AbstractAt Crypto '84, Shamir originally proposed the concept of identity (ID)‐based cryptosystems and signature schemes. In this paper, a new realization scheme of a cryptosystem based on this concept is proposed for which the common‐key generation based on ID‐information requires neither a public directory nor interactive preparation for communication.For the principal operations of common‐key generation it is necessary to compute powers of integers modulo the product of two large Sophie Germain (SG) primes. The basis for security, as in the RSA cryptosystem, depends on the computational difficulty of factoring this product into its constituent primes. In particular, as a realization of a cryptosystem of the new ID‐based type, we permit the generation of nonsymmetric common keys and generate two different common keys for each pair of users. One key is used for enciphering and the other is used for deciphering when they are applied to a common‐key cryptosystem. The result is a very secure realization of an ID‐based cryptosystem which prevents both the disclosure of the center's secrets and a conspiracy by nonparticipants to forge a secret key between users since the exponent is nonsymmetric in the step before executing the exponentiation and it is a proper value betw