Valiant’s Universal Circuits Revisited: An Overall Improvement and a Lower Bound

Zhao, Shuoyao; Yu, Yu; Zhang, Jiang; Liu, Hanlin

doi:10.1007/978-3-030-34578-5_15

Cited by 11 publications

(24 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We include size optimizations, achieving a linear concrete improvement for all UCs. Moreover, we show that our 2/4 hybrid method for generating UCs improves over the 4-way UCs, i.e., both over Valiant's 4-way UC and over the optimized 4-way UC of [72].…”

Section: Our Contributions and Outlinementioning

confidence: 84%

“…3.3) and 4-way UCs (Sect. 3.4) and the improved building block proposed by Zhao et al [72] for the latter.…”

Section: Our Contributions and Outlinementioning

confidence: 99%

“…We detail the steps of our algorithm for a practical realization of Valiant's UC construction and implement the 2-way and recently optimized 4-way UCs as well as our 2/4 hybrid UC construction. We note that our implementation is the first implementation that includes the optimization of Zhao et al [72], which achieves the best size ∼ 4.5n log 2 n to date. We describe the architecture of our UC compiler (Sect.…”

Section: Our Contributions and Outlinementioning

confidence: 99%

“…The asymptotic complexity of the 4-way UC is ∼ 4.75n log 2 n which is smaller than that of the 2-way UC of ∼ 5n log 2 n [66]. The 4-way UC has been further improved in [72], where its size is reduced to ∼ 4.5n log 2 n. An asymptotically depth-optimal construction with depth (d) that simulates circuits with depth d was proposed in [17], but it has a significantly larger size of O(n 3 d/ log n). In our paper, due to the applications in cryptography that we revisit in Sect.…”

Section: Introductionmentioning

confidence: 99%

“…In our paper, due to the applications in cryptography that we revisit in Sect. 1.1, we concentrate on the existing size-optimized UCs, especially that proposed by Valiant [66] with asymptotic size (n log n) with the optimization presented by Zhao et al in [72].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient and Scalable Universal Circuits

et al. 2020

View full text Add to dashboard Cite

A universal circuit (UC) can be programmed to simulate any circuit up to a given size n by specifying its program inputs. It provides elegant solutions in various application scenarios, e.g., for private function evaluation (PFE) and for improving the flexibility of attribute-based encryption schemes. The asymptotic lower bound for the size of a UC is (n log n), and Valiant (STOC'76) provided two theoretical constructions, the so-called 2-way and 4-way UCs (i.e., recursive constructions with 2 and 4 substructures), with asymptotic sizes ∼ 5n log 2 n and ∼ 4.75n log 2 n, respectively. In this article, we present and extend our results published in (Kiss and Schneider EUROCRYPT'16) and (Günther et al. ASIACRYPT'17). We validate the practicality of Valiant's UCs by realizing the 2-way and 4-way UCs in our modular open-source implementation. We also provide an example implementation for PFE using these sizeoptimized UCs. We propose a 2/4-hybrid approach that combines the 2-way and the 4-way UCs in order to minimize the size of the resulting UC. We realize that the bottleneck in universal circuit generation and programming becomes the memory consumption of the program since the whole structure of size O(n log n) is handled by the algorithms in memory. In this work, we overcome this by designing novel scalable algorithms for the UC generation and programming. Both algorithms use only O(n) memory at any point in time. We prove the practicality of our scalable design with a scalable proof-of-concept implementation for generating Valiant's 4-way UC. We note that this can be extended to work with optimized building blocks analogously. Moreover, we substantially improve the size of our UCs by including and implementing the recent optimization of Zhao et al. (ASIACRYPT'19) that reduces the asymptotic size of the 4-way UC to ∼ 4.5n log 2 n. Furthermore, we include their optimization in the implementation of our 2/4-hybrid UC which yields the smallest UC construction known so far.

show abstract

Section: Our Contributions and Outlinementioning

confidence: 84%

“…3.3) and 4-way UCs (Sect. 3.4) and the improved building block proposed by Zhao et al [72] for the latter.…”

Section: Our Contributions and Outlinementioning

confidence: 99%

Section: Our Contributions and Outlinementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient and Scalable Universal Circuits

et al. 2020

View full text Add to dashboard Cite

show abstract

Linear-Complexity Private Function Evaluation is Practical

Holz

Kiss

Rathee

et al. 2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Machine Learning (ML) is having a significant impact on computer security: on the one hand, ML can be used to build defensive systems such as malware and network attack detection; on the other hand, ML data and models are increasingly targeted by effective attacks. Identifying and alleviating threats to ML data assets is therefore essential. The main purpose of this talk is to discuss from the point of view of the security practitioner the foundations and the open issues toward a methodology for identifying threats and vulnerabilities of ML models, based on ML-specific definitions of CIA3-R security properties. We also discuss the idea of using Distributed Ledger Technology (DLT) to support a security control framework for countering such threats, making changing ML inference results or stealing ML data less attractive for attackers.

show abstract

$$\textsf {LogStack}$$: Stacked Garbling with $$O(b \log b)$$ Computation

Heath

Kolesnikov

2021

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Valiant’s Universal Circuits Revisited: An Overall Improvement and a Lower Bound

Cited by 11 publications

References 27 publications

Efficient and Scalable Universal Circuits

Efficient and Scalable Universal Circuits

Linear-Complexity Private Function Evaluation is Practical

$$\textsf {LogStack}$$: Stacked Garbling with $$O(b \log b)$$ Computation

Contact Info

Product

Resources

About