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In this paper, the authors construct a strongly unforgeable ID-based signature scheme without random oracles. The signature size of the scheme is smaller than that of other schemes based on varieties of the Diffie - Hellman problem or the discrete logarithm problem. The security of the scheme relies on the difficulty to solve three problems related to the Diffie - Hellman problem and a one-way isomorphism. In 1984, Shamir introduced the concept of ID-based cryptosystems, in which the private key of an entity was generated from his identity information (e.g. an e-mail address, a telephone number, etc.) and a master key of a trusted third party called a Private Key Generator (PKG).
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