Extraction of Symmetry Properties Using Correlation with Rotated and Reflected Images.

At Crypto '84, Shamir originally proposed the concept of identity (ID)-based cryptosystems and signature schemes, ln 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 commonkey 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 nonpartici pants to forge a secret key between users since the exponeait is nonsymmetric in the step before executing the exponentiation and it is a proper value between two users partial one; thus, it can extract the symmetrical property that exists only partially. Although a large amount of computation and storage capacity is required, the method is fundamental, versatile, and suited to the parallel computation. [ABSTRACT FROM AUTHOR]