Cryptography Reference
In-Depth Information
Now for any language, such as English, with a twenty-six-letter alphabet, in
which each letter has the
same
frequency, we get
= 26(1
/
26)
2
=0
.
038
,
IC
which is approximately half of the above Index of Coincidence for English.
Hence, the Index of Coincidence helps us in determining if the ciphertext comes
from a monoalphabetic or polyalphabetic cipher in the following manner. The
closer the
is to 0
.
065, the more likely it is that the message came from a
monoalphabetic cipher. If the
IC
is much less than 0
.
065, the cipher is most
likely polyalphabetic since frequencies are evened out by polyalphabetic cryp-
tosystems. Hence, the closer the
IC
is to 0
.
038, the greater the chance is that
the cipher is polyalphabetic. This was a major contribution by Friedman since
he tied a mathematical tool, statistical analysis, to the study of cryptography.
Another young professor did the same in another area of mathematics.
Lester S. Hill published a short paper [123] in which he put a cipher, known
today as the
Hill Cipher
(which we will study in detail on page 111), into an
algebraic framework. This was a reinvention and expansion of Porta's idea (see
page 54). Hill obtained his Ph.D. in mathematics from Yale in 1926. He was
hired to teach mathematics at Hunter College in New York in 1927, and he
remained there until his retirement in 1960. He was the first to successfully
use general algebraic concepts to reveal cryptography through mathematics.
A.A. Albert (see Footnote 2.15 on page 97) was so impressed with Hill's ideas
that he used them in some simple cryptosystems with his own tailoring to suit
the situation at hand. Hill's rigorous mathematical approach was certainly
one of the pioneering efforts that helped to build today's solid grounding of
cryptography in mathematics. Hill died in Lawrence Hospital in Bronxville,
New York, after suffering though a lengthy illness.
Now we return to the life of the Friedmans. Soon after his marriage to
Elizabeth, William became the director of the Department of Codes and Ci-
phers, among his other duties, at Riverbank. After the outbreak of World War
I, Riverbank offered its services to the government, and since no such federal
agency existed at the time, Riverbank became the
de facto
cryptographic center
for the American government. One of the first accomplishments the Friedmans
achieved was the following. The Germans had been encouraging Hindu radicals
to work toward independence from Britain in the hopes of diverting attention
and strength from the war effort. Some of these radicals, who lived in the United
States, were sending messages about arms shipments. It turns out they were try-
ing to buy arms in the United States and ship them from the West Coast. The
Friedman's deduced that the codebook used by these radicals was a German-
English dictionary published in 1880. This aided William in his testimony given
at the trial of 135 Hinduradicals in San Francisco.
The Friedmans quit Riverbank toward the end of 1920. In 1921, Friedman
joined the American Black Chamber, where he eventually headed the Research
and Development Division and stayed there until its dissolution in 1929. One
man may be said to be chiefly responsible for the creation and (possibly) the
dissolution of the American Black Chamber.
IC
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