TY - GEN
T1 - Perfect MPC over Layered Graphs
AU - David, Bernardo
AU - Deligios, Giovanni
AU - Goel, Aarushi
AU - Ishai, Yuval
AU - Konring, Anders
AU - Kushilevitz, Eyal
AU - Liu-Zhang, Chen Da
AU - Narayanan, Varun
N1 - Publisher Copyright:
© 2023, International Association for Cryptologic Research.
PY - 2023
Y1 - 2023
N2 - The classical “BGW protocol” (Ben-Or, Goldwasser, and Wigderson, STOC 1988) shows that secure multiparty computation (MPC) among n parties can be realized with perfect full security if t< n/ 3 parties are corrupted. This holds against malicious adversaries in the “standard” model for MPC, where a fixed set of n parties is involved in the full execution of the protocol. However, the picture is less clear in the mobile adversary setting of Ostrovsky and Yung (PODC 1991), where the adversary may periodically “move” by uncorrupting parties and corrupting a new set of t parties. In this setting, it is unclear if full security can be achieved against an adversary that is maximally mobile, i.e., moves after every round. The question is further motivated by the “You Only Speak Once” (YOSO) setting of Gentry et al. (Crypto 2021), where not only the adversary is mobile but also each round is executed by a disjoint set of parties. Previous positive results in this model do not achieve perfect security, and either assume probabilistic corruption and a nonstandard communication model, or only realize the weaker goal of security-with-abort. The question of matching the BGW result in these settings remained open. In this work, we tackle the above two challenges simultaneously. We consider a layered MPC model, a simplified variant of the fluid MPC model of Choudhuri et al. (Crypto 2021). Layered MPC is an instance of standard MPC where the interaction pattern is defined by a layered graph of width n, allowing each party to send secret messages and broadcast messages only to parties in the next layer. We require perfect security against a malicious adversary who may corrupt at most t parties in each layer. Our main result is a perfect, fully secure layered MPC protocol with an optimal corruption threshold of t< n/ 3, thus extending the BGW feasibility result to the layered setting. This implies perfectly secure MPC protocols against a maximally mobile adversary.
AB - The classical “BGW protocol” (Ben-Or, Goldwasser, and Wigderson, STOC 1988) shows that secure multiparty computation (MPC) among n parties can be realized with perfect full security if t< n/ 3 parties are corrupted. This holds against malicious adversaries in the “standard” model for MPC, where a fixed set of n parties is involved in the full execution of the protocol. However, the picture is less clear in the mobile adversary setting of Ostrovsky and Yung (PODC 1991), where the adversary may periodically “move” by uncorrupting parties and corrupting a new set of t parties. In this setting, it is unclear if full security can be achieved against an adversary that is maximally mobile, i.e., moves after every round. The question is further motivated by the “You Only Speak Once” (YOSO) setting of Gentry et al. (Crypto 2021), where not only the adversary is mobile but also each round is executed by a disjoint set of parties. Previous positive results in this model do not achieve perfect security, and either assume probabilistic corruption and a nonstandard communication model, or only realize the weaker goal of security-with-abort. The question of matching the BGW result in these settings remained open. In this work, we tackle the above two challenges simultaneously. We consider a layered MPC model, a simplified variant of the fluid MPC model of Choudhuri et al. (Crypto 2021). Layered MPC is an instance of standard MPC where the interaction pattern is defined by a layered graph of width n, allowing each party to send secret messages and broadcast messages only to parties in the next layer. We require perfect security against a malicious adversary who may corrupt at most t parties in each layer. Our main result is a perfect, fully secure layered MPC protocol with an optimal corruption threshold of t< n/ 3, thus extending the BGW feasibility result to the layered setting. This implies perfectly secure MPC protocols against a maximally mobile adversary.
UR - http://www.scopus.com/inward/record.url?scp=85172330636&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-38557-5_12
DO - 10.1007/978-3-031-38557-5_12
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AN - SCOPUS:85172330636
SN - 9783031385568
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 360
EP - 392
BT - Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings
A2 - Handschuh, Helena
A2 - Lysyanskaya, Anna
T2 - Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings
Y2 - 20 August 2023 through 24 August 2023
ER -