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1. We consider a DES-based encryption scheme, which operates on 16-bit blocks of plaintext and uses sub-key of length 12. A sketch of the encryption with first-round is given in Figure 1:

Figure 1
Consider the following bit sequence as the input data:
1011000110101100
a) Describe L1 and R1 with respect to R0, R1 and K1.
b) The 16 bits of the input are first reorganized by the following initial permutation (IP).
8 13 4 9
16 5 12 1
7 14 3 10
15 6 11 2
That is the permuted input has bit 8 of the input as its first bit, bit 13 as its second bit and so on.
(i) Write down the permuted input.
(ii) Compute the inverse permutation namely IP −1.

c) Let the 16 bits of the permuted input block consist of an 8 bit block L followed by an 8 bit block R. The internal structure of the cipher function f (see f in Figure 1) is given in Figure 2.


Figure 2
E denotes an expansion function which takes a block of 8 bits as input and yields a block of 12 bits as output according to the table given below. (The first two bits of output are the bits in position 8 and 2 and so on.)
8 2 4
1 3 2
6 1 7
5 3 8
Write down the expanded output.
d) S denotes the substitution function which takes a block of 3 bits and yields a block of 2 bits. Function is given with a table which contains the decimal representations. (ex: (101)2 = 5, so from the table, 5 corresponds to 3 which is (11)2.)

Write down the output bit sequence with a given sub-key K1 = 101101100010.
e) Write down L1 and R1 as a bit sequence.
f) Combine L1 and R1 into 16-bits bit sequence and apply the inverse permutation (IP −1 ).

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