Data Encryption Standard

Overview:

The data encryption standard is probably the most widely used conventional encryption algorithm.

A detailed study of DES provides an understanding of the principles used in other conventional encryption algorithms.

Compared to public-key encryption schemes such as RSA, the structure of DES and most conventional encryption algorithms, is very complex.

Accordingly, we begin with a simplified version of DES, called S-DES.

Classroom experience indicates that a study of this simplified version enhances understanding of DES.

S-DES:

It is an educational algorithm rather than a secure encryption algorithm.

The S-DES encryption algorithm takes an 8-bit block of plaintext (e.g. 10111101) and a 10-bit key as input and produces an 8-bit block of ciphertext as output.

Whereas the original DES uses 64-bit block of plaintext and 56-bit key.

The S-DES decryption algorithm takes an 8-bit block of ciphertext and the same 10-bit key to produce the original plaintext.

The encryption algorithm involves FIVE functions:

o An initial Permutation (IP) o A complex function labeled fk – involves permutation and substitution o A simple permutation function that switches the two halves of the data o The function fk again o A permutation function that is the inverse of the IP (IP-1)

See figure 3.1 for complete process of S-DES.

10-bit key

ENCRYPTION DECRYPTION

P10 8-bit plaintext 8-bit plaintext

Shift IP IP-1

P8 K1 K1 fK fK

Shift SW SW

P8 K2 K2 fK fK

IP-1 IP

8-bit ciphertext 8-bit ciphertext

Figure 3.1 Simplified DES Scheme 10-bit key

10

P10

5 5

LS-1 LS-1

5 5

P8 8 K1

LS-2 LS-2

5 5

P8 8 K2

Figure 3.2 Key Generation for Simplified DES 8-bit plaintext 8

IP 4 f 4 K E/P 8 F 8 + K1 4 4

S0 S1 2 2

P4 4

+ 4

SW 4 f 4 K E/P 8 F 8 + K2 4 4

S0 S1 2 2

P4 4

+ 4

IP-1 8 8-bit ciphertext

Figure 3.3 Simplified DES Encryption Detail

S-DES Key Generation for S-DES: An Example

10-bit key: 1-2-3-4-5-6-7-8-9-x 1-0-1-0-0-0-0-0-1-0

P10: 3-5-2-7-4-x-1-9-8-6 1-0-0-0-0-0-1-1-0-0

5-bits 5-bits 1-0-0-0-0 0-1-1-0-0

LS-1: Circular left LS-1 LS-1 shift by 1 bit => 0-0-0-0-1 1-1-0-0-0

Merge: 1-2-3-4-5-6-7-8-9-x 0-0-0-0-1 0-0-0-0-1-1-1-0-0-0 1-1-0-0-0

P8: 6-3-7-4-8-5-x-9 0-0-0-0-1 1-0-1-0-0-1-0-0 1-1-0-0-0 This is the key K1

LS-2: Circular left LS-2 LS-2 shift by 2 bits => 0-0-1-0-0 0-0-0-1-1

Merge: 1-2-3-4-5-6-7-8-9-x 0-0-1-0-0-0-0-0-1-1

P8: 6-3-7-4-8-5-x-9 0-1-0-0-0-0-1-1 This is the key K2

S-DES S-DES: An Example

8-bit plain text: 1-2-3-4-5-6-7-8 1-1-1-1-0-0-1-1

IP: 2-6-3-1-4-8-5-7 1-0-1-1-1-1-0-1

Left 4-bits: Right 4-bits: Right 4-bits: 1-0-1-1 1-2-3-4 1-1-0-1 1-1-0-1

E/P: Expansion/Permutation: 4-1-2-3-2-3-4-1 1-1-1-0-1-0-1-1

XOR: 1-1-1-0-1-0-1-1 1-0-1-0-0-1-0-0 (Key K1) 0-1-0-0-1-1-1-1

Left 4-bits: Right 4-bits: 0-1-0-0 1-1-1-1

First &Last bits: First &Last bits: 0,0 = 0 1,1 =3 Second & Third bits: Second & Third bits: 1,0 = 2 1,1 = 3

S0 0 1 2 3 row = 0 row = 3 S1 0 1 2 3 0 1 0 3 2 column = 2 column = 3 0 0 1 2 3 1 3 2 1 0 Use S0 Box Use S1 Box 1 2 0 1 3 2 0 2 1 3 3 3 2 3 0 1 0 3 3 1 3 2 3 2 1 0 3 In bits: In bits: 1-1 1-1

New 4-bits: 1-2-3-4 1-1-1-1

P4: 2-4-3-1 1-0-1-1 1-1-1-1

XOR: 1-0-1-1 1-1-1-1 0-1-0-0 1-1-0-1 (Left 4-bits) (Right 4-bits)

SWITCH

Left bits: Right bits: Right 4-bits: 1-1-0-1 1-2-3-4 0-1-0-0 0-1-0-0

E/P: Expansion/Permutation: 4-1-2-3-2-3-4-1 0-0-1-0-1-0-0-0

XOR: 0-0-1-0-1-0-0-0 0-1-0-0-0-0-1-1 (Key K2) 0-1-1-0-1-0-1-1

Left 4-bits: Right 4-bits: 0-1-1-0 1-0-1-1

First &Last bits: First &Last bits: 00 = 0 11 =3 Second & Third bits: Second & Third bits: 11 = 3 01 = 1

S0 0 1 2 3 row = 0 row = 3 S1 0 1 2 3 0 1 0 3 2 column = 3 column = 1 0 0 1 2 3 1 3 2 1 0 Use S0 Box Use S1 Box 1 2 0 1 3 2 0 2 1 3 2 1 2 3 0 1 0 3 3 1 3 2 3 2 1 0 3

In bits: In bits: 1-0 0-1

New 4-bits: 1-2-3-4 1-0-0-1

P4: 2-4-3-1 1-1-0-1 0-1-0-1

XOR: 1-1-0-1 0-1-0-1 1-0-0-0 0-1-0-0 (Left 4-bits) (Right 4-bits)

1-2-3-4-5-6-7-8 1-0-0-0-0-1-0-0

IP-1: 4-1-3-5-7-2-8-6 0-1-0-0-0-0-0-1 (This is the 8-bit cipher text)

BRUTE-FORCE ATTACK: With 10-bit key, there are only 210 = 1024 possibilities. Given a ciphertext, an attacker can try each possibility and analyze the result to determine if it is a reasonable plaintext.

CRYPTANALYSIS: Assume some 8-bit plaintext and the corresponding ciphertext are known and 10-bit key is unknown. S-box makes the S-DES non-linear and makes the cryptanalysis difficult.

Possible non-linear equation for the 4-bit (a, b, c, d) input to S-box and the 4-bit (q, r, s, t) output from the S-Box would be: q=abcd+ab+ac+b+d r=abcd+abd+ab+ac+ad+a+c+1