Chapter 3-4 Symmetric Cryptography AES PDF

Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Course Cryptography (Classic & Modern) https://www.tutorialspoint.com/cryptography/ cryptography_need_for_encryption.htm...

Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Course Cryptography (Classic & Modern) https://www.tutorialspoint.com/cryptography/ cryptography_need_for_encryption.htm College of Computer Science, King Khaled University 'KKU', KSA okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA CHAPTER 3-4 : Symmetric Cryptography, AES... AES History, and Principle…  AES Description…  Essential AES Steps: o SubBytes o ShiftRows o MixColumns o AddRoundKey  AES Key EXPANSION… okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Early 1970s: Horst Feistel designs Lucifer at IBM key-len = 128 bits ; block-len = 128 bits 1973: NBS asks for block cipher proposals. IBM submits variant of Lucifer. AE 1976: NBS adopts DES as a federal standard S H key-len = 56 bits ; block-len = 64 bits is to 1997: DES broken by exhaustive search ry … 2000: NIST adopts Rijndael as AES to replace DES Widely deployed in banking (ACH) and commerce okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA In 1997 the NIST (National Institute of Standards and Technology) launched a new call for projects to develop AES (Advanced Encryption Standard), an encryption algorithm intended to replace DES A ES H i s t or y … okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES algorithm (Rijndael algorithm) : A ES Hi st o Symmetrical Block Cipher Algorithm or y … o Plain text in blocks of 128 Bits and converts them to ciphertext o keys of 128, 192, and 256 Bits. o AES algorithm is considered secure, it is in the worldwide DES AES standard. Developed 1977 2000 Symmetric Block Symmetric Block Cipher Type Cipher Cipher Block size 64 bits 128 bits Key length 56 bits 128/192/256 bits Security Rendered insecure Considered secure okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Block Ciphers Built by Iterations A ES key k Hi st or y … key expansion k1 k2 k3 kn c R(k1, R(k2, R(k3, R(kn, m ) ) ) ) R(k,m) is called a round function for 3DES (n=48), for AES-128 (n=10) okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College atDan King Kh Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES - Applicability A ES Hi st or y … AES development was initiated in 1997 by the NIST. AES was adopted as the standard method of encryption in June 2003 for securing classified information, including data from the government. In addition, it became the 1st open cipher that the National Security Agency ‘NSA’ has authorised for use in the public domain to protect national security systems and Top Secret data. ISO/IEC 18033-3 standard from the International Organisation for Standardisation also includes AES and describes block ciphers that improve data confidentiality. One of the most widely used symmetric key cryptography algorithms nowadays for a variety of encryption uses in both commercial and government settings is AES. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College atDan King Kh Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES – Applicability Here are a few examples −  Information on storage devices, like USB drives and hard drives.  Apps for electronic communication.  Libraries for programming.  Web Browsers. A ES Hi st  Compression of Files and Discs. or y …  Wireless Systems.  Databases.  Passwords and Login Credentials.  VPNs. This standard can be used in addition to, other FIPS-approved cryptographic algorithms. Instead of using this standard, federal departments or agencies that use cryptographic devices to secure sensitive (unclassified) information can use the same devices to protect sensitive data. Additionally, organisations outside of the federal government can adopt and apply this standard. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College atDan King Kh Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA A ES AES Main Features : Hi st or y …  AES is a subset of Rijndael Block Cipher.  AES is the Successor of (DES) and is stronger and faster than DES.  