Cryptography Symmetric Key Algorithm (CSE)

Computer –Based Symmetric Key Cryptographic Algorithm

Ciphers • Mechanism that decides the process of encryption/decryption • Stream Cipher: Bit-by-bit encryption / decryption • Block Cipher: Block-by-block encryption / decryption

Types of Cipher Algorithm Types Stream Ciphers Block Ciphers

Stream Cipher Example Pay 100 010111001 100101011 ZTU91_^%D + 11001001 Plain text Cipher text XOR operation with the key In normal format In binary format

Block Cipher Example FOUR _AND_ FOUR Plain text Encrypt Encrypt Encrypt VFa% VFa% *yT1x Cipher text (a) The Encryption Process at the sender’s end VFa% VFa% *yT1x Cipher text Decrypt Decrypt Decrypt FOUR _AND_ FOUR Plain text (b) The Decryption Process at the receiver’s end

Algorithm Modes • Add randomness to block cipher • Otherwise, block cipher becomes predictable • Four main modes

Algorithm Modes Algorithm Modes Electronic Code Book (ECB) Cipher Block Chaining (CBC) Cipher Feedback (CFB) Output Feedback (OFB) These two modes work on block ciphers. These two modes work on block ciphers acting as stream ciphers.

Encryption in ECB Mode Encrypt Plain text block 1 Key Cipher text block 1 Step 1 Encrypt Plain text block 2 Key Cipher text block 2 Step 2 Encrypt Plain text block n Key Cipher text block n Step n

Decryption in ECB Mode Decrypt Cipher text block 1 Key Plain text block 1 Step 1 Decrypt Cipher text block 2 Key Plain text block 2 Step 2 Decrypt Cipher text block n Key Plain text block n Step n

Encryption in CBC Mode Encrypt Plain text block 1 IV Cipher text block 1 Step 1 Encrypt Plain text block 2 Cipher text block 2 Step 2 Encrypt Plain text block n Cipher text block n Step n Key XOR XOR Key Key XOR

Decryption in CBC Mode Decrypt Cipher text block 1 IV Plain text block 1 Step 1 Decrypt Cipher text block 2 Plain text block 2 Step 2 Decrypt Cipher text block n Plain text block n Step n Key XOR XOR Key Key XOR

Encryption in CFB Mode IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text 8 bits Cipher text 8 bits IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text 8 bits IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text 8 bits Cipher text 8 bits Cipher text 8 bits

Encryption in OFB Mode IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits Cipher text j bits IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits IV (Shift register) Encrypt Key Take just the leftmost 8 bits XOR Plain text j bits Cipher text j bits Cipher text j bits

Symmetric Key Cryptography • Same key used for encryption and decryption • Examples: DES, IDEA, RC5, Blowfish, AES • Quite popular and fast

Symmetric Key Cryptography Plain text Encrypt with symmetric key Plain text Decrypt with symmetric key Sender (A) Net wor k Receive r (B) Cipher text Cipher text

Conceptual View of DES 64-bit Plain text 56-bit Key DES 64-bit Cipher text Block 1 64-bit Plain text 56-bit Key DES 64-bit Cipher text Block 2 64-bit Plain text 56-bit Key DES 64-bit Cipher text Block n 

Discarding of every 8th bit of the original key 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

Key discarding process Original 64-bit key Key discarding process Resulting 56 bit key

Broad Level Steps in DES Initial Permutation (IP) LPT RPT 16 rounds 16 rounds Key Key Final Permutation (FP) Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Plain text (64 bits) Cipher text (64 bits)

Idea of Initial Permutation(IP) Bit position in the plain text block To be overwritten with the contents of this bit position 1 2 3 … 64 58 50 42 … 7

Initial Permutation(IP) table 58 50 42 34 26 18 10 2 60 52 44 36 28 20 12 4 62 54 46 38 30 22 14 6 64 56 48 40 32 24 16 8 57 49 41 33 25 17 9 1 59 51 43 35 27 19 11 3 61 53 45 37 29 21 13 5 63 55 47 39 31 23 15 7

Details of One Round in DES Key Transformation Expansion Permutation S-Box Substitution P-Box Permutation XOR and Swap

Key transformation Round 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Number of key bits shifted 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1

Compression permutation 14 17 11 24 1 5 3 28 15 6 21 10 23 19 12 4 26 8 16 7 27 20 13 2 41 52 31 37 47 55 30 40 51 45 33 48 44 49 39 56 34 53 46 42 50 36 29 32

Expansion permutation •Division of 32-bit RPT into eight 4 bit blocks

RPT expansion permutation process

RPT expansion permutation table 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

S-box Subtitution Key Transformation (Compress key from 56 bits to 48 bits) Expansion permutation (Expand RPT from 32 bits to 48 bits) 48 bit key 48 bit RPT XOR S- box Substitution

S-Box Substitution 48 bit Input block 6 bit sub block 6 bit sub block 6 bit sub block S-box 1 S-box 2 S-box 8 4 bit Output 4 bit Output 4 bit Output 32 bit Output block

S-box 1 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0 15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 13

Selecting an entity in a s-box based on the 6-bit input 4 bit column number b1 b6 b2 b3 b4 b5 2 bit row number

P-box Permutation 16 7 20 21 29 12 28 17 1 15 23 26 5 18 31 10 2 8 24 14 32 27 3 9 19 13 30 6 22 11 4 25

