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Abstract mathematics simplified

india Updated: Nov 15, 2006 18:45 IST
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AFTER A last minute scramble to reach the office/dating venue/airport in time you suddenly realise that you’ve left your wallet behind. Well, you sigh gratefully, “Thank God for the ATM (automated teller machine)”.

And PGP, you might well add. Pretty Good Privacy, or PGP as it’s commonly known, is  an algorithm-based cryptography package that allows customers to withdraw money from ATMs using a Personal Identification Number (PIN), a secret code and a microprocessor card. Making sure the buck only stops where it’s supposed to.

The algorithm-based system is just one example of abstract mathematical research finding practical applications in securing online transmission, be it data or cash, ensuring that the virtual world is virtually theft free.

The linkage between classical arithmetic and online security was the subject of a fascinating lecture by French savant Michel Waldschmidt titled ‘From Classical Arithmetic to Information Science: Some applications of abstract research’.  The lecture, organised jointly by Alliance Francaise and Devi Ahilya University, was delivered at the University auditorium on Tuesday afternoon.

Addressing a packed hall comprising would-be engineers, computer specialists and a horde of students from South Indian Cultural Association (SICA) School, the bearded Professor traced the growth of classical arithmetic over a 2000-year-old period, from Euclid on to Agrawal, Kanyal and Saxena - the IIT troika who found a quick solution to a timeless problem: How to determine whether a given number is a prime number.

Numbers are basic not only for mathematics but for all sciences; a deeper knowledge of their properties is fundamental for further progress, declared Waldschmidt, a recipient of the Prix Marquet by the French Academy of Sciences and the Distinguished Award by the Hardy-Ramanujam Society.

Although there’ve been remarkable achievements, especially during the last few years, a number of questions remain unanswered, added the Frenchman who serves as the vice-president of the International Centre of Pure and Applied Mathematics.

An unexpected fallout of abstract mathematical research was its use in improving online security by providing nearly fool-proof cryptology including the celebrated Ron Rivest, Adi Shamir, and Leonard Adleman (RSA) encryption algorithm that employs prime numbers.

“With virtual cash transactions increasingly common online security is a major concern. Mathematics, which has many unsolved problems that involve millions of digits, provides the tools needed for encryption,” Waldschmidt told the Hindustan Times.

He, however, added that nascent techniques could pose a major challenge to arithmetic-based encryption techniques. “Systems based on Elliptic curves, Jacobian of elliptical curves and Quantam cryptography, especially the last, have displayed promises during lab tests. However, it’s too early to predict whether these will replace algorithm-based encryption techniques.’’

DAVV acting Vice Chancellor Dr Rajkamal, Director Alliance Francaise de Bhopal Frank Lelarge, Coordinating Secretary Alliance Francaise Neha Dawar and Neha Bhagat were among those who attended the lecture.

The proceedings concluded with the acting V-C presenting a memento to Professor Michel Waldschmidt. Director, Electronic Media Research Centre, Prabhakar Singh proposed a vote of thanks.