Secure Multi-Party Matrix Multiplication Based on Strassen-Winograd Algorithm

Jean-Guillaume Dumas (1) , Pascal Lafourcade (2) , Julio Lopez Fenner (3) , David Lucas (1) , Jean-Baptiste Orfila (1) , Clément Pernet (1) , Maxime Puys (4)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
3 UFRO - Universidad de la frontera [Tecumo, Chile] = University of La Frontera [Tecumo, Chile] = Université de La Frontera [Tecumo, Chili]
4 VERIMAG - IMAG - VERIMAG

This paper presents how to adapt Strassen-Winograd matrix multiplication algorithm to the context of secure multiparty computation. We consider that each player owns only one row of both input matrices and learns one row of the product matrix, without revealing their input to other players. After presenting some building block protocols, we describe how to perform a secure execution of Strassen-Winograd. Then, a comparison is made with a variant of the best known algorithm, relaxed to this setting. It first shows that, asymptotically, the communication volume is reduced from O(n 3) to O(n 2.81), as expected. Furthermore, a finer study on the amount of communication shows that the improvement occurs for matrices with dimension as small as n = 81.

Domains: Cryptography and Security [cs.CR]

Jean-Guillaume Dumas, Pascal Lafourcade, Julio Lopez Fenner, David Lucas, Jean-Baptiste Orfila, et al.. Secure Multi-Party Matrix Multiplication Based on Strassen-Winograd Algorithm. 2018. ⟨hal-01781554v2⟩