XOR and Swap Original 64 bit Plain text block 32 bit LPT block 32 bit RPT block 1. Key transformation 2. Expansion Permutation 3. S-box Substitution 4. P-box Permutation XOR 32 bit LPT block 32 bit RPT block Next Round

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

Modified Versions of DES • Double DES: Perform DES twice with two different keys • Triple DES with Three Different Keys • Triple DES with Two Different Keys

Double DES Encryption Original Plain Text Encrypt K1 Cipher Text Encrypt K2 Cipher Text

Double DES Decryption Original Plain Text Decrypt K2 Decrypt K1 Cipher Text Cipher Text

Double DES Mathematically Expressed P Encrypt K1 Temporary result (T) Encrypt K2 C EK1(P) EK2(EK1(P)) T = EK1(P) C = EK2(EK1(P))

Triple DES Original Plain Text Encrypt K1 Cipher Text 1 Encrypt K2 Cipher Text 2 Encrypt K3 Final Cipher Text

Triple DES with Two Keys Original Plain Text Encrypt K1 Cipher Text 1 Decrypt K2 Cipher Text 2 Encrypt K1 Final Cipher Text

Broad Level Steps in IDEA ( International Data Encryption Algorithm) Input Plain Text (64 bits) P1 (16 bits) P2 (16 bits) P3 (16 bits) P4 (16 bits) Round 1 K1 . . K6 Round 2 K7 . . K12  Round 8 K43 . . K48 Output Transformation K49 . . K52 C1 (16 bits) C2 (16 bits) C3 (16 bits) C4 (16 bits) Output Cipher Text (64 bits)

Details of one round in IDEA Step 2: Add *P2 and K2 Step 3: Add * P3 and K3 Step 1: Multiply * P1 and K1 Step 4: Multiply *P4 and K4 Step 5: XOR the result of step 1 and step 3 Step 6: XOR the result of step 2 and step 4 Step 7: Multiply* the result of step 5 with K5

Details of one round in IDEA Step 9: Multiply * the results of Step 8 with K6 Step 10: Add* the results of step 7 and step 9 Step 8: Add * the results of Step 6 and step 7 Step11: XOR the results of step 1 and step 9 Step 12: XOR the result of step 3 and step 9 Step 13: XOR the result of step 2 and step 10 Step 14: XOR the result of step 4 and step 10

Modulo operation •Addition with modulo 216 i.e. addition modulo 65536 •Multiplication with modulo 216 + 1 i.e. multiplication modulo 65537.

Detail of sub key generation and use • Bit position 1-96 of the key are used. 97-128 remain unused. •Bit 97-128 are first used. Circular left shift of 25 bits occurs. As per new key bit position 26-89 are used. Bit position 90- 128 and 1-25 remain unused.

Details of the output transformation Step 2: Add * R2 and K2 Step 3: Add*R3 and K3 step 1: Multiply *R1 and K1 Step 4: Multiply * R4 and K4

Encryption using RC5 First, divide the original plain text into two blocks of equal size. Call them as A and B. Add A and S[0] to produce C. Add B and S[1] to produce D. 1. XOR C and D to produce E. 4. XOR D and F to produce G. 2. Circular-left shift E by D bits. 3. Add E and S[2i] to produce F. 5. Circular-left shift G by F bits. 6. Add G and S[2i + 1] to produce H. Increment i by 1. Check: Is i > r? Stop Yes No Note: First perform all the left-hand side steps, and then come to the right hand side steps, as indicated by the step numbers. Call F as C (i.e. C = F) Call H as D (i.e. D = H)

RC5 Encryption A = A + S[0] B = B + S[1] For i = 1 to r A = ((A XOR B) <<< B) + S[2i] B = ((B XOR A) <<< A) + S[2i + 1] Next i

RC5 Decryption For i = r to 1 step –1 (i.e. decrement i each time by 1) B = ((B – S[2i + 1]) >>> A) XOR A A = ((A – S[2i]) >>> B) XOR B Next i B = B – S[1] A = A – S[0]

Blowfish Plain text (64 bits) 32 bits 32 bits XOR P1 (32 bits) F XOR XOR P2 (32 bits) F XOR 13 more rounds XOR F XOR P16 (32 bits) XOR P18 (32 bits) XOR P17 (32 bits) 32 bits 32 bits Cipher text (64 bits)

Blowfish Function 32-bit XL block S-box 1 8 bits 32 bits S-box 2 8 bits 32 bits XOR S-box 3 8 bits 32 bits XOR S-box 4 8 bits 32 bits XOR 32-bit output

The Description of Rijndael • Do the following one –time initialization process –Expand the 16 byte key to get the actual Key block to be used –Do one time initialization of the 16 byte plain text block( called as State) –XOR the State with the Key block

The Description of Rijndael • For each round do the following –Apply S-box to each of the plain text bytes –Rotate row k of the plain text block by k bytes –Perform a mix columns operation –XOR the state with the key block

Rijndael (AES) Step 1: Byte Substitution Step 2: Shift Rows Step 3: Mix Columns Step 4: Round Key Addition Repeat these four steps 10, 12 or 14 times.

AES Key Generation 16-byte key Expanded into 11 arrays, each of size 4 x 4

AES Key Expansion – 1 16-byte key To be expanded into 11 arrays, each of size 4 x 4 Copied, as is

Cryptography Symmetric Key Algorithm (CSE)

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