CryptoDB
New Tight Bounds on the Local Leakage Resilience of the Additive (n,n)-Threshold Scheme Determined by the Eigenvalues of Circulant Matrices
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| Conference: | ASIACRYPT 2025 |
| Abstract: | Recently, Benhamouda et al. proposed a framework to evaluate the local leakage resilience of the n shares of (k,n)-threshold scheme. Lletting (X_1,X_2, ... ,X_n) be the n shares, the leakage is defined as (Y_1, Y_2, ..., Y_n) , where Y_i is the output of a deterministic mapping belonging to {0,1, ..., L-1} with the input X_i. We evaluate the worst-case total variational distance V between the conditional probability distributions of two leakages given two secrets s and s'. In this paper, we propose a new method to evaluate V more precisely than the existing methods for the (n,n)-threshold scheme over a finite field with p elements, where p>= 3 is an arbitrary prime number. For the case of L=2, we show that V converges to zero of order O(( sin (\pi / 2p ))^{-n}). We also characterize the class of leakage functions that attains V. For the case of L > 2, we succeed in obtaining an upper bound of V by using the theory of majorization. The order of the obtained upper bound is smaller than the existing upper bound and is proved to be tight under a certain assumption. |
BibTeX
@inproceedings{asiacrypt-2025-36128,
title={New Tight Bounds on the Local Leakage Resilience of the Additive (n,n)-Threshold Scheme Determined by the Eigenvalues of Circulant Matrices},
publisher={Springer-Verlag},
author={Hiroki Koga and Hiroto Abe},
year=2025
}