International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Homomorphic Encryption for Finite Automata

Nicholas Genise
Craig Gentry
Shai Halevi
Baiyu Li
Daniele Micciancio
DOI: 10.1007/978-3-030-34621-8_17
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Abstract: We describe a somewhat homomorphic GSW-like encryption scheme, natively encrypting matrices rather than just single elements. This scheme offers much better performance than existing homomorphic encryption schemes for evaluating encrypted (nondeterministic) finite automata (NFAs). Differently from GSW, we do not know how to reduce the security of this scheme from LWE, instead we reduce it from a stronger assumption, that can be thought of as an inhomogeneous variant of the NTRU assumption. This assumption (that we term iNTRU) may be useful and interesting in its own right, and we examine a few of its properties. We also examine methods to encode regular expressions as NFAs, and in particular explore a new optimization problem, motivated by our application to encrypted NFA evaluation. In this problem, we seek to minimize the number of states in an NFA for a given expression, subject to the constraint on the ambiguity of the NFA.
  title={Homomorphic Encryption for Finite Automata},
  booktitle={Advances in Cryptology – ASIACRYPT 2019},
  series={Advances in Cryptology – ASIACRYPT 2019},
  author={Nicholas Genise and Craig Gentry and Shai Halevi and Baiyu Li and Daniele Micciancio},