Depth Optimized Efficient Homomorphic Sorting

Çetin, Gizem S.; Doröz, Yarkın; Sunar, Berk; Savaş, Erkay

doi:10.1007/978-3-319-22174-8_4

Cited by 34 publications

(23 citation statements)

References 22 publications

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“…The seminal work by Ç etin et al [18] in 2015 implemented two low-depth sorting algorithms both relying on a matrix to perform all comparisons at the outset, and achieving a multiplicative circuit depth of O(log N + log n), where N is the total number elements to be sorted, and n is the number of bits encoding each element. Ç etin also introduced the concept of using SIMD to accelerate sorting performance, although it is used in this case to sort multiple lists rather than accelerate sorting of a single list.…”

Section: Our Contributionmentioning

confidence: 99%

“…A common binary equality circuit implementation with optimisation for packed ciphertexts (albeit described for integers) is based on [34,35,18]. The equality test also holds for a two's complement scaled-to-integer encoding of a real number and is depicted as: equal(a, b) = n−1 i=0 (a i ⊕ b i ⊕ 1).…”

Section: Equality Circuitmentioning

confidence: 99%

“…Only one type of comparison circuit is required in combination with the equal circuit, to derive all other comparison relationships (ie., <, >, , ; see below). To enable a lessthan comparison, there are two binary circuits of note [22,18]. One determines the comparison logically while the other is derived from the addition circuit.…”

Section: Comparison Circuitmentioning

confidence: 99%

“…The following demonstrators will look at accelerating sorting methods including the odd-even transposition sort and the Direct Sorting algorithm of Ç etin's work [18]. Both are ideal candidates for the parallel primitive algorithms described in this paper.…”

Section: Sortingmentioning

confidence: 99%

“…The Direct Sort algorithm relies on calculating the sum of all elements within each matrix column, which returns the index of each X j in the sorted array. For further details see [18].…”

Section: Algorithm 3 Parallel Equalitymentioning

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%

Section: Equality Circuitmentioning

confidence: 99%

Section: Comparison Circuitmentioning

confidence: 99%

Section: Sortingmentioning

confidence: 99%

“…The Direct Sort algorithm relies on calculating the sum of all elements within each matrix column, which returns the index of each X j in the sorted array. For further details see [18].…”

Section: Algorithm 3 Parallel Equalitymentioning

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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Linear Depth Integer-Wise Homomorphic Division

Okada

Cid

Hidano

et al. 2019

Information Security Theory and Practice

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We propose a secure integer-wise homomorphic division algorithm on fully homomorphic encryption schemes (FHE). For integerwise algorithms, we encrypt plaintexts as integers without encoding them into bit values, while in bit-wise algorithms, plaintexts are encoded into binary and bit values are encrypted one by one. All the publicly available division algorithms are constructed in bit-wise style, and to the best of our knowledge there are no known integer-wise algorithm for secure division. We derive some empirical results on the FHE library HElib and show that our algorithm is 2.45x faster than the fastest bit-wise algorithm. We also show that the multiplicative depth of our algorithm is O(l), where l is the integer bit length, while that of existing division algorithms is O(l 2 ). Furthermore, we generalise our secure division algorithm and propose a method for secure calculation of a general 2variable function. The order of multiplicative depth of the algorithm, which is a main factor of the complexity of a FHE algorithm, is exactly the same as our secure division algorithm.

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Homomorphic Rank Sort Using Surrogate Polynomials

Çetin

Sunar

2019

Progress in Cryptology – LATINCRYPT 2017

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Depth Optimized Efficient Homomorphic Sorting

Cited by 34 publications

References 22 publications

Efficient Parallel Binary Operations on Homomorphic Encrypted Real Numbers

Efficient Parallel Binary Operations on Homomorphic Encrypted Real Numbers

Linear Depth Integer-Wise Homomorphic Division

Homomorphic Rank Sort Using Surrogate Polynomials

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