Q. Explain one round of cipher. You can assume that key expansion is done by a separate process. Don’t need to explain that. You can assume that your encryption function takes an array of N keys, where N is the number of rounds in your cipher.

Structure of cipher is similar to SPN.

Keylength=32 , Blocklength=32

Assuming Kr is the round key used in the round We divide the input into 8 blocks of 4 bits each,the following are done in 1 round of cipher

1.Substitution: 4x4 sbox is used here.

The operations in substitution are:

a.Finding inverse in field$(2^4)$
If input is 0000 ,then ouput is 0,inverse of input infield$(2^4)$ otherwise . The irreducible polynomial used here is $x^4+x^3+1$. But this may ensure fixed points i.e s(0000)=0000 s(0001)=0001

b.Xoring with an appropriate 4 bit number c=0011 Xoring with 0011 after obtaining inverse ensures no fixed points Substitution layer is the confusion layer.

2.Permutation layer:

This has 2 operations:

a.Linear Transformation For ensuring permutation we use MDS matrix as they ensure high branch number

MDS matrix choosen M is $$ \begin{pmatrix} 2&3&1&1\\ 1&2&3&1\\ 1&1&2&3\\ 3&1&1&2\\ \end{pmatrix} $$

We divide the input say a1a2a3a4a5a6a7a8(where ai corresponds to 1 block of 4 bits) and apply the transformation M*$$ \begin{pmatrix} a1&a2\\ a3&a4\\ a5&a6\\ a7&a8\\ \end{pmatrix} $$

b.Shifting Let the input be b1b2b3b4b5b6b7b8 after applying linear transformation to given input,then it would result in b5b6b7b8b1b2b3b4 after applying shifting Permutation layer is the diffusion layer in the cipher

3.Xoring with round key This ensures mixing between round input and round key