Abstract
It is shown how a chosen-public-key attack can compromise the ID-based cryptosystem of S. Tsujii and T. Itoh (1989), as well as most of the existing public-key cryptosystems. The authors present a scheme which can withstand the chosen-public-key attack, based on the concept of an cryptosystem. The security of the scheme is equivalent to factoring the product of two large primes or solving the discrete logarithm problem. It enciphers data using the receiver's ID directly without the help of a third party.