Cryptography Reference
In-Depth Information
Frequency of Letters Ending Words in English
Table 1.5
E,T,S,D,N,R,Y
Table 1.5 is a list of the most common letters to
end
a word, in order of
frequency distribution, which is an example of
positional frequency
, wherein the
frequency count of the position of a given letter is taken in ratio with the total
number of letters occurring in that position over all English texts.
Now to illustrate al-Kindı's idea, suppose that we have the letter
g
occurring
most often (in word endings) in a ciphertext for a plaintext known to be in
English. Then we would deduce that the letter
e
is the most likely candidate
for the plaintext letter. If the second most frequently occurring letter is
k
in
ciperhtext, then we would guess, via Table 1.5, that the corresponding plaintext
letter is
t
, and so on. Similarly, one could use Table 1.4 on the most frequently
occurring words to deduce the plaintext.
Of course, the above tables are not written in stone. There can be the
problem of too little ciphertext to make any reasonable statistical inferences (as
with the Phaistos disk, see page 2). Moreover, it could be a specialized language
about some esoteric subject in which case the frequencies will deviate from the
standard. There is no table, or perhaps even set of tables, which can definitively
lay claim to being
the
one that is canonical for all situations in a given language.
Yet, the above tables will provide us with a general overview and therefore a
working template to discuss cryptanalytic matters throughout the text as they
arise, and we will bring more to the fore as we need them.
Another contribution from Arab civilization, albeit of less significance than
that of al-Kindı, dates to 855. The author Abu Bakr A
.
mad ben 'Ali ben
Wah
.
shiyya an-Nabati published his book,
Kitab shauq almustahamf i ma'rifat
rumuz al-aqlam
,or
Book of the Frenzied Devotee's Desire to Learn About the
Riddles of Ancient Scripts
, in which numerous cipher alphabets were included
that were typically used for magic spells. Almost five hundred years later, in
1350, 'Abd al-Ra
.
man Ibn Khaldun created his work,
The Muqaddimah
,an
historical survey detailing how government bureaucrats used symbols including
“the names of perfumes, fruits, birds, or flowers” as a code for regular let-
ters in order to encipher correspondence among oGcials of the tax and army
bureaus. The name of this particular kind of cryptography was called
qirmeh
,
which sprang up later in sixteenth-century Egypt, and even was used in financial
record-keeping of Istanbul and Syria as late as the nineteenth century.
Another major work to come out of the Arab influence on cryptology was
completed in Egypt in 1412 by an author named, Shihab al-Dın abu 'l-'Abbas
A
.
mad ben 'Ali ben A
.
mad 'Abd Allah al-Qalqashandi. (We will just call him
Qalqashandi.) His work was a prodigious fourteen-volume encyclopedia called
.
ub
.
al-a 'sha
. Our interest is in the section on cryptology. Some parts of the
section deal with steganographic techniques, such as invisible ink, and the hiding
of messages within letters. Qalqashandi claimed that most of his cryptological
ideas came from an author of the fourteenth century, none of whose writings are
extant, but cites a list of seven cryptosystems deriving from these writings. The
Search WWH ::
Custom Search