Classical &ontemporyryptology 1 AESAES

Classical &ontemporyryptology 2 Advanced Encryption Standard Since DES was becoming less reliable as new cryptanalysis techniques were developed, the National Institute of Standards and Technology (NIST) put out a notice in early 1999 requesting submissions for a new encryption standard. The requirements were: Since DES was becoming less reliable as new cryptanalysis techniques were developed, the National Institute of Standards and Technology (NIST) put out a notice in early 1999 requesting submissions for a new encryption standard. The requirements were: – A symmetric block cipher with a variable length key (128, 192, or 256 bits) and a 128-bit block – It must be more secure than TripleDES – It must be in the public domain – royalty free world wide – It should remain secure for at least 30 years Fifteen algorithms were submitted from ten different countries. Fifteen algorithms were submitted from ten different countries.

Classical &ontemporyryptology 3 Submitted Algorithms Australia – LOKI97 Belgium – RIJNDAEL Canada – CAST-256 – DEAL Costa Rica – FROG France – DFC Germany – MAGENTA Japan – E2 Korea – CRYPTON USA – HPC – MARS – RC6 – SAFER+ – TWOFISH UK, Israel, Norway – SERPENT

Classical &ontemporyryptology 4 Selection Process NIST relied on public participation: NIST relied on public participation: – algorithm proposals – cryptanalysis – efficiency testing AES Timetable AES Timetable – Round 1: Aug April 15, 1999 – Submit papers for 2nd AES conference: Feb 1, 1999 – Second AES conference: March 22-23, 1999 – Announcement of (about) five finalists – Round 2 analysis of finalists: 6-9 months – Third AES Conference – Selection of AES Algorithm

Classical &ontemporyryptology 5 AES Finalists MARS (IBM) MARS (IBM) RC6 (Rivest, et. al.) RC6 (Rivest, et. al.) Rijndael (top Belgium cryptographers) Rijndael (top Belgium cryptographers) Serpent (Anderson, Biham, Knudsen) Serpent (Anderson, Biham, Knudsen) Twofish (Schneier, et. al.) Twofish (Schneier, et. al.) And the winner was... Pronounced “rain-doll”

Classical &ontemporyryptology 6 Introduction to Rijndael One of the fastest and strongest algorithms One of the fastest and strongest algorithms – Variable block length: 128, 192, 256 bits – Variable key length: 128, 192, 256 bits – Variable number of rounds (iterations): 10, 12, 14 – Number of rounds depend on key/block length

Classical &ontemporyryptology 7 Rijndael Structure The general structure of Rijndael is shown below The general structure of Rijndael is shown below – Rather than using just a substitution and a permutation at each stage like DES, Rijndael consists of multiple cycles of Substitution, Shifting, Column mixing and a KeyAdd operation. KeyAdd subkey Plaintext block SubstitutionShiftRowMixColumnKeyAdd subkey Final round? no yes KeyAdd Ciphertext block ShiftRowSubstitution

Classical &ontemporyryptology 8 Initial Step The process begins by grouping the plaintext bits into a column array by bytes. The process begins by grouping the plaintext bits into a column array by bytes. – The first four bytes form the first column; the second four bytes form the second column, and so on. – If the block size is 128 bits then this becomes a 4x4 array. For larger block sizes the array has additional columns. – The key is also grouped into an array using the same process. a 0,0 a 1,0 a 2,0 a 3,0 a 0,1 a 1,1 a 2,1 a 3,1 a 0,2 a 1,2 a 2,2 a 3,2 a 0,3 a 1,3 a 2,3 a 3,3 a 3,0 a 2,0 a 1,0 a 0,0 a 3,1 a 2,1 a 1,1 a 0,1 a 3,2 a 2,2 a 1,2 a 0,2 a 3,3 a 2,3 a 1,3 a 0,3

Classical &ontemporyryptology 9 SubstitutionSubstitution The substitution layer uses a single S-box (rather than the 8 Sboxes used in DES). The Rijndael S-box is a 16 x 16 array The substitution layer uses a single S-box (rather than the 8 Sboxes used in DES). The Rijndael S-box is a 16 x 16 array – Each element in the current column array serves as an address into the S-box where the first four bits identify the S-box row and the last 4 bits identify the S-box column. – The S-box element at that location replaces the current column array element. a 3,0 a 2,0 a 1,0 a 0,0 a 3,1 a 2,1 a 1,1 a 0,1 a 3,2 a 2,2 a 1,2 a 0,2 a 3,3 a 2,3 a 1,3 a 0,3 b 3,0 b 2,0 b 1,0 b 0,0 b 3,1 b 2,1 b 1,1 b 0,1 b 3,2 b 2,2 b 1,2 b 0,2 b 3,3 b 2,3 b 1,3 b 0,3 SBox a 1,2 b 1,2

