From the Riddles of Ancient Egypt to Cryptography in the Renaissance — 3500 Years in the Making - Codes: The Guide to Secrecy from Ancient to Modern Times - page 46

list is of historical significance insofar as it marked the first intermingled use of
both substitution and transposition ciphers (a common feature of modern-day
cryptosystems). Furthermore, it provided the first cipher ever to have more than
one ciphertext for a given plaintext symbol. Of greatest note are the tables of
letter frequency analysis and other cryptanalytic analyses such as letters that
cannot occur together in the same word. Here, again, is a contribution from the
Arab civilization to cryptanalysis. Such cryptanalytic techniques are the reason
that, for instance, simple substitution ciphers (the monographic ones) are so
easy to cryptanalyze, because the frequency of letters in the ciphertext is the
same as the frequency of letters in the plaintext. Thus, once the language is
known, the plaintext can usually be relatively easily deduced. Hence, from the
above, we may conclude that cryptanalysis was therefore born with the Arabs.
Outside cryptography, Arab scholars enlightened Europe's exit from the
Dark Ages by preserving much of the mathematics from antiquity. One of
the major reasons for this was a vision had by Caliph al-Ma'm ¯ n (809-893). In
this epiphany, he was visited by Aristotle, after which he was compelled to have
all the Greek classics translated into Arabic.
Another story is that of the Persian mathematician and astronomer,
Mu ¯ ammed ibn M ¯ s ¯ al-Khw ¯ rizm ¯ , who lived under the caliphate of al-
Ma'm ¯ n. We owe al-Khw ¯ rizm ¯ for the introduction of the Hindu-Arabic num-
ber system. Around roughly 825, he completed a book on arithmetic, which
was later translated into Latin in the twelfth century under the title Algorithmi
de numero Indorum . This topic was one of the principal means by which the
Hindu-Arabic number system was introduced to Europe after being launched
in the Arab world. This accounts for the widespread, but mistaken, belief that
our numerals are arabic in origin. (Numerals dating from 150BC have been
found inscribed in a cave at Nana Ghat, close to Bombay, India. Moreover,
the first documented appearance of a zero, 1.3 as we know it, is an inscription
on a birch-bark manuscript dated 400 AD, discovered in 1881 at Bakhashali,
a village in northwest India.) Not long after the Latin translations appeared
in Europe, readers began contracting al-Khw ¯ rizm ¯ 's name until it became the
norm to associate algorithm with these numerals. (Today we use the term “al-
gorithm” to mean any methodology following a set of rules to achieve a goal.)
Al-Khw ¯ rizm ¯ also wrote a book on elementary algebra, Hisab al-jabr wa'l-

muqabala . The word algebra is derived from al-jabr or restoration . 1.4 His third
major work was Kit ¯ b ¯¯ rat al-ar ¯ , which translates best as Geography . This
assisted in his construction of a world map for al-Ma'm ¯ n, including a determi-
nation of the circumference of the earth by measuring the length of a degree of
a meridian through the Plain of Sinj ¯ r in Iraq, amazing achievements!

1.3 The goose-egg symbol 0 for the zero is sifr in Arabic, from which our zero is ultimately
derived. In the thirteenth century AD, the term sifra was introduced into the German language
as cifra , from which we get our present-day word cipher .
1.4 In the Spanish work Don Quixote (Part I in 1605, and Part II in 1615), by Miguel de
Cervantes, the term algebrist is used for bone-setter or restorer .