The Hardware Side of Cryptography

23 May 2008

Designing the Atbash encoder / decoder

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

1 Comment »

  1. UZXVH RH VVM XLNKFGVIKILTIZNNZ WZG RP TVNZZPG SVY LN TVARXSGVM GV SVIPVMMVM. RNKVO TVAVTW DVIPG SVG ZOH VVM HLLIG TLLTOV ELLI KOZZGQVH. RM KOZZGH EZM VVM LLIW ELVI QV VXSGVI VVM ZUYVVOWRMT RM. SVG KILTIZNNZ TZZG WZM LMORMV ALVPVM ZZI VVM NZGXS. ZOH QV YRQELLIYVVOW VVM ULGL EZM NZWLMMZ FKOLZWG, WZM RMWG UZXVH ZOOV DVYHRGVH DZZILK ULGL’H EZM NZWLMMZ HGZZM (VM TVOLLU NV, WZG RQM VI SVVO EVVO). DZG RP MRVG DRHG, RH WZG SVG KILTIZNNZ LLP UZNRORVOVWVM PZM ERMWVM, NRGH AV TVMLVT LK VOPZZI ORQPVM. AL SVY RP QFOORV DVYHRGVH TVELMWVM. RP TVYIFRPGV ZOH KILVU VVM ULGL EZM QFOORV YVRWV NLVWVIH VM PDZN LK QFOORV KVIHLLMORQPV KZTRMZ’H GVIVXSG.ELVI SRVILMWVI QV V-NZROZWIVH RM VM WIFP LK VMGVI ELLI WV ELOTVMWV ZZMDRQARMT.

    Comment by x — 23 December 2009 @ 6:04 pm


RSS feed for comments on this post. TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Blog at WordPress.com.

%d bloggers like this: