When HEAAN Meets FV: A New Somewhat Homomorphic Encryption with Reduced Memory Overhead

Abstract

We demonstrate how to reduce the memory overhead of somewhat homomorphic encryption (SHE) while computing on numerical data. We design a hybrid SHE scheme that exploits the packing algorithm of the HEAAN scheme and the variant of the FV scheme by Bootland et al. The ciphertext size of the resulting scheme is 3-18 times smaller than in HEAAN to compute polynomial functions of depth 4 while packing a small number of data values. Furthermore, our scheme has smaller ciphertexts even with larger packing capacities (256-2048 values).

Secure genotype imputation using homomorphic encryption

“…In 1978, Rivest [24] first proposed the HE scheme's assumption, which allowed various calculations over encrypted data. Nowadays, HE schemes are generally classified into three types: Partially Homomorphic Encryption (PHE) [25], Somewhat Homomorphic Encryption (SWHE) [26][27][28], and Fully Homomorphic Encryption (FHE) [21,29] according to calculation depth and capacity. PHE can allow homomorphic multiplications or homomorphic additions with limited calculation depth.…”

On the IND-CCA1 Security of FHE Schemes

“…Chenal and Tang ((R)LWE) [11] Bra12 [19], BGV [15], BV11a [16], BV11b [17], GSW [20] CKKS [21], FV [22], BCIV [23], AN [24], CLPX [25], CIL [26], BV14 [27], BL [28], CCS [29], CM [30], CGGI [31], Jou [32], BP [33], AH [34], PS [35], CS17 [36] Loftus et al * (Ideal Lattice) [37] Gen [2], GH * [3], SV * [38] SS * [39], SV14 * [40] Zhang et al (AGCD) [41] and CMNT [42], vDGHV [43] CNT [44], CS15 [45] Chenal and Tang (AGCD) [11] CLT [46], CCKLLTY [47], KLYC [48] Dahab et al (NTRU) [18] BLLN [49], LATV * [50] RC * [51] Fauzi et al (other) [52] LGM [53] Section 5.2 (AGCD) Per [54], BBL [55] Section 5.3 (other) DHPSSWZ [56], AFFHP [57] We grouped schemes into five...…”

“…BGV [15] CKKS [21] Bra12 [19] FV [22] FV [22] BCIV [23], AN [24], CLPX [25], CIL [26], AH [34] GSW [20] BV14 [27], BL [28], CM [30], CCS [29], CGGI [31], PS [35], BP [33], Jou [32] Gen [2] SS [39] SV [38] GH [3], LMSV [37], SV14 [40] vDGHV [43] CLT [46], KLYC [48], CNT [44], CCKLLTY [47], CMNT [42] Finally, we note that, for simplicity, some encryption schemes are presented as a symmetric key, rather than as a public key. For all the schemes where this is the case, there is a standard transformation to make the scheme a public key (see, e.g., [43]): the secret key remains the same, and the public key is a set of different encryptions of the additive identity element in the message space, e.g., zero.…”