Arithmetic Using Word wise Homomorphic Encryption

Homomorphic encryption has progressed rapidly in both efficiency and versatility since its emergence in 2009. Meanwhile, a multitude of pressing privacy needs—ranging from cloud computing to healthcare management to the handling of shared databases such as those containing genomics data—call for immediate solutions that apply fully homomorpic encryption (FHE) and somewhat homomorphic encryption (SHE) technologies. Further progress towards these ends requires new ideas for the efficient implementation of algebraic operations on word-based (as opposed to bit-wise) encrypted data. Whereas handling data encrypted at the bit level leads to prohibitively slow algorithms for the arithmetic operations that are essential for cloud computing, the word-based approach hits its bottleneck when operations such as integer comparison are needed. In this work, we tackle this challenging problem, proposing solutions to problems—including comparison and division—in word-based encryption via a leveled FHE scheme. We present concrete performance figures for all proposed primitives.