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Notes on Two Fully Homomorphic Encryption Schemes Without Bootstrapping”, Cryptology ePrint Archive, Report 2015/519
, 2015
"... Abstract. Recently, IACR ePrint archive posted two fully homomorphic encryp-tion schemes without bootstrapping. In this note, we show that these schemes are trivially insecure. Furthermore, we also show that the encryption schemes of Liu and Wang [6] in CCS 2012 and the encryption scheme of Liu, Ber ..."
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Abstract. Recently, IACR ePrint archive posted two fully homomorphic encryp-tion schemes without bootstrapping. In this note, we show that these schemes are trivially insecure. Furthermore, we also show that the encryption schemes of Liu and Wang [6] in CCS 2012 and the encryption scheme of Liu, Bertino, and Xun [5] in ASIACCS 2014 are insecure either. 1
Noise-Free Symmetric Fully Homomorphic Encryption Based on Non-Commutative Rings
"... A framework of noise-free symmetric fully homomorphic en-cryption (FHE) is proposed in this work. Different from the frameworks that are defined over non-commutative group-s, our framework is constructed from matrices over non-commutative rings. The scheme is one-way secure against chosen plaintext ..."
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A framework of noise-free symmetric fully homomorphic en-cryption (FHE) is proposed in this work. Different from the frameworks that are defined over non-commutative group-s, our framework is constructed from matrices over non-commutative rings. The scheme is one-way secure against chosen plaintext attacks (OW-CPA) based on the factor-ization problem of matrices over noncommutative rings as well as the hardness of an overdefined system of multivari-ate polynomial equations over the given non-commutative algebraic structure. On the basis of this framework, a ver-ifiable FHE is proposed, where the receiver can check the validity of ciphertexts.
