Cryptography Club October 1, 2003
JJArmbruster
Tri-Numeral Alphabets
Introduction
The purpose of this document is to familiarize the reader with some elementary methods of enciphering English characters by using Tri-Numeral alphabets. While developing these systems, certain characteristics will be brought forth that illustrate both the strengths and weaknesses of the system. The primary goal will be to avoid elementary cryptanalysis methods and explore interesting and alternative methods of hiding information.
A Tri-Numeral Alphabet
A / 111 / J / 211 / S / 311B / 112 / K / 212 / T / 312
C / 113 / L / 213 / U / 313
D / 121 / M / 221 / V / 321
E / 122 / N / 222 / W / 322
F / 123 / O / 223 / X / 323
G / 131 / P / 231 / Y / 331
H / 132 / Q / 232 / Z / 332
I / 133 / R / 233 / 333
The Tri-Numeral Alphabet
The Tri-Numeral alphabet, as illustrated above can be used to encipher characters in several ways. The first method to be considered is straight substitution. The method of enciphering with substitution is illustrated below:
PT:ALPHABRAVO
A = 111,L = 213,P = 231, H = 132, A = 111
B = 112,R = 233,A = 111,V = 321,O = 223
CT:111213231132111112233111321223
It is known that simple substitution methods are not considered secure. Given a sufficient amount of text, it is possible to perform frequency analysis on the text and search for known properties of the English language. One observation of the system is that individual character frequency data is kept constant (with respects to considering blocks of 3 units in the cipher text). It would be nice if we could improve upon this method by adding a transformation that would obscure a frequency attack.
:: A Note on Key space ::
A permutation cipher using the standard twenty six letter English alphabet has 26! = 403291461126605635584000000 possible keys. However, most permutation ciphers can be broken in a matter of minutes!
Activity:Construct a transformation, which would rid the possibility of a
frequency attack on the given cipher text and describe it in the space below:
One method that can be used is a transposition transformation. Suppose a keyword was agreed upon in advance (where the keyword is an English word of more than two distinct characters). Consider the previous ciphertext and the following key:
K:DELTA
CT:111 213 231 132 111 112 233 111 321 223
D / E / L / T / A1 / 1 / 1 / 2 / 1
3 / 2 / 3 / 1 / 1
3 / 2 / 1 / 1 / 1
1 / 1 / 2 / 2 / 3
3 / 1 / 1 / 1 / 3
2 / 1 / 2 / 2 / 3
The transposition is performed by first constructing a matrix using the keyword. Once the matrix is written, the values of the cipher text are written inside, row by row as illustrated below:
The transformation is performed by reading off the columns in alphabetic order according to the key. Given the keyword DELTA, the first column would be A, the second column would be D and so forth onto T. This transformation is illustrated below:
A:111 333
D:133 132
E:122 111
L:131 212
T:211 212
The characters in order are then written into rows and transmitted across the wire. The new addition to the previous system has resulted in the following overall transformation:
K:DELTA
PT:ALPHABRAVO
CT1:111213231132111112233111321223
CT:111333133132122111131212211212
:: Historical note ::
A field cipher named ADFGX was used during WWI by the Germans. To encipher, a keyword was chosen. The first transformation was a digraph substitution based on a Polybius square. The second transformation was columnar transposition. On June 1, 1928 the cipher was replaced by ADFGVX. French Cryptanalysist Georges Painvin and the Bureau du Chiffre successfully deciphered several messages written using ADFGVX. This work led to the halt of the German offensive on June 9, 1918.
The final Tri-Numeral method which will be discussed concerns steganography or hiding the existence of information in a medium. This method, using a Tri-Numeral alphabet was first used by Abbe Tritheme. The medium which data will be hiding is normal English sentences. The plaintext is first transformed using the Tri-Numeral alphabet table. The text is then transformed by constructing English words based on the number of syllables requested by the intermediate text. The process is illustrated below:
PT:BARK
CT1:112 111 233 212
1Who
1is
2telling
1me
1not
1to
2manage
3laborious
3 property
2Someone
1named
2Joseph
CT: Who is telling me not to manage laborious property? Someone
named Joseph.
This cipher system is one that is rather amusing to experiment with. It is observed that constructing sentences to fit to the numerical values given is not very difficult. However, it should be noted that this is a substitution cipher. The security of the system fully depends on the individual who intercepts it, not realizing there is a cipher hidden within. In general, basing the security of the cipher system on this is not good enough.
:: Kerckhoffs’s Principle ::
When assessing a cryptosystem, it is always assumed that the enemy knows the method being used. This principle was brought forth in “La Cryptographie Militaire” by Auguste Kerckhoffs (1883).