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Waters, in 2009, introduced an important technique, called dual-system encryption, to construct Identity-Based Encryption (IBE) and related schemes. The resulting IBE scheme was described in the setting of symmetric pairing. A key feature of the construction is the presence of random tags in the ciphertext and decryption key. Later work by Lewko and Waters has removed the tags and proceeding through composite-order pairings has led to a more efficient dual-system IBE scheme using asymmetric pairings whose security is based on non-standard but static assumptions. In this paper, the authors have systematically simplified Waters 2009 IBE scheme in the setting of asymmetric pairing. The simplifications retain tags used in the original description.
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