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108-Bit Elliptic-Curve Encryption Key Cracked

Irish mathematician Robert Harley and researchers at the National Institute for Research in Computer Science and Control (INRIA) of France have jointly cracked the elliptic-curve cryptography (ECC), equivalent to a key length of 108 bits, and computed the secret key. The encrypted data was ECC2K-108, released in November 1997 by Certicom Corp of Canada together with a list of public keys, in a contest to decrypt it.

The ECDL key-breaking project involved 1,300 volunteers in 40 nations. The parallel Pollard rho method proposed in 1998 was used in computation, reducing the amount of calculations to about a tenth required by the brute-force approach. The method compares pairs of calculation results, making use of the so-called “birthday paradox,” whereby the probabilities that two people will share a birthday reached 50% with only 23 people in the group.

Even this simplified calculation, however, required 9,500 computers running in parallel for four months, connected via the Internet. This works out to roughly 500 years of processing on a single 450MHz personal computer. This is thought to be about the same safety level achieved with the key length of about 600 bits of the RSA encryption developed by RSA Security Inc, which is now the de facto encryption standard for public-key encryption.

(July 2000 Issue, Nikkei Electronics Asia)

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