An important research area in the past decade is to search for efficient cryptographic schemes that do not rely for their security on the controversial random oracle assumption. In this paper, we continue this line of endeavors and report our success in identifying a very efficient public key encryption scheme whose formal security proof does not require a random oracle. Specifically, we show how to modify a universal hash based public key encryption scheme proposed by Zheng and Seberry at Crypto'92, in such a way that the resultant scheme not only preserves efficiency but also admits provable security against adaptive chosen ciphertext attack without a random oracle. We also compare the modified Zheng-Seberry scheme with related encryption schemes in terms of efficiency and underlying assumptions, supporting our conclusion that the modified Zheng-Seberry scheme is preferable to its competitors.
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