The Philadelphia Inquirer from Philadelphia, Pennsylvania on May 16, 1982 · Page 42
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The Philadelphia Inquirer from Philadelphia, Pennsylvania · Page 42

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Philadelphia, Pennsylvania
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Sunday, May 16, 1982
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Page 42
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4-C Sunday. May 16, 1982 Philadelphia Inquirer Secret math code cracked, posing a problem anew ByLeeDembart Los Angeles Times Service LOS ANGELES A new secret code, previously thought to be unbreakable, has been broken in a stunning mathematical accomplishment that underlines the difficulty of maintaining security for computer networks and electronic communications. The feat was achieved in the last few weeks by Adi Shamir, a computer scientist at the Weizmann Institute in Rehovot, Israel, who privately communicated his results to several colleagues in the United States, including the inventors of the system he broke. One of them, Ralph C. Merkle, formerly of Stanford and now with a computer company, Elxsi, based in Sunnyvale, Calif., in 1976 had offered a $100 prize to anyone who could break the code. Last week, Shamir . received a $100 check from Merkle. "I am quite impressed," Merkle said. "It is undeniably a great breakthrough." - The need to develop unbreakable ... codes has grown enormously in recent years as society has become increasingly dependent on computers, which are extremely insecure. It is well known that a determined criminal or prankster can gain access to private records in virtually any computer. One scheme for thwarting such attacks is to encode the data in computer memories so that even if someone gets in, he cannot read or manipulate it. The projected growth of electronic mail highlights the need for a similar encoding system to keep private communications private. In 1976, in a paper titled "New Directions in Cryptography," Whitfield Diffie and Martin E. Hellman of Stanford University proposed a revolutionary system of codes based on difficult mathematical problems that even by the most sophisticated crypt-analysts would take millions of years to break. "The breakthrough bids fair to revolutionize the entire field of secret communication," Martin Gardner wrote in Scientific American. The Diffie-IIellman paper gave a theoretical framework for the codes, and two competing systems were proposed to make use of the idea, which is based on the fact that some mathematical processes are easy to perform but difficult to undo. As a result, they are called trapdoor functions, so called because it is easy to fall through a trapdoor but hard to climb out. Unlike traditional codes, the metlv od of encoding and the method of decoding are different, so knowing how to encode does not help in know ing how to decode. Because the en coding method can be publicly known, these are called public key cryptosystems. One of the systems, proposed by Shamir, Ronald L. Rivest and Leon ard M. Adleman, who were all then at the Massachusetts Institute of Tech-nolgy, was based on the virtual impossibility of factoring very large numbers into their constituent primes. For example, it is easy to' determine that 55 can be factored into 5 times 11, but it is very, very hard to figure out the factors of a 100-digit number. Rivest, Shamir and Adleman have a standing offer of $100 to anyone who can crack a code written in their scheme, which they call RSA. Adleman, who is now at the University of Southern California, said of his group's $100 prize and the $100 that Shamir has just collected: "It's not the money; it's like getting the ear of a bull." He insisted that it was unlikely that anyone would be able to break an RSA code. "While there have been incremental improvements in factoring," he said, "it is recognized that no breakthroughs have occurred and none are expected." The other coding system, developed by Merkle and Hellman, is based on a different problem, called the knapsack problem. This is the one that Shamir successfully broke. . Suppose there is a knapsack that can hold a given amount of material and a collection of objects all of the different sizes and weif hts that you would like to take with you on a trip. What is the optimum number that can be carried in the knapsack? A similar problem: Suppose there is a long line of known length and a collection of sticks of different lengths. Can some number of sticks be placed end to end so that they exactly equal the length of the line? A similar problem: Suppose there is some large number, called the target number, and a series of, say, 100 numbers that go with it. Can nuni bers be selected from the series so that their sum is exactly equal to the target number? It turns out that if the numbers are large, these are very difficult prob lems. 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