Analog Secure Distributed Matrix Multiplication
Abstract
In this paper, we present secure distributed matrix multiplication (SDMM) schemes over the complex numbers with good numerical stability and small mutual information leakage by utilizing polynomial interpolation with roots of unity. Furthermore, we give constructions utilizing the real numbers by first encoding the real matrices to smaller complex matrices using a technique we callcomplexification. These schemes over the real numbers enjoy many of the benefits of the schemes over the complex numbers, including good numerical stability, but are computationally more efficient. To analyze the numerical stability and the mutual information leakage, we give some bounds on the condition numbers of Vandermonde matrices whose evaluation points are roots of unity.
Fields of Study & Subjects
Polynomial and algebraic computation
Cryptography and Residue Arithmetic
Matrix Theory and Algorithms
Publication details
- Journal / source
- IEEE Transactions on Information Theory
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Volume
- 72
- Issue
- 7
- Pages
- 4751–4765
- Publication date
- 4 May 2026
- Language
- EN