A digital signature scheme secure against adaptive chosen-message attacks
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Recently, Canetti et al [11] gave a generic construction (called CHK construction) of public key encryption (PKE) from a selective identity-based encryption scheme combined with a strong one-time signature scheme. Later, few schemes were proposed to improve the efficiency of CHK construction [11], for example, Boneh-Katz scheme [8] replaced a strong one-time signature with a message authentication code and Boyen-Mei-Waters scheme [9] was constructed directly from Waters' IBE scheme. But, both constructions have either trade-off the publicly verifiable property or security against adaptive chosen-ciphertext attack. We ask a question whether it is possible to construct an efficient and publicly verifiable PKE scheme from a selective IBE scheme with a weak one-time signature scheme. In this paper, we provide an affirmative answer and construct a public key encryption scheme which preserves the publicly verifiable property and is secure against adaptive chosen-ciphertext attack. The construction of the proposed scheme is based on Boneh-Boyen identity-based encryption (IBE) scheme [5] and a weak one-time signature scheme (using Waters' signature scheme [24]) built within Boneh-Boyen IBE scheme. In this construction, one-time signature scheme is not required to be strongly existential unforgeable as Waters' signature scheme is not a strongly existential unforgeability. We also show that the proposed scheme is ”almost” as efficient as the original Boneh-Boyen IBE scheme.