Leveled FHE with Matrix Message Space

Up to now, almost all fully homomorphic encryption (FHE) schemes can only encrypt bit or vector. In PKC 2015, Hiromasa et al. [12] constructed the only leveled FHE scheme that encrypts matrices and supports homomorphic matrix addition and multiplication. But the ciphertext size of their scheme is somewhat large and the security of their scheme depends on some special kind of circular security assumption.

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