It is a symmetric key , symmetric block cipher.  It operates on 128-bit (16 bytes) data , 192 or 256...  The cipher key may be of 128 bits, 192 or 256 bits.  All computations are performed on bytes rather than bits.  AES gives full specification and design details. Implemented using languages C and Java for software protection. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College atDan King Kh Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA CHAPTER 3-4 : Symmetric Cryptography, AES...  Revision (10Slds) : Symmetric Cryptography, Essential Encryption Algorithms  AES History, and Principle…  AES Description…  Essential AES Steps: o SubBytes o ShiftRows o MixColumns o AddRoundKey  AES Key EXPANSION… okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College atDan King Kh Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Fy2te = 8Bits AES : Elements of Field(B 8 ) Elements of Field F28 : bits’ vectors (or bytes) representing binary polynomials. Example the byte given by 0x83 in hexadecimal, gives the bit pattern 1, 0, 0, 0, 0, 0, 1, 1 since , 0x83 = 8 · 16 + 3 = 131 , in decimal. Bit pattern directly : 8 in binary is 1, 0, 0, 0 and 3 in 4-bit binary is 0, 0, 1, 1 and one simply concatenates these two bit strings together. Bit pattern corresponds to the binary polynomial : x7 + x okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College atDan King Kh Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES : Elements of Field(B Fy2te = 8Bits) 8 Arithmetic in F28 is performed using polynomial arithmetic modulo the irreducible polynomial : m(x) = x8 + x4 + x3 + x + 1. Rijndael identifies 32-bit words with polynomials in F28 [X] of degree less than ‘4’. In a big-endian format, smallest index corresponds to the least important coefficient. Hence, the word : a0ǁa1ǁa2ǁa3 will correspond to the polynomial : a3X3 + a2X2 + a1X + a0. Arithmetic: polynomials in F 8 [X] , modulo reducible polynomial: M okhtar BEN HMIDA, Dr. & Full Professor, Head2of ATMS Lab, Expert in Signal Processing , CS College atDan King Kh Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES G Description AES winner, decided in 2000, the Rijndael Algo, by Daemen and Rijmen. Rijndael.. Block Cipher which does not rely on the basic design of the Feistel cipher. However, Rijndael does have a number of similarities with DES. It uses a repeated number of rounds to obtain security and each round consists of Substitutions and Permutations, plus a key addition phase. Rijndael in addition has a strong mathematical structure, as most of its okhtar BEN operations HMIDA, are based Dr. & Full Professor, Head ofon ATMSarithmetic in the Lab, Expert in Signal field, Processing F2 8 (Byte CS = College at King Kh Dan Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA ES : Byte Matrix 4x4 ; ‘S’ vs ‘Ki’ Rijndael is a parametrized algorithm: Block Cipher sizes of 128, 192 or 256 bits… It can also accept keys of size 128, 192 or 256 bits. For each combination of block and key size, a different number of rounds is specified. Ex: Block size of 128 bits and a key size of 128 bits, in which case 10 rounds are specified. s0,0operates Rijndael s0,1 s0,2 s0,3 on an k0,0called internal ‘4X4 Matrix’ of Bytes, k0,1 the k0,2state k0,3 s1,0 matrix ‘S’s:1,1 s1,2 s1,3 Each k1,0 k1,1 k1,2 k1,3 ‘S’ round key ‘K s2,0 s2,1 s2,2 s2,3 i k2,0 k2,1 k2,2 k2,3 s3,0 s3,1 s3,2 s3,3 ’ k3,0 k3,1 k3,2 k3,3 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College atDan King Kh Boneh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 : Enc vs Dec Key - Iterations 128 bits - 10 iterations 192 bits - 12 iterations 256 bits - 14 iterations Example: Data and key are 128 bits okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 : Enc Plain Text : 128Bits AddRoundKey SubBytes En c n d s Key - Iterations R ou ShiftRows ry pt MixColumns 128 bits - 10 io n iterations AddRoundKey 192 bits - 12 SubBytes iterations Rou Las ShiftRows 256 bits - 14 nd t AddRoundKey iterations Example: Data and key are 128 bits Cipher Text : 128Bits okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 : Enc… okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 : Enc… K0, K0,1 K0,2 K0, 0 0 3 K1, K1,1 K1,2 K1, 3 s0, s0, s0, s0, 0 1 2 3 s1, s1, s1, s1, K2, K2,1 K2,2 K2, 0 1 2 3 Key Expansion : The round keys are calculated from the 0 0 3 K3, K3,1 K3,2 K3, 3 s2, s2, s2, s2, 0 1 2 3 s3, s3, s3, s3, cipher key using Rijndael's block cipher schedule. 