Feistel Cipher and DES Feistel Cipher Structure Horst

Feistel Cipher and DES

Feistel Cipher Structure • Horst Feistel devised the feistel cipher – based on concept of product cipher • partitions input block into two halves • process through multiple rounds which: • perform a substitution on left data half • based on round function of right half & sub key • then have permutation swapping halves • implements Shannon’s substitution-permutation network concept

Feistel Cipher Structure (1973) • Virtually all conventional block encryption algorithms including data encryption standard (DES) are based on Feistel Cipher Structure. • The plaintext is divided into two halves Then the two halves pass through n rounds of processing then combine to produce the cipher block. • Each round has as input and derived from the previous round as well as a sub-key derived from the overall

Feistel Cipher Structure (1973) q All rounds have the same structure q A substitution is performed on the left half of the data. This is done by applying a round function to the right half of the data followed by the XOR of the output of that function and the left half of the data.

Classical Feistel Network

Classical Feistel Network

Design Features of Feistel Network Ø Block Size: (larger block means greater security) 64 bits. Ø Key Size: 56 -128 bits. Ø Number of Rounds: a single round offers inadequate security, a typical size is 16 rounds. Ø Sub-key Generation Algorithms: greater complexity should lead to a greater difficulty of cryptanalysis. Ø Round function: Again, greater complexity generally means greater resistance to cryptanalysis.

Design Features of Feistel Network. Ø Round function: Again, greater complexity generally means greater resistance to cryptanalysis. Ø Fast Software encryption/Decryption: the speed of execution of the algorithm is important. Ø Ease of Analysis: to be able to develop a higher level of assurance as to its strength Ø Decryption: use the same algorithm with reversed keys.

Feistel Encryption and Decryption

Simplified DES (S-DES) • Developed by Prof. Edward Schaefer of Santa Clara University 1996. • Takes 8 bit block of plain text and 10 bit key as input and produce an 8 bit block cipher text output. • The encryption algorithm involves 5 functions: initial permutation (IP); a complex function fk which involves substitution and permutation depends on the key; simple permutation function (switch) SW; the function fk again and final inverse of the initial permutation( IP-1).

Simplified DES Scheme

Overview • We can express the encryption algorithm as a composition function: IP-1 fk 2 SW fk 1 IP OR ; Ciphertext=IP-1(fk 2(SW(fk 1(IP(plaintext))))) Where, K 1=P 8(shift(P 10(key))) K 2 =P 8 (shift(P 10(key)))) • The decryption algorithm is: Plaintext=IP-1 (fk 1(SW(fk 2(IP(Ciphertext)))))

Key Generation for S-DES

Key Generation for S-DES • First permute the key in the following way: P 10 3 • • 5 2 7 4 10 1 9 8 6 Ex: (1010000010)is permuted to (1000001100) Perform a circular left shift to each bits of the key: Ex: (10000 01100) (00001 11000) Next apply P 8 6 3 7 • This yields K 1=(10100100) 4 8 5 10 9

Continue… • Then perform again 2 bit circular shift left on each of the five bits: (00001)(11000) (00100)(00011) • Finally apply again P 8: • Then K 2=(01000011)

S-DES Encryption

S-DES Encryption • The i/p 8 -bit block plaintext is first permuted using the IP function: IP 2 6 3 1 4 8 5 7 • At the end of the algorithm the inverse permutation is used : IP-1 4 1 3 5 7 • IP-1(IP(X))=X; • Ex: IP{(10110101)}=(01111100) • IP-1 {01111100}=(10110101) 2 8 6

The Function fk • Let L and R be the left most 4 bits and rightmost 4 bits of the 8 bits input fk (L, R)=(L F(R, SK), R) • Where SK is a sub key and the is bit-by-bit XOR function. • Ex: if the o/p of the IP is (10111101) and F(1101, SK)=(1110) for some SK then fk(10111101)=(1011) (1110)=(0101)

Continue… • Recall the first operation is an expansion and permutation to first 4 bits as follows: E/P 4 1 2 3 4 1 • We can depict the result as : n 4 n 1 n 2 n 3 n 4 n 1 • The 8 bit key K 1 is added to this value using XOR: n 4+K 11 n 1+ K 12 n 2 +K 13 n 3 +K 14 n 2 +K 15 n 3 +K 16 n 4 +K 17 n 1 +K 18

Continue… • Let us rename these bits: P 0, 0 P 0, 1 P 0, 2 P 0, 3 P 1, 0 P 1, 1 P 1, 2 P 1, 3 • The first row of the matrix 4 bits are fed into the Sbox S 0 to produce 2 bit o/p and the remaining 2 bits are fed to S 1 to produce another 2 bits

S-Box • The s-box operates as follows: (P 0, 0, P 0, 3 ) determine the row of the S 0 matrix and (P 0, 1, P 0, 2 )determine the column: • Ex: if (P 0, 0, P 0, 3 ) =(00), (P 0, 1, P 0, 2 )=(10) then the o/p is from row 0 and column 2 in S 0 which is equal to 3, i. e. , (11) in binary. • In a similar way we can produce the other two bits

The Switch Function (SW) • SW interchange the left and right 4 bits so that the second instance of f. K operates on a different 4 bits.