Previously, i have derived both equations and schematic of ROT13 encoder/decoder. Today, i’ m going to derive another equations and schematic, which is Atbash cipher. Atbash cipher works based on substitution. The substitution table is generated by reversing the order of alphabetic character. Well, let’s see the truth table first.
Atbash Cipher Truth Table
Lets define input bits as [x1x2x3x4x5x6x7x8] and output bits as [y1y2y3y4y5y6y7y8]. We could see directly from truth table that [y1y2y3] always be the same as [x1x2x3]. Therefore, we can coclude that:
To complete the design Atbash encoder / decoder, First we have to completely derive equations for each of output bits, draw the circuit and test the circuit. We will proceed to that stage step by step.
First, we map y4 as a function of x4x5x6x7x8 into Karnaugh-Map diagram. That process results this diagram below.
Then we can define y4 as:
Second, the mapping of y5 as a function of x4x5x6x7x8 into Karnaugh-Map diagram results this diagram below.
The boolean function of y5 then defined as:
Third, the mapping of y6 as a function of x4x5x6x7x8 into Karnaugh-Map diagram results this diagram below.
The boolean function of y6 then defined as:
Forth, the mapping of y7 as a function of x4x5x6x7x8 into Karnaugh-Map diagram results this diagram below.
The boolean function of y7 then defined as:
Fifth, the mapping of y8 as a function of x4x5x6x7x8 into Karnaugh-Map diagram results this diagram below.
The boolean function of y8 then defined as:
Last, the complete circuit of Atbash Encoder / Decoder then drawn as follow
I have tested the schematic above, and it works the same as specification (truth table). You may freely use, modify and redistribute this design under the term of GNU Free Documentation License. You may view benchmarking results on links below.
BENCHMARKING
A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z
RELATED STUFF
Reference:
Atbash Cipher
