A realization scheme for the identity‐based cryptosystem
Hatsukazu Tanaka · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1990
Abstract At Crypto ′84, A. Shamir [1] presented the new concept of identity‐based cryptosystems. Yet no realization scheme has yet been proposed. This paper proposes a scheme for realizing an identity‐based cryptosystem which modifies Shamir's original concept without losing its essential characteristics. The fundamental idea of this realization scheme is based on the well‐known one‐way functions, “the difficulty of calculating a discrete logarithm” and “the difficulty of factoring the composite of two large primes.” As long as all the users in the system keep their own secret keys secure, this cryptosystem is perfectly secure. Even if there is a conspiracy among users in the system, this system remains secure when the number of conspirators is less than a certain number which has been determined during the design phase. In this way, a threshold scheme for a secret information sharing system is realized. This paper presents a detailed analysis of this threshold scheme and shows how to evaluate the secret key of the center when the number of conspiring users is over the threshold. In addition, a scheme which facilitates a reduction in the amount of computation needed to generate a common key is also presented.