0 1 2 3 Pre−Transformation: One process namely Add_Round_Key. XOR is performed on each data byte with a byte of the round key. Byte Substitution (SubBytes) : The 16 input bytes are substituted by looking up a fixed table (S-box) given in design. The result is in a matrix of four rows and four columns. Shiftrows : Each of the four rows of the matrix is shifted to the left. Any entries that 'fall off' are re-inserted on the right side of row. Shift is carried out as follows −  First row is not shifted.  Second row is shifted one (byte) position to the left.  Third row is shifted two positions to the left.  Fourth row is shifted three positions to the left.  The result is a new matrix consisting of the same 16 bytes but shifted with respect to each other. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 : Enc… K0, K0,1 K0,2 K0, 0 0 3 K1, K1,1 K1,2 K1, 3 s0, s0, s0, s0, 0 1 2 3 s1, s1, s1, s1, K2, K2,1 K2,2 K2, 0 1 2 3 0 3 s2, s2, s2, s2, MixColumns : Each column of four bytes is now transformed K3, K3,1 K3,2 K3, 0 3 0 1 2 3 s3, s3, s3, s3, using a special mathematical function. 0 1 2 3 This function takes as input the four bytes of one column and outputs four completely new bytes, which replace the original column. The result is another new matrix consisting of 16 new bytes. It should be noted that this step is not performed in the last round. Addroundkey : The 16 bytes of the matrix are now considered as 128 bits and are XORed to the 128 bits of the round key. If this is the last round then the output is the ciphertext. Otherwise, the resulting 128 bits are interpreted as 16 bytes and we begin another similar round. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA s0, s0, s0, s0, 0 1 2 3 s1, s1, s1, s1, 0 1 2 3 s2, s2, s2, s2, 0 1 2 3 s3, s3, s3, s3, 0 1 2 3 K0, K0,1 K0,2 K0, 0 3 Key Expansion : The round K1, K1,1 K1,2 K1, keys are calculated from the s0, s0, s0, s0, 0 1 2 3 0 3 cipher key using Rijndael's block s1, s1, s1, s1, K2, K2,1 K2,2 K2, 0 3 cipher schedule. 0 1 2 3 K3, K3,1 K3,2 K3, s2, s2, s2, s2, 0 1 2 3 0 3 s3, s3, s3, s3, okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , 0 1 2 CS3 College at King Kh AES 128 : Plain Text : 128Bits Enc vs Dec En c n d s R ou ry pt io n Rou Las nd t Cipher Text : 128Bits  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA CHAPTER 3-4 : Symmetric Cryptography, AES...  Revision : Symmetric Cryptography, Essential Encryption Algorithms  AES History, and Principle…  AES Description…  Essential AES Steps: (04) : Step 0 First !!! o Setp 1 : SubBytes o Step 2 : ShiftRows o Step 3 : MixColumns o Step 4 : AddRoundKey  AES Key EXPANSION… okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 bit input (‘S’ 16 bytes) Round Step 0 128 bit round key + XOR S(i) = k xor rol(k,4) xor rol(k,5) tep1 16 8x8 S boxes S S xor rol(k,6) xor rol(k,7) xor 0x63 where k = i-1 in GF(28), tep2 ShiftRow rol = rotate byte left S s tep3 S Multiply by M in GF(28) 23 1 1 Mixcolumn over polynomial 12 3 1 x8+x4+x3+x+1 where M= p4 s 11 2 3 Ste 31 1 2 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Step 0: AddRoundKey Binary Xor addition: ‘S’ bytes of the data with the ‘K’ bytes of the key okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Step ‘1’ Now, SubBytes (Step1): (Substittion of Bytes S- b ox 4x4) St e p 1 There are two types of S-Boxes used in Rijndael: One for Encryption rounds and one for Decryption rounds, each one being the inverse of the other. The S-Boxes of DES were chosen by searching through a large space of possible S-Boxes, so as to avoid attacks such as differential cryptanalysis. The S-Box of Rijndael is chosen to have a simple mathematical structure, which allows one to formally argue how resilient the cipher is from differential and linear cryptanalysis. Not only does this mathematical