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Low-Rank Masking for Single-Server Matrix Multiplication
Researchers prove rank-r additive masks for outsourced matrix multiplication achieve maximal-correlation secrecy of at most q^-r, with a matching lower bound.
An arXiv paper analyzes statistical privacy for outsourcing matrix multiplication over a finite field to a single server using additive masks of rank at most r. Uniform rank-ball masks and products of independent uniform factors yield maximal-correlation secrecy bounded by q^{-r}, with encoding and decoding costing O(n^2 r) field operations. The authors prove an asymptotically matching lower bound for r=o(n), showing these samplers are optimal among input-independent additive masks even with secret invertible transformations. They also show every such mask requires delta approaching 1 in entry-level (epsilon, delta)-differential privacy for fixed field size.
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Network Security Trends: August
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Proximity Gaps for Gabidulin Codes and Applications
Researchers prove proximity-gap bounds for rank-metric and Gabidulin codes, enabling the first polynomial commitment scheme framework based on rank-metric error-correcting codes.
The paper proves every linear rank-metric code admits a proximity gap for deltas up to (d-1)/(3n) with error at most q^(e+1)/q^m, and improves the gap to (d-1)/(2n) for Gabidulin codes with error at most 10q^(n-1)/q^m, matching bounds for Reed-Solomon codes. A constructed infinite family of constant-rate Gabidulin codes shows the (d-1)/(2n) bound is tight, and a counterexample establishes a lower bound on the error at the d/(3n) gap. Applications include an IOPP for interleaved Gabidulin codes adapted from the Ligero IOPP and a q-linearized polynomial commitment scheme adapted from Ligero-based PCS, reportedly the first PCS framework based on rank-metric codes.
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