Classical &ontemporyryptology 10 Row Shift Operation A row shift operation is applied to the output of the S-box in which the four rows of the column array are cyclically shifted to the left. A row shift operation is applied to the output of the S-box in which the four rows of the column array are cyclically shifted to the left. – The first row is shifted by 0, the second by 1, the third by 2, and the fourth by 3 b 3,0 b 2,0 b 1,0 b 0,0 b 3,1 b 2,1 b 1,1 b 0,1 b 3,2 b 2,2 b 1,2 b 0,2 b 3,3 b 2,3 b 1,3 b 0,3 b 3,3 b 2,2 b 1,1 b 0,0 b 3,0 b 2,3 b 1,2 b 0,1 b 3,1 b 2,0 b 1,3 b 0,2 b 3,2 b 2,1 b 1,0 b 0,3 No shift Shift 1 Shift 2 Shift 3

Classical &ontemporyryptology 11 Matrix Multiply Column mixing is accomplished by a matrix multiplication operation. Column mixing is accomplished by a matrix multiplication operation. – The shifted column array is multiplied by a fixed matrix b 3,3 b 2,2 b 1,1 b 0,0 b 3,0 b 2,3 b 1,2 b 0,1 b 3,1 b 2,0 b 1,3 b 0,2 b 3,2 b 2,1 b 1,0 b 0,3 Matrix Multiply c 3,3 c 2,2 c 1,1 c 0,0 c 3,0 c 2,3 c 1,2 c 0,1 c 3,1 c 2,0 c 1,3 c 0,2 c 3,2 c 2,1 c 1,0 c 0,3 c 3,1 c 2,0 c 1,3 c 0,2 b 3,1 b 2,0 b 1,3 b 0,2

Classical &ontemporyryptology 12 Key Add The final operation adds a subkey derived from the original key to the column array The final operation adds a subkey derived from the original key to the column array – This completes one round of AES c 3,3 c 2,2 c 1,1 c 0,0 c 3,0 c 2,3 c 1,2 c 0,1 c 3,1 c 2,0 c 1,3 c 0,2 c 3,2 c 2,1 c 1,0 c 0,3 d 3,3 d 2,2 d 1,1 d 0,0 d 3,0 d 2,3 d 1,2 d 0,1 d 3,1 d 2,0 d 1,3 d 0,2 d 3,2 d 2,1 d 1,0 d 0,3 k 3,3 k 2,2 k 1,1 k 0,0 k 3,0 k 2,3 k 1,2 k 0,1 k 3,1 k 2,0 k 1,3 k 0,2 k 3,2 k 2,1 k 1,0 k 0,3 XOR This is repeated 9 more times

Classical &ontemporyryptology 13 Key Schedule The key is grouped into a column array and then expanded by adding 40 new columns. The key is grouped into a column array and then expanded by adding 40 new columns. – If the first four columns (given by the key) are C(0), C(1), C(2) and C(3) then the new columns are generated in a recursive manner. If i is not a multiple of 4 then column i is determined by: C(i) = C(i-4) XOR C(i-1) If i is not a multiple of 4 then column i is determined by: C(i) = C(i-4) XOR C(i-1) If i is a multiple of 4 then column i is determined by: C(i) = C(i-4) XOR T(C(i-1)) If i is a multiple of 4 then column i is determined by: C(i) = C(i-4) XOR T(C(i-1)) – Where T(C(i-1)) is a transformation of C(i-1) implemented as: 1. Cyclically shift the elements of C(i-1) by one byte 2. Use each of these 4 bytes as input into the S-box to create four new bytes e,f,g,h. 3. Calculate a round constant r(i) = 2(i-4)/4 4. Create the transformed column as: (e XOR r(i), f, g, h) The round key for the ith round consists of the columns C(4i), C(4i+1), C(4i+2), C(4i+3). The round key for the ith round consists of the columns C(4i), C(4i+1), C(4i+2), C(4i+3).

Classical &ontemporyryptology 14 Key Generation Flow For what’s worth: For what’s worth: W(i) XOR Rot W(i+4) XOR W(i+1) XOR W(i+2) W(i+5) XOR W(i+3) W(i+6) XOR W(i+7) S-Box RCON