Accelerating residue-to-binary conversion of very high cardinality moduli set for fully homomorphic encryption

Truong Phu Truan Ho, Chip-Hong Chang
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Abstract

Recent hardware implementations of fully homomorphic encryption (FHE) exploit very high cardinality arbitrary moduli sets to parallelize large integer arithmetic. However, the benefit they gained are heavily offset by the slow residue-to-binary conversion due to the large modulo operations and limited number theoretic properties of arbitrary moduli. This paper presents a fast residue-to-binary (R2B) conversion method by transforming a large number of residues of arbitrary moduli into only three residues before the conversion. It exploits the smaller and parallel operations of base extension for the mapping to {2n−1, 2n, 2n +1} and the highly efficient adder-based R2B converter of the latter to achieve 2.25 ∼ 6.8 times speedup over recent R2B converters, which translates to approximately 10.2% to 32.08% of overall speed improvement for their FHE implementations.
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加速全同态加密的高基数模集残二转换
最近的完全同态加密(FHE)的硬件实现利用非常高的基数任意模集来并行化大整数运算。然而,由于大的模运算和任意模有限的数论性质,他们所获得的好处被缓慢的残数到二进制转换严重抵消。本文提出了一种快速残数到二值(R2B)转换方法,该方法在转换前将任意模的大量残数转换为仅三个残数。它利用了映射到{2n−1,2n, 2n +1}的更小和并行的基扩展操作,以及后者的高效基于加法器的R2B转换器,比最近的R2B转换器实现了2.25 ~ 6.8倍的速度提升,这意味着其FHE实现的总体速度提高了约10.2%至32.08%。
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