A new probabilistic public key algorithm based on elliptic logarithms

Afonso Comba de Araujo NetoRaul Fernando Weber

This paper introduces a new probabilistic public key algorithm based on elliptic curves and show that it is secure. The security of the scheme is solely based on the difficulty of the elliptic curve discrete logarithm problem while at the same time it has a constant message expansion for one encryption of a plaintext of any practical size. In the alternative algorithms, like Cramer-Shoup and PSEC, for a large plaintext, either the message expansion is proportional to its size or an additional security assumption is needed. Although some restrictions are posed on the public part of the key, we show how to easily find the needed parameters, and also suggest ways to make the public key as small as possible.

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