Thursday, October 12, 2017

DIANA - A Fast Reciprocal One Time Pad Table

There are various ways to perform one-time pad encryption with letter pads. The Vigenére table is a well known method to encrypt or combine plain and key text into cipher text and vice versa. However, Vigenére has some serious drawbacks. It is cumbersome, time consuming and finding the cross section between letter and key is prone to mistakes. Also, key and cipher text must be processed in the same order by both sender and receiver.

A way faster and easier system is the reciprocal DIANA table. For each column letter there is a normal alphabet and a reversed alphabet. For each column, the reversed alphabet is shifted one position against the previous reversed alphabet and the table is statistically secure (1/26 chance to produce any cipher letter). Such reciprocal tables come in various formats but they all use the same principle. Note that this table is not compatible with the Vigenére table.

Thanks to its reciprocal properties, encryption and decryption are identical and require only a single column. The order of plain, key and cipher letter don't matter and may even differ for sender and receiver. The table is easy to use and it's virtually impossible to make a mistake.

The DIANA Reciprocal One-time Pad Table ( download .txt file format)

To encrypt, we either write plaintext under key or key underneath plaintext. The choice is yours. For each combination of key and plain letter we take the table column that corresponds to the first letter and search underneath it for the second letter on the left. The lower-case letter to its right is the result.

In the example below we wrote the plaintext above the key. To encrypt T with X, find column T in the table, go downward to letter X and find cipher letter j at its right. Thanks to the reciprocal system it doesn't matter whether you combine T with X or X with T. Quite handy!
Plaintext : T H I S   I S   T H E  S E C R E T
OTP-Key   : X V H E   U W   G T P  N O P G D Z 
----------------------------------------------
Ciphertext: J X K D   X L   A Z G  U H I C S H

In groups : JXKDX LAZGU HICSH
To decrypt, take column X, go downward to J and find plain letter t at its right. Again, the order of key and cipher letter don't matter. The beauty of this system is the ease and speed of finding plain and cipher letters in whatever order you like best.

There is also a method to memorise the DIANA table and speed up the process even more. When encrypting F + G = O, we can decrypt this as O + G = F, but also as G + O = F. We call this the trigram combination FGO. Because of the reciprocal property, we can use the trigram FGO for any possible combination, that is, FGO, FOG, OFG, OGF, GFO and GOF.

Thus, if you encrypt or decrypt any letter from a trigram with another letter from that trigram you will always get the remaining letter of that trigram, regardless of the order. We therefore only need to remember the trigram FGO and instantly know every variation of the trigram. This reduces the number of combinations to memorise from 676 to 126. FGO can easily be remembered as the word "FOG".

Any user can create his list of mnemonics by memorising the 126 possible trigrams in any desired order. Some other examples are TAG (derived from AGT), BAY (derived from ABY), AIR (as itself), FDR (Franklin D Roosevelt, derived from DFR), HRB (HR Bureau), NNZ (Northern New Zealand), AMN (A-Mu-Nition), BGS (Better Get Smart), MBM (My Best Mate), JTX (Jump The Ex), VHX (Very Hot Ex), WXG (Wild X-Games) or OXO (the game). Tickle your imagination to find your own.

Everyone has his own connotations to easily remember the trigrams. Well trained operators can encrypt and decrypt on-the-fly at high speed without using any table, which is sheer impossible with Vigenére's 676 bigram combinations.

The full list of trigrams (in alphabetic order) to be memorised as any desired combination (e.g. ABY is also AYB, BAY, BYA, YAB and YBA):

AAZ ABY ACX ADW AEV AFU AGT AHS AIR AJQ 
AKP ALO AMN BBX BCW BDV BEU BFT BGS BHR
BIQ BJP BKO BLN BMM BZZ CCV CDU CET CFS
CGR CHQ CIP CJO CKN CLM CYZ DDT DES DFR
DGQ DHP DIO DJN DKM DLL DXZ DYY EER EFQ
EGP EHO EIN EJM EKL EWZ EXY FFP FGO FHN
FIM FJL FKK FVZ FWY FXX GGN GHM GIL GJK
GUZ GVY GWX HHL HIK HJJ HTZ HUY HVX HWW
IIJ ISZ ITY IUX IVW JRZ JSY JTX JUW JVV
KQZ KRY KSX KTW KUV LPZ LQY LRX LSW LTV
LUU MOZ MPY MQX MRW MSV MTU NNZ NOY NPX
NQW NRV NSU NTT OOX OPW OQV ORU OST PPV
PQU PRT PSS QQT QRS RRR


With one-time letter pads, punctuations and figures in the plaintext are usually spelled out. However, to limit the message length you generally omit punctuations where it doesn't affect readability. Alternatively, you could use rare letter combinations as a prefix to convert figures or punctuations into letters, for instance QQ or XX.

In that case XXF could be used to switch to figures and XXL to switch to letters, with ABCDEFGHIJ representing the digits 1234567890. Thus, 2581 would become XXFBEHAXXL or XXFBBEEHHAAXXL to exclude errors, which is more economical than having to write out 2581 in letters. XXP could be a period, XXK a comma and XXS a slant. XXC could be Code, a prefix for three or four-letter codes to replace long words or sentences, like XXCABC, where ABC represents “Request further information” or "My location is..."

And the best of all, one-time pad encrypted messages are absolutely unbreakable if the one-time pads are used once only (hence one-time) and destroyed immediately after use. Of course, the letters should be truly random (no algorithm based pseudo-random) and generated either by hardware or a dedicated computer, never connected to the Internet, and printed on a dedicated printer.

You can download the Reciprocal OTP Table and the Reciprocal Trigram List (right-click and save). More technical and historical information about various one-time letter pads and one-time figure pads at Cipher Machines and Cryptology.

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