structure help protect against okhtar differential cryptanalysis, BEN HMIDA, Dr. but it also convinces users that it has & Full Professor, Head of ATMS Lab, Expert in Signal Processing , not CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA SubBytes Now, (s) = [s ,... , s ] tep 1 Sand (Step1) Each byte 0 7 of the Rijndael state matrix is taken in turn considered as an element of F2 8. The S-Box can be mathematically described in two steps: (1) The multiplicative inverse in F28 of s is computed to produce a new byte (x) = [x0,... , x7]. [0,... , 0], which has no multiplicative inverse, one(x) Element (y) uses the convention that this y 0 x0 1 is mapped to zero. 1 0 0 0 1 1 1 1 1 F2 e y x 1 (x) is then mapped, via the following affine F2 1transformation, to the byt ven b (2) The bit-vector 0 is g :T 1 1 0 0 0 1 1 1 bit- vector (y):y2 x2 0 = he i y3 1 1 1 0 0 0 1 1 * x3 + 0 new y4 x4 1 1 1 1 1 0 0 0 1 y‘ 1 y5 x5 y’ 1 0 0 0 1 1 1 1 0 y6 x6 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh 1 1 1 1 1 0 0 0  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA SubBytes Now, (Step1) The multiplicative inverse in F2 8 of (s) is (x) = [x0,... , x7]. St e p With F2 TRANSFORMATION, we get a new byte (y) = F2(x) ; (y) = [y0,... , y7]. 1 The matrix multiplication can be calculated by the following algorithm: 1. Store the multiplicative inverse of the input number in two 8-bit unsigned temporary variables: (s) and (x). 2. Rotate the value (s) one bit to the left; if the value of (s) had a high bit (eighth bit from the right) of one, make the low bit of (s) one; otherwise the low bit of (s) is zero. 3. Xor the value of (x) with the value of (s), storing the value in (x). 4. For three more iterations, repeat steps two and three; steps two and three are done a total of four times. 5. The value of (x) will now have the result of the multiplication. After the matrix multiplication is done, Xor the value by the decimal number 99 (the hexadecimal number 0x63, the binary number 1100011, and the bit string 11000110 representing the number in LSb first notation). okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA SubBytes (y) (x) (Step1) The new byte is given by ‘y’. y0 x0 1 1 0 0 0 1 1 1 1 y1 x1 1 Decryption S-Box is obtained y2 1 1 0 0 0 1 1 1 x2 0 by first inverting the affine trans- y3 = x3 0 1 1 1 0 0 0 1 1 * + 0 formation and then taking the y4 x4 y5 1 multiplicative inverse. 1 1 1 1 0 0 0 1 x5 1 y6 x6 1 0 0 0 1 1 1 1 0 These byte substitutions can y7 x7 1 1 1 1 1 0 0 0 either be implemented using table look-up or by 0 0 1 1 1 1 1 0 implementing circuits, or code, 0 0 0 1 1 1 1 1 Now, which implement the inverse operation in F28 and the affine St e p transformation. 1 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA SubBytes Now, (Step1) St e p Substitute each element of the data block ; by 1 corresponding element in the substitution table (denoted S-Box), [ Rijndael ]. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh SubBytes S-box Now, (Step1) Step 1 SubBytes X is Y is Left (4Bit R i gh s) (Step1) t (4B of S0,1 its) o fS 0, 1 S-box Now, St e p 1  SubBytes Now, (Step1) Each individual byte of State Matrix is S- St e p mapped into a new byte in the following way: box 1 The leftmost 4 bits of the byte are used as a row value and the rightmost 4 bits are used as a column value. These (row and column) values serve as indexes into the S-box to select a unique 8-bit output value. For example, the hexadecimal value {EA} references: row E, column A of the S-box, which contains the value {87}. Accordingly, value {EA} is mapped into https://www.chiragbhalodia.com/search?q=AES value {87}. https://www.youtube.com/watch?v=I68uBhHdnM4 SubBytes Now, (Step1) S- St e p box 1 SubBytes (Step1) Now, St e p 1 S- box S−Box is a predetermined Substitution table: Substitute Bytes at each encryption round. AES S−Box is a key element of the AES algorithm's security because it is made to withstand a variety of cryptographic attacks. S−Box (fixed T) by its complexly and nonlinearly substituting input values with corresponding output values, adds nonlinearity and improves security to cryptographic methods.  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA SubBytes (Step1)  Non−linearity − The relationship between the input and output values is not a straightforward mathematical function since S−Boxes are made to be nonlinear. The non−linearity of this system helps in preventing multiple cryptographic attacks, including asymmetric and linear cryptanalysis.  Confusion − S−Boxes are necessary to achieve the encryption property of confusion. They make sure that there is a complex connection between Ciphertext and Plaintext, which makes it difficult for attackers to work out patterns and details about the encrypted data.  Fixed and Predefined − A cryptographic algorithm's S−Boxe is a fixed and well−known part. Transparency and confidence in the encryption process are ensured by its public awareness and standard design.  Substitution − S−Boxes carry out substitution process, substituting corresponding output value from the S−Box for each input value. This replacement takes place either bit by bit or byte by byte, dependent upon how the algorithm is constructed. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 bit input (‘S’ 16 bytes) Round Now, St e p 2 Step 0 128 bit round key + XOR S(i) = k xor rol(k,4) xor rol(k,5) tep1 16 8x8 S boxes S S xor rol(k,6) xor rol(k,7) xor 0x63 where k = i-1 in GF(28), tep2 ShiftRow rol = rotate byte left S s tep3 S Multiply by M in GF(28) 23 1 1 Mixcolumn over polynomial 12 3 1 x8+x4+x3+x+1 where M= p4 s 11 2 3 Ste 31 1 2 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA ShiftRows (Step2): Now, S t ep ShiftRows operation in Rijndael performs a cyclic shift on the state matrix. 2 Each row is shifted by different offsets. For the version of Rijndael we are considering this: Circular shift of lines li by i-1 bytes >>permutation Inverse of ShiftRows operation is simply a similar shift but in the opposite direction. 1 byte Such operation ensures offset that the columns of state matrix ‘S’ ‘interact’ with 2 byte each other over a number offset okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , of rounds. CS College at King Kh Now, St e p 2 Now, St e p 2  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 bit input (‘S’ 16 bytes) Round Now, St e p 3 Step 0 128 bit round key + XOR S(i) = k xor rol(k,4) xor rol(k,5) tep1 16 8x8 S boxes S S xor rol(k,6) xor rol(k,7) xor 0x63 where k = i-1 in GF(28), tep2 ShiftRow rol = rotate byte left S s tep3 S Multiply by M in GF(28) 23 1 1 Mixcolumn over polynomial 12 3 1 x8+x4+x3+x+1 where M= p4 s 11 2 3 Ste 31 1 2 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Now, MixColumns (Step3): St e p 3 security.  MixColumns Transform attempts to add diffusion and strengthen encryption  Operation on columns of state matrix: Column as a polynomial over a finite field F28. MixColumns provide confusion and make Encryption process resistant to various cryptanalysis techniques. ttps://www.youtube.com/watch?v=WPz4Kzz6vk4 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA MixColumns (Step3): We consider each column [a0,a1,a2,a3] of the state in turn (as a Word = 04 Bytes = 32 Bits) and consider it as a Polynomial of degree less than four (04) with coefficients in F2. 8 The new column [b0,b1,b2,b3] is produced by taking this polynomial : a(X) = a0 + a1X+ a2X2 + a3X3 and multiplying it by the polynomial : c(X) = 0x02 + 0x01 ·X+ 0x01 ·X2 + 0x03 ·X3;Modulo : M(X) = X4 + 1. This operation is conveniently represented by the following matrix operation in F2 8 , b0 0x02 0x03 0x01 0x01 a0 b10x01 0x02 0x03 0x01 = a1 * Now, b 0x01 0x01 0x02 0x03 a2 St e p 2 b30x03 0x01 0x01 0x02 a3 3 In F28 ; the above matrix is invertible, hence the inverse of the MixColumns operation can also be implemented using a matrix multiplication such as that above. https://www.youtube.com/watch?v=WPz4Kzz6 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh MixColumns (Step3): Now, St e p https://www.youtube.com/watch?v=WPz4Kzz6vk4 3 Exercise (Step3): Now, St e p 3 Exercise (Step3): Now, St e p 3 Exercise (Step3): Now, St e p 3 Exercise (Step3): Now, St e p 3 Exercise (Step3): Now, St e p 3 Exercise (Step3): Advantages  Diffusion is introduced into the encryption process using MixColumns, which mixes the bytes in each state matrix column. Now,  It increases overall encryption security by ensuring that each byte in St e p the state matrix affects many bytes in subsequent encryption rounds. 