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Article Dans Une Revue IACR Communications in Cryptology Année : 2024

Secure Multi-Party Linear Algebra with Perfect Correctness

Jules Maire
Damien Vergnaud

Résumé

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.

Dates et versions

hal-04603234 , version 1 (06-06-2024)

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Jules Maire, Damien Vergnaud. Secure Multi-Party Linear Algebra with Perfect Correctness. IACR Communications in Cryptology, 2024, ⟨10.62056/avzojbkrz⟩. ⟨hal-04603234⟩
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