http://www.hinduonnet.com/thehindu/thscrip/print.pl?file=2004042600110200.htm&date=2004/04/26/&prd=ew&
Cracking secrets
A WHOLE book of secrets is what S.C. Coutinho gives in The Mathematics of
Ciphers, published by Universities Press (www.orientlongman.com) . "A
leisurely journey, with many stops to appreciate the scenery and
contemplate sites of historical interest", the author promises to reach the
final destination - RSA system of cryptography. Since the work has grown
out of lectures to first-year students of computer science, there is no
presumption of mathematics knowledge. "Cryptography is the art of
disguising a message so that only its legitimate recipient can understand
it." That should explain why we don't understand many election speeches.
Perhaps the `twin sister' of cryptography could help, cryptoanalysis: `the
art of breaking a cipher'. The most widely used public key cryptosystems is
RSA, invented in 1978 by Rivest, Shamir and Adleman. Put simply, "every
user has a personal pair of primes that must be kept secret" though the
product of these primes is made public. What's the big deal, you might ask;
factor the product and you would get the two prime numbers, won't you?
"However, if the primes have more than 100 digits each, the time and
resources required to factor `n' are such that the system becomes very hard
to break." This is the trapdoor of RSA - computing product is easy, not
factoring. For this, the `exact computation' of computer comes handy.
Greeks distinguished between logistics (the science that deals with
numbered things, not numbers) and arithmetic (nature of numbers with the
mind only).
The book is full of stories that would make you like math and computing
too. For instance, geometry originated in Egypt where the pharaoh
distributed land to people in rectangular plots on which he levied an
annual tax. "If the Nile swept away part of the plot, the surveyors had to
be called in to calculate how much land had been lost." Because the owner
would be eligible for a reduced tax, proportional to the land lost.
To find primes from the ocean of numbers, you can use the `sieve of
Erathostenes', named after a Greek mathematician born around 284 BC. He was
nicknamed `Beta' because his contemporaries believed that he hadn't reached
a truly eminent position. When you apply the sieve to a list of positive
integers, composite numbers pass through but primes get retained. Good read
for the vacation to sharpen your numbers.
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R. A. Hettinga
The Internet Bearer Underwriting Corporation http://www.ibuc.com/
44 Farquhar Street, Boston, MA 02131 USA
"... however it may deserve respect for its usefulness and antiquity,
[predicting the end of the world] has not been found agreeable to
experience." -- Edward Gibbon, 'Decline and Fall of the Roman Empire'
