New Algorithms and Analyses for Sum-Preserving Encryption.

We continue the study of sum-preserving encryption schemes, in which the plaintext and ciphertext are both integer vectors with the same sum. Such encryption schemes were recently constructed and analyzed by Tajik, Gunasekaran, Dutta, Ellia, Bobba, Rosulek, Wright, and Feng (NDSS 2019) in the context of image encryption. Our first main result is to prove a mixing-time bound for the construction given by Tajik et al. using path coupling. We then provide new sumpreserving encryption schemes by describing two practical ways to rank and unrank the values involved in sum-preserving encryption, which can then be combined with the rank-encipher-unrank technique from formatpreserving encryption. Finally, we compare the efficiency of the Tajik et al. construction and our new ranking constructions based on performance tests we conducted on prototype implementations.