Abstract
In this paper we study monoid homomorphic encryption schemes over \((\mathbb {F}_2,\cdot )\). Such encryption schemes occur naturally by forgetting the addition operation in a Ring Homomorphic Encryption scheme over \(\mathbb {F}_2\) (if it exists). We study the structure of such schemes and analyze their security against quantum adversaries. We also present the only two monoid homomorphic encryption schemes over \((\mathbb {F}_2,\cdot )\) that exist in the literature and we raise the question of the existence of other such schemes. For one of the two schemes we present experimental results that show its performance and efficiency.
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Acknowledgments
We are very grateful to Mihai Togan for his comments and suggestions. This research was partially supported by the Romanian National Authority for Scientific Research (CNCS-UEFISCDI) EUREKA 62 / 2017 under the project PN-III-P3-3.5-EUK-2016-0038.
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Barcau, M., Paşol, V., Pleşca, C. (2019). Monoidal Encryption over \((\mathbb {F}_2,\cdot )\). In: Lanet, JL., Toma, C. (eds) Innovative Security Solutions for Information Technology and Communications. SECITC 2018. Lecture Notes in Computer Science(), vol 11359. Springer, Cham. https://doi.org/10.1007/978-3-030-12942-2_37
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DOI: https://doi.org/10.1007/978-3-030-12942-2_37
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