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Cryptography: substitution-permutation network

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Consider the following 2x2 s-box

x | S(x)
---|-------
0 | 3
1 | 1
2 | 0
3 | 2

Consider 2-round SPN (substitution-permutation network) with a block length of 4 bits. If the key mixing is done using a mod-4 addition operation before each round and after the last round, determine the ciphertext corresponding to the message m=15.

Assume the round keys as k1=11, k2=10, and k3=7.

Mod-4 operation is to solved by picking two bits blocks each time and treating them individually without propagating carry forward to next set of two bits blocks.

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Solution Summary

Solution gives detailed step-by-step computation in the sequence "key mixing, first round, key mixing, second round, key mixing".

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Numbers, in brackets below, indicate the corresponding 4 bits representation of message and key values.

m=15 (1111)
k1=11 (1011)
k2=10 (1010)
k3=7 (0111)

Bits are numbered from right(0) to left(3).
X10 indicates 2 bits value formed from (bit1 bit0) and X32 indicates 2 bits value formed from (bit3 bit2). Same is the case with Y10, ...

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