3  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES 128 bit input (‘S’ 16 bytes) Round Now, St e p 2 Step 0 128 bit round key + XOR S(i) = k xor rol(k,4) xor rol(k,5) tep1 16 8x8 S boxes S S xor rol(k,6) xor rol(k,7) xor 0x63 where k = i-1 in GF(28), tep2 ShiftRow rol = rotate byte left S s tep3 S Multiply by M in GF(28) 23 1 1 Mixcolumn over polynomial 12 3 1 x8+x4+x3+x+1 where M= p4 s 11 2 3 Ste 31 1 2 okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh Now, St e p 4 Exercise (Step4): Now, St e p 4 Exercise (Step4): Now, St e p 4  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA CHAPTER 3-4 : Symmetric Cryptography, AES...  Revision : Symmetric Cryptography, Essential Encryption Algorithms  AES History, and Principle…  AES Description…  Essential AES Steps: (04) : Step 0 First !!! o Setp 1 : SubBytes o Step 2 : ShiftRows o Step 3 : MixColumns o Step 4 : AddRoundKey  AES Key EXPANSION… !!! okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh AES 128 : Plain Text : 128Bits Enc vs Dec En c n d s R ou ry pt io n Rou Las nd t Cipher Text : 128Bits  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES Key EXPANSION… !!!  Key Schedule. The only thing left to describe is how Rijndael computes the round keys from the main key.  Main key is 128 bits long, and we need to produce 11 round keys K0,... ,K11  All of which consist of four 32-bit words.  Each word corresponding to a column of a matrix as described above.  The key schedule makes use of a round constant which we shall denote by : RCi = xi (mod x8 + x4 + x3 + x + 1).  We label the round keys as (W4i,W4i+1,W4i+2,W4i+3) where i is the round.  The initial main key is first divided into four 32-bit words (k0, k1, k2, k3).  Round keys (computed Algorithm), where RotBytes: function which rotates a word to left by a single byte, and SubBytes: Rijndael encryption S-Box to every byte in a word. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA Algorithm 8.3: Rijndael Key Schedule o W0 = K0,W1 = K1,W2 = K2,W3 = K3 o for i= 1 to 10 do o T=RotBytes(W4i−1) o T=SubBytes(T) o T= TXorRCi o W4i = W4i−4 XorT o W4i+1 = W4i−3 XorW4i o W4i+2 = W4i−2 XorW4i+1 o W4i+3 = W4i−1 XorW4i+2 o end okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh  Cryptography (Classic) College of Computer Science ; King Khalid University ; KKU - KSA AES is widely used in many applications which require secure data storage and transmission: Wireless security: AES is used in securing wireless networks, such as Wi-Fi networks, to ensure data confidentiality and prevent unauthorized access. Database Encryption: AES can be applied to encrypt sensitive data stored in databases. This helps protect personal information, financial records, and other confidential data from unauthorized access in case of a data breach. Secure communications: AES is widely used in protocols like such as internet communications, email, instant messaging, and voice/video calls. It ensures that the data remains confidential. Data storage: AES is used to encrypt sensitive data stored on hard drives, USB drives, and other storage media, protecting it from unauthorized access in case of loss or theft. Virtual Private Networks (VPNs): AES is commonly used in VPN protocols to secure the communication between a user’s device and a remote server. It ensures that data sent and received through the VPN remains private and cannot be deciphered by eavesdroppers. Secure Storage of Passwords: AES encryption is commonly employed to store passwords securely. Instead of storing plaintext passwords, the encrypted version is stored. This adds an extra layer of security and protects user credentials in case of unauthorized access to the storage. okhtar BEN HMIDA, Dr. & Full Professor, Head of ATMS Lab, Expert in Signal Processing , CS College at King Kh