temp; } }
- 28. Click to editMaster title style 28 Real World Software Application 28
- 29. Click to editMaster title style 29 End To End Encryption in Chat Systems 29 • WhatsApp has now became world’s leading chat portal for end to end users and also for groups. • The security system which it follows is End to End Encryption(E2EE). • E2EE uses AES (Cipher Block Chaining(CBC) Mode) and public key cryptography to secure the chat between two users or among the group members. • In this AES plays an important role to encrypt the data. • (User1->text)->encrypted text->decrypted text->(text->User2)
- 30. Click to editMaster title style 30 Thank You