Speeding-Up Parallel Computation of Large Smooth-Degree Isogeny Using Precedence-Constrained Scheduling

Phalakarn, Kittiphon; Suppakitpaisarn, Vorapong; Hasan, M.A.

doi:10.1007/978-3-031-22301-3_16

Cited by 2 publications

(9 citation statements)

References 19 publications

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“…Although PCP and CCP provide faster implementations in the multi-core setting when compared to the use of optimal strategies of [FJP14], the formers still do not fully utilize all cores as much as possible. This issue was analyzed by Phalakarn et al [PSH22] who then proposed the precedence-constrained scheduling (PCS) technique as described below.…”

Section: Precedence-constrained Scheduling (Pcs) Techniquementioning

confidence: 99%

“…This task dependency graph is then used to schedule operations to processor's cores. The work of [PSH22] applied to the task dependency graph two scheduling algorithms, Hu's [Hu61] and Coffman-Graham's [CJG72] algorithms, to obtain a scheduling (Lines 8 and 14-16). In short, a scheduling is a sequence S = S 1 , • • • , S n where S t is a set of points to be computed in iteration t and #S t is no more than the number of processor's cores.…”

Section: Precedence-constrained Scheduling (Pcs) Techniquementioning

confidence: 99%

“…Although speeding-up at the strategy-level is important, there is no implementation that attempts to do so beyond PCP. To demonstrate how the computation can be further sped-up at the strategy-level for vectorized and parallel software implementation, we consider the recent work of Phalakarn et al [PSH22] which has proposed the precedenceconstrained scheduling (PCS) technique to evaluate strategies. In that work, the isogeny computation is considered to have two orthogonal axes: strategy construction and strategy evaluation, i.e., the order in which operations are performed affects the strategy cost.…”

Section: Introductionmentioning

confidence: 99%

“…This work presents two software implementations of the degree-e isogeny computation, which aim to further speed-up this operation at the strategy-level by exploiting parallelism and the PCS technique. Since [PSH22] did not consider any implementation aspects, we also provide analyses and modifications on how to effectively apply the PCS technique to the unique execution environment of each implementation. For comparison purposes, the implementations are based on the SIKEp751 parameter set of SIKE.…”

Section: Introductionmentioning

confidence: 99%

“…We use OpenMP for multi-threading with extensive techniques to handle synchronization among cores. Moreover, we include an optimization of [COR22] and modify the scheduling algorithm of [PSH22] to take advantage of this optimization. As a result, we are able to obtain speed-ups of up to 12.53%, 12.57%, and 14.36% when compared to [COR22] using two, three, and four cores, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Vectorized and Parallel Computation of Large Smooth-Degree Isogenies using Precedence-Constrained Scheduling

Phalakarn¹,

Suppakitpaisarn²,

Rodríguez-Henríquez³

et al. 2023

TCHES

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Strategies and their evaluations play important roles in speeding up the computation of large smooth-degree isogenies. The concept of optimal strategies for such computation was introduced by De Feo et al., and virtually all implementations of isogeny-based protocols have adopted this approach, which is provably optimal for single-core platforms. In spite of its inherent sequential nature, several recent works have studied ways of speeding up this isogeny computation by exploiting the rich parallelism available in vectorized and multi-core platforms. One obstacle to taking full advantage of this parallelism, however, is that De Feo et al.’s strategies are not necessarily optimal in multi-core environments. To illustrate how the speed of vectorized and parallel isogeny computation can be improved at the strategylevel, we present two novel software implementations that utilize a state-of-the-art evaluation technique, called precedence-constrained scheduling (PCS), presented by Phalakarn et al., with our proposed strategies crafted for these environments. Our first implementation relies only on the parallelism provided by multi-core processors. The second implementation targets multi-core processors supporting the latest generation of the Intel’s Advanced Vector eXtensions (AVX) technology, commonly known as AVX-512IFMA instructions. To better handle the computational concurrency associated with PCS, we equip both implementations with extensive synchronization techniques. Our first implementation outperforms the implementation of Cervantes-Vázquez et al. by yielding up to 14.36% reduction in the execution time, when targeting platforms with two- to four-core processors. Our second implementation, equipped with four cores, achieves up to 34.05% reduction in the execution time compared to the single-core implementation of Cheng et al. of CHES 2022.

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Section: Precedence-constrained Scheduling (Pcs) Techniquementioning

confidence: 99%

Section: Precedence-constrained Scheduling (Pcs) Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Vectorized and Parallel Computation of Large Smooth-Degree Isogenies using Precedence-Constrained Scheduling

Phalakarn¹,

Suppakitpaisarn²,

Rodríguez-Henríquez³

et al. 2023

TCHES

View full text Add to dashboard Cite

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On the Parallelization of Square-Root Vélu’s Formulas

Chávez-Saab,

Ortega,

Pizarro-Madariaga

2024

Preprint

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A primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies. This computation traditionally relied on Vélu’s formulas, an approach with time complexity linear in the degree but which was further enhanced by Bernstein, De Feo, Leroux, and Smith to a square-root complexity. The improved square-root Vélu’s formulas exhibit a degree of parallelizability which has not been exploited in major implementations. In this study, we introduce a theoretical framework for parallelizing isogeny computations and provide a proof-of-concept implementation in C with OpenMP. While the parallelization effectiveness exhibits diminishing returns with the number of cores, we still obtain strong results when using a small number of cores. Concretely, our implementation shows that for large degrees it is easy to achieve speedup factors of up to 1.74, 2.54 and 3.44 for 2, 4 and 8 cores, respectively.

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Speeding-Up Parallel Computation of Large Smooth-Degree Isogeny Using Precedence-Constrained Scheduling

Cited by 2 publications

References 19 publications

Vectorized and Parallel Computation of Large Smooth-Degree Isogenies using Precedence-Constrained Scheduling

Vectorized and Parallel Computation of Large Smooth-Degree Isogenies using Precedence-Constrained Scheduling

On the Parallelization of Square-Root Vélu’s Formulas

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