International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 30 June 2015

Jing Li, Licheng Wang
ePrint Report ePrint Report
In this paper, we propose a noise-free symmetric fully homomorphic encryption (FHE) based on matrices over noncommutative rings. The scheme is secure against chosen plaintext attacks based on the factorization problem of matrices over noncommutative rings as well as the hardness of an overdefined system of multivariate polynomial equations over the given non-commutative algebraic structure. Meanwhile, the new proposal is efficient in terms of computational cost and the sizes of plaintext/ciphertext. On the basis of this framework, a verifiable FHE is proposed, where the receiver can check the validity of ciphertexts. Furthermore, any attacker fails to construct a valid ciphertext without making query of encryption oracle, then the verifiable FHE scheme maybe secure against non-adaptively chosen ciphertext attacks (IND-CCA1).

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