Oblivious Linear Group Actions and Applications

Attrapadung, Nuttapong; Hanaoaka, Goichiro; Matsuda, Takahiro; Morita, Hiraku; Ohara, Kazuma; Schuldt, Jacob C. N.; Teruya, Tadanori; Tozawa, Kazunari

doi:10.1145/3460120.3484584

Cited by 7 publications

(10 citation statements)

References 20 publications

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“…In the second application, we show that we can construct a more efficient protocol for B2A conversion than an existing one by applying the main theorem to the secure table lookup protocol, achieving approximately eight times shorter CR size. Here, B2A conversion is a function which maps boolean share (x 0 , x 1 ) to arithmetic share (y 0 , y 1 ) such that y 0 + y Using CR, the computation cost and the communication complexity become small, and therefore many recent works (e.g., [4], [5], [7], [11], [12]) adopted the CR model. From a theoretical viewpoint in CR model, it is a major open problem whether it is possible to make the communication complexity sublinear in the circuit size.…”

Section: Applicationsmentioning

confidence: 99%

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Correlated Randomness Reduction in Domain-Restricted Secure Two-Party Computation

HIWATASHI,

NUIDA

2024

IEICE Trans. Fundamentals

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Secure two-party computation is a cryptographic tool that enables two parties to compute a function jointly without revealing their inputs. It is known that any function can be realized in the correlated randomness (CR) model, where a trusted dealer distributes input-independent CR to the parties beforehand. Sometimes we can construct more efficient secure two-party protocol for a function g than that for a function f , where g is a restriction of f . However, it is not known in which case we can construct more efficient protocol for domain-restricted function. In this paper, we focus on the size of CR. We prove that we can construct more efficient protocol for a domain-restricted function when there is a "good" structure in CR space of a protocol for the original function, and show a unified way to construct a more efficient protocol in such case. In addition, we show two applications of the above result: The first application shows that some known techniques of reducing CR size for domain-restricted function can be derived in a unified way, and the second application shows that we can construct more efficient protocol than an existing one using our result.

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Section: Applicationsmentioning

confidence: 99%

“…In the online protocol, the parties securely compute a function with their inputs and the CR distributed by the offline protocol. Some papers (e.g., [4], [5], [7]) assume that a trusted dealer runs the offline protocol, i.e., a trusted dealer generates and distributes CR.…”

Section: Introductionmentioning

confidence: 99%

Correlated Randomness Reduction in Domain-Restricted Secure Two-Party Computation

HIWATASHI,

NUIDA

2024

IEICE Trans. Fundamentals

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“…For arithmetic-input unit vectorization, our protocol is the same as the one-time truth table protocol from [12] when using one-hot vectors. For boolean inputs, we propose a new protocol, which can be considered as a variant of the XOR-permutation action proposed in [6]. These schemes require preprocessing; that is, some appropriate correlated randomness is required and is generated in the offline phase.…”

Section: Core Protocol: Unit Vectorizationmentioning

confidence: 99%

“…IfThen, Pow and Mult Protocols We refer to existing protocols for computing IfThen, Pow and Mult. In this paper, we employ the protocols Π Mux , Π Polyval , Π Mult proposed in [6]. Each of the protocol requires one online communication round.…”

Section: A Secure Equality Testmentioning

confidence: 99%

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Memory and Round-Efficient MPC Primitives in the Pre-Processing Model from Unit Vectorization

Attrapadung¹,

Morita

Ohara³

et al. 2022

Proceedings of the 2022 ACM on Asia Conference on Computer and Communications Security

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In this paper, we propose memory-and round-efficient protocols for securely evaluating arithmetic primitives. We focus on secure twoparty computation over the ring Z 2 𝑘 that achieves security against semi-honest adversaries and works in the pre-processing model. Our protocols rely on the unit vectorization technique introduced by Boyle et al. (TCC 2019). The unit vectorization technique provides online-optimal protocols for several fundamental operations in the pre-processing model. However, a relatively large memory cost for correlated randomness is required, which might become an obstacle in a large-scale application. In order to achieve both memory and communication efficiency, we propose a size reduction method that uses unit vectorization only for short-length inputs, and based on this, construct two-round protocols for equality test, detecting the most significant non-zero bit, detecting wrap-around, and less-than comparison. In addition, as applications of these results, we provide practically efficient protocols for integer division, integer square root, integer logarithm, and modular exponentiation. CCS CONCEPTS• Theory of computation → Cryptographic protocols.

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