Cryptography Reference
In-Depth Information
2.3 Combined Substitution: Digram Substitutions
Though 'digram substitution' is a term that sounds rather scientific, it hides
something very simple. In Section 2.1, we substituted
single
characters by
other characters based on a fixed rule. With digrams, we substitute
character
pairs
by other characters or character pairs. According to [BauerMM, 4.1.1],
the oldest representation of such a method dates back to 1563, and the inventor
was Giovanni Porta. He constructed 625 hieroglyphs for all possible 25*25
pairs of successive letters, where 'J' is substituted by 'I', and blanks were
omitted, and lowercase letters were converted to uppercase letters.
This method can theoretically be attacked similar to simple substitution, namely
using frequency analysis. However, as we have seen in Table 2.1, the frequen-
cies of single digrams do not differ as much as the frequencies of letters. In
this case, it is normally a good idea to consider the characteristic pattern of
the language more intensely and, above all, exploit the fact that many digrams
virtually never occur. (Even a negative statement can be extremely helpful in
cryptanalysis!)
Moreover, the statistical analysis is generally more sophisticated, compared
with the Gold Bug example. Since the statistical distribution of digrams is
more even than it is with letters (see Table 2.1), we would arrange them by their
frequencies and then try to find a match in the digram frequencies of a typical
language, where deviations are legitimate to a certain extent. Moreover, we have
to pay attention to side conditions, for example, that certain digrams follow one
another either almost never or particularly often, and that single frequencies
depend on one another. Digrams blur the structure of the language, but don't
remove it. Everything together produces a huge puzzle, but it shouldn't pose
an insurmountable hurdle for today's computer technology.
My dad, who was a radio operator in World War II, taught me another method,
which also uses only 25 uppercase letters. The key consists of two squares
arranged next to each other, 5*5. The alphabet is entered in secret sequence in
each of these squares:
HQEFK
WHSFK
RYBOD
LPDNQ
NUGIS
EIUXY
APCMZ
VBOAM
LWJVX
RCGTZ
