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Motivated by applications in large storage systems, the authors initiate the study of incremental deterministic public-key encryption. Deterministic public-key encryption, introduced by Bellare, Boldyreva, and O'Neill (CRYPTO '07), provides a realistic alternative to randomized public-key encryption in various scenarios where the latter exhibits inherent drawbacks. A deterministic encryption algorithm, however, cannot satisfy any meaningful notion of security for low-entropy plaintexts distributions, and Bellare et al. demonstrated that a strong notion of security can in fact be realized for relatively high-entropy plaintext distributions. In order to achieve a meaningful level of security, a deterministic encryption algorithm should be typically used for encrypting rather long plaintexts for ensuring a sufficient amount of entropy.
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