Differential Cryptanalysis on S-DES

In this paper differential attack on S-DES is carried out. S-DES is the reduced version of DES algorithm. This algorithm operates on 8-bit message block with 10-bit key and DES operates on 64-bit message block with 56-bit key. This paper analyzed the differential attack on S-DES. Differential attack is used to break a cipher by trying each possible key.


INTRODUCTION
Security is the main concerns of the organizations participating in the information revolution.
Although cyber space has become new arena of information exchange and commerce, it can become a place for new forms of old crimes. Cryptographers are constantly searching for the perfect security system, a system that encrypts quickly but is hard or impossible to break. [1]

S-DES
S-DES is a reduced version of the DES algorithm. It has similar properties to DES but deals with a much smaller block and key size (operates on 8-bit message blocks with a 10-bit key). It was designed as a test block cipher for learning about modern cryptanalytic techniques such as differential cryptanalysis. It is a variant of Simplified DES. The same key is used for encryption and decryption. Though, the schedules of addressing the key bits are altered so that the decryption is the reverse of encryption. An input block to be encrypted is subjected to an initial permutation IP. Then, it is applied to two rounds of key-dependent computation. Finally, it is applied to a permutation which is the inverse of the initial permutation. [2]

DIFFERENTIAL ATTACK ON S-DES
Differential cryptanalysis is a chosen plaintext/ chosen ciphertext attack. [3] In which the attacker is able to select inputs to a cipher and examine the Output. Differential cryptanalysis provides a good understanding of the possible weakness of cipher and techniques to overcome them. Differential cryptanalysis involves the analysis of the effect of the plaintext pair difference on the resulting ciphertext difference. [4]Consider the following basic linear cipher function: C = P K We take the difference pair of ciphertext with no information about key: C C' = P K P' K C C'= P P' The above equation shows us the difference between the plaintext is the same as the difference between ciphertext because of linearity of the function. [4] ΔY given ΔX X Y 0 1 2 3 4 5 0000 01 00 10 01 00 11 01 0001 11 00 10 10 11 11 01 0010 00 00 01 01 11 11 10 0011 01 00 01 10 00 11 10 0100 10 00 10 01 00 11 01 0101 00 00 10 10 11 11 01 Table-1: Difference pair table for So S-DES is not a linear function. Thus, the difference between ciphertext is not equal to difference between plaintext. In S-DES, the difference in a ciphertext pair for a specific difference of a plaintext pair is influenced by the key [5].

Difference pairs of an s-box
The input difference pairs of an S-Box is denoted as ΔX and output difference pairs of an S-Box is denoted as ΔY.
Where, ΔX = X' X'' And ΔY = Y' Y'' X' and X'' are the plaintext and Y' and Y'' are output of difference pair table.

Difference distribution table
In this table row is represented by ΔX and column by ΔY and the element represents the number of occurrences.
 With the help of this table we can obtained the input and output values from their differences. [5] We have ΔX = 12 and ΔY = 3, Number of occurrence = 2. Then input pair is (6,10) & (10,6)  We can also find the key bits which are involved in S-Box if the input pairs and output difference are known. [5] Assuming X'=6, X''=10 and the S-Box is So.Then Y'=3 and Y''=0 & ΔY=3.Let the inputs of S-Box X'&X'' are xoring with same key and we will find the output I'&I''.I'=X' K and I''=X'' K. because we used the same key so key has no influenced on the input difference value so from the above analysis-ΔX= ΔI=6 10=12 Now from the distribution table we obtained that ΔX=12 and ΔY = 3 have the 2 possible values, so there are two possible value for the key.since ΔI=12 then the possible value I that can satisfy the distribution table is 4 and 8 for these value ΔY must be equal to zero. K=X I, the first possible key is obtained from K=I' X'=4 6=2 and K=I' X''=4 10=14. so the obtained keys are 2 and 14.in the same manner, K=I'' X'=8 6=14 and K=I'' X''=8 10=2.

Differential characteristics
With the help of differential characteristics we find the subkey, k'' used in the last round. We create a differential characteristic using the following difference pair. [6] ΔX= 12, ΔY=3

Implementation steps
Step followed in differential cryptanalysis as follows 1. The plaintext is encrypt with unknown key. 2. Now for finding the ΔI encrypt the plaintext with assumed key.

RESULT
This section shows that the result obtained by running the differential attack on S-DES in C. Round 1 input differential characteristics, ΔUi=96 When S -Box input are 2 & 10, possible key 2 & 10 are applied on S-Box & ciphertext is cracked by key 10 then key 10 is actual key.

CONCLUSION
The represented result shows that the differential attack found 8 bit of the subkey of the last round. These sub key bits are the actual 8 bits of the S-DES 10 bit key, 2 bit are still missing i.e. found by matching of 2 2 possibilities.