Mathematical Advances Strengthen IT Security

European Science Foundation (05/11/09) Valleley, Sofia

A new cryptography approach based on the mathematical theory of elliptic curves is considered a leading candidate to replace the widely used RSA public key security system. Elliptic curves could enable more efficient cryptography and provide an optimum combination of security and processing efficiency.

The European Science Foundation (ESF) recently held a workshop to discuss the potential for elliptic curves and other modern techniques of mathematics in cryptography and information technology security.

"The impact of the elliptic curve method for integer factorization has played a role in introducing elliptic curves to cryptographers, albeit for attacking the underlying problem on which RSA is based (the difficulty of factoring integers)," says David Kohel, convenor of the ESF workshop, from the Institut de Mathematiques de Luminy in Marseille, France. Kohel says the advantage of elliptic curve cryptography is its immunity to the specialized attacks that have degraded the strength of RSA, meaning smaller keys can be used to provide the same levels of protection.

"In general, the cryptographer has the benefit over the cryptanalyst (the person attacking the cryptosystem) as he or she can select the key size for any desired level of security, provided everyone has the same base of knowledge of best attacks on the underlying cryptosystem," he says.