Secure Multi-Party Linear Algebra with Perfect Correctness
Authors
Jules Maire, Damien Vergnaud
Jules Maire
Sorbonne Université, CNRS, LIP6, Paris, France
jules dot maire at lip6 dot fr
jules dot maire at lip6 dot fr
Damien Vergnaud
Sorbonne Université, CNRS, LIP6, Paris, France
damien dot vergnaud at lip6 dot fr
damien dot vergnaud at lip6 dot fr
Keywords:
Secure Multi-Party Computation
Linear Algebra
Preparata-Sarwate Algorithm
Moore-Penrose Pseudo-Inverse
Abstract
We present new secure multi-party computation protocols for linear algebra over a finite field, which improve the state-of-the-art in terms of security. We look at the case of unconditional security with perfect correctness, i.e., information-theoretic security without errors. We notably propose an expected constant-round protocol for solving systems of m linear equations in n variables over Fq with expected complexity O(k n^2.5 + k m) (where complexity is measured in terms of the number of secure multiplications required) with k > m(m+n)+1. The previous proposals were not error-free: known protocols can indeed fail and thus reveal information with probability Omega(poly(m)/q). Our protocols are simple and rely on existing computer-algebra techniques, notably the Preparata-Sarwate algorithm, a simple but poorly known “baby-step giant-step” method for computing the characteristic polynomial of a matrix, and techniques due to Mulmuley for error-free linear algebra in positive characteristic.
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History
Submitted: 2024-01-09
Accepted: 2024-03-05
Published: 2024-04-09
Accepted: 2024-03-05
Published: 2024-04-09
How to cite
Jules Maire and Damien Vergnaud, "Secure Multi-Party Linear Algebra with Perfect Correctness," IACR Communications in Cryptology, vol. 1, no. 1, Apr 09, 2024, doi: 10.62056/avzojbkrz.
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