Sorting Method for Fully Homomorphic Encrypted Data Using the Cryptographic Single-Instruction Multiple-Data Operation

Kim, Pyung; Lee, Younho; Yoon, Hyunsoo

doi:10.1587/transcom.2015ebp3359

Cited by 6 publications

(3 citation statements)

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“…Kim et al [20], appears to be the first work to report using SIMD batching to accelerate sorting performance within a single list. The authors employ HElib to implement a bitonic sorting algorithm, which is a data independent (ie.…”

Section: Our Contributionmentioning

confidence: 99%

“…The bitonic sort algorithm has a O(N log 2 N ) comparison complexity and a multiplicative depth of O(log n · log 2 N ). Additional details can be found in [20,21]. Whilst benchmarking Ç etin's work, [20] argues that the multiplicative circuit width in addition to its depth are important in determining the number of recryptions required for sorting large lists, which is the most dominant bottleneck in all FHE operations.…”

Section: Our Contributionmentioning

confidence: 99%

“…Additional details can be found in [20,21]. Whilst benchmarking Ç etin's work, [20] argues that the multiplicative circuit width in addition to its depth are important in determining the number of recryptions required for sorting large lists, which is the most dominant bottleneck in all FHE operations. The sorting algorithm based on the comparison matrix (having O(N 2 ) comparators) was shown to have a large width, and ultimately requiring more recryptions compared to the bitonic sort, despite the latter having a larger multiplicative circuit depth.…”

Section: Our Contributionmentioning

confidence: 99%

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Efficient Parallel Binary Operations on Homomorphic Encrypted Real Numbers

Basilakis

Javadi

2021

IEEE Trans. Emerg. Topics Comput.

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A number of homomorphic encryption application areas, such as privacy-preserving machine learning analysis in the cloud, could be better enabled if there existed a general solution for combining sufficiently expressive logical and numerical circuit primitives to form higherlevel algorithms relevant to the application domain. Logical primitives are more efficient in a binary plaintext message space, whereas numeric primitives favour a word-based message space before encryption. In a step closer to an overall strategy of combining logical and numeric operation types, this paper examines accelerating binary operations on real numbers suitable for somewhat homomorphic encryption. A parallel solution based on SIMD can be used to efficiently perform addition, subtraction and comparison operations in a single step. The result maximises computational efficiency, memory space usage and minimises multiplicative circuit depth. Performance of these primitives and their application in min-max and sorting operations are demonstrated. In sorting real numbers, a speed up of 25-30 times is observed.

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Section: Our Contributionmentioning

confidence: 99%