The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
최근에는 알려진 MPC 중에서 높은 효율성을 달성하기 위한 방법으로 RSSS(Replicated Secret Sharing Scheme)를 기반으로 하는 MPC(Multi-party Computation) 프레임워크가 주목을 받고 있습니다. 그러나 RSSS 기반 MPC는 연산의 곱셈 횟수에 비례하여 많은 양과 통신량이 필요하기 때문에 대수 연산과 같은 여러 무거운 계산에는 여전히 비효율적입니다(다른 비밀 공유 기반 MPC의 경우에는 해당되지 않음). ). 본 논문에서는 기수가 공개이고 지수가 비공개인 경우에 가장 많이 사용되는 대수 연산 중 하나인 모듈식 지수화를 위한 RSSS 기반 삼자 계산 프로토콜을 제안합니다. 우리가 제안한 방식은 점근적 의미와 실제적 의미 모두에서 간단하고 효율적입니다. 점근적 효율성에 대해 제안된 방식은 다음을 요구합니다. O(n)-비트 통신 및 O(1) 라운드, 여기서 n 는 최상의 설정에서 비밀 값 크기인 반면, 이전 체계에서는 다음을 요구합니다. O(n2)-비트 통신 및 O(n) 라운드. 실질적인 효율성 측면에서는 분산 환경(예: 분산 원장)에서 안전한 키 관리에 유용한 분산 서명 시나리오에 대한 실험을 통해 프로토콜의 성능을 보여줍니다. 사례 중 하나로서, 우리의 구현은 3,072비트 이산 로그 그룹과 256비트 지수에 대해 대략 300ms의 모듈식 지수화를 수행합니다. 이는 WAN 설정에서도 128비트 보안에 허용되는 매개변수입니다.
Kazuma OHARA
the NEC corporation,the University of Electro-Communications
Yohei WATANABE
the University of Electro-Communications,National Institute of Advanced Industrial Science and Technology (AIST)
Mitsugu IWAMOTO
the University of Electro-Communications
Kazuo OHTA
the University of Electro-Communications
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Kazuma OHARA, Yohei WATANABE, Mitsugu IWAMOTO, Kazuo OHTA, "Multi-Party Computation for Modular Exponentiation Based on Replicated Secret Sharing" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 9, pp. 1079-1090, September 2019, doi: 10.1587/transfun.E102.A.1079.
Abstract: In recent years, multi-party computation (MPC) frameworks based on replicated secret sharing schemes (RSSS) have attracted the attention as a method to achieve high efficiency among known MPCs. However, the RSSS-based MPCs are still inefficient for several heavy computations like algebraic operations, as they require a large amount and number of communication proportional to the number of multiplications in the operations (which is not the case with other secret sharing-based MPCs). In this paper, we propose RSSS-based three-party computation protocols for modular exponentiation, which is one of the most popular algebraic operations, on the case where the base is public and the exponent is private. Our proposed schemes are simple and efficient in both of the asymptotic and practical sense. On the asymptotic efficiency, the proposed schemes require O(n)-bit communication and O(1) rounds,where n is the secret-value size, in the best setting, whereas the previous scheme requires O(n2)-bit communication and O(n) rounds. On the practical efficiency, we show the performance of our protocol by experiments on the scenario for distributed signatures, which is useful for secure key management on the distributed environment (e.g., distributed ledgers). As one of the cases, our implementation performs a modular exponentiation on a 3,072-bit discrete-log group and 256-bit exponent with roughly 300ms, which is an acceptable parameter for 128-bit security, even in the WAN setting.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1079/_p
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@ARTICLE{e102-a_9_1079,
author={Kazuma OHARA, Yohei WATANABE, Mitsugu IWAMOTO, Kazuo OHTA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Multi-Party Computation for Modular Exponentiation Based on Replicated Secret Sharing},
year={2019},
volume={E102-A},
number={9},
pages={1079-1090},
abstract={In recent years, multi-party computation (MPC) frameworks based on replicated secret sharing schemes (RSSS) have attracted the attention as a method to achieve high efficiency among known MPCs. However, the RSSS-based MPCs are still inefficient for several heavy computations like algebraic operations, as they require a large amount and number of communication proportional to the number of multiplications in the operations (which is not the case with other secret sharing-based MPCs). In this paper, we propose RSSS-based three-party computation protocols for modular exponentiation, which is one of the most popular algebraic operations, on the case where the base is public and the exponent is private. Our proposed schemes are simple and efficient in both of the asymptotic and practical sense. On the asymptotic efficiency, the proposed schemes require O(n)-bit communication and O(1) rounds,where n is the secret-value size, in the best setting, whereas the previous scheme requires O(n2)-bit communication and O(n) rounds. On the practical efficiency, we show the performance of our protocol by experiments on the scenario for distributed signatures, which is useful for secure key management on the distributed environment (e.g., distributed ledgers). As one of the cases, our implementation performs a modular exponentiation on a 3,072-bit discrete-log group and 256-bit exponent with roughly 300ms, which is an acceptable parameter for 128-bit security, even in the WAN setting.},
keywords={},
doi={10.1587/transfun.E102.A.1079},
ISSN={1745-1337},
month={September},}
부
TY - JOUR
TI - Multi-Party Computation for Modular Exponentiation Based on Replicated Secret Sharing
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1079
EP - 1090
AU - Kazuma OHARA
AU - Yohei WATANABE
AU - Mitsugu IWAMOTO
AU - Kazuo OHTA
PY - 2019
DO - 10.1587/transfun.E102.A.1079
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2019
AB - In recent years, multi-party computation (MPC) frameworks based on replicated secret sharing schemes (RSSS) have attracted the attention as a method to achieve high efficiency among known MPCs. However, the RSSS-based MPCs are still inefficient for several heavy computations like algebraic operations, as they require a large amount and number of communication proportional to the number of multiplications in the operations (which is not the case with other secret sharing-based MPCs). In this paper, we propose RSSS-based three-party computation protocols for modular exponentiation, which is one of the most popular algebraic operations, on the case where the base is public and the exponent is private. Our proposed schemes are simple and efficient in both of the asymptotic and practical sense. On the asymptotic efficiency, the proposed schemes require O(n)-bit communication and O(1) rounds,where n is the secret-value size, in the best setting, whereas the previous scheme requires O(n2)-bit communication and O(n) rounds. On the practical efficiency, we show the performance of our protocol by experiments on the scenario for distributed signatures, which is useful for secure key management on the distributed environment (e.g., distributed ledgers). As one of the cases, our implementation performs a modular exponentiation on a 3,072-bit discrete-log group and 256-bit exponent with roughly 300ms, which is an acceptable parameter for 128-bit security, even in the WAN setting.
ER -