On the Leakage of Massey Secret Sharing Schemes under Linear Computations
Researchers extend leakage attacks on Massey secret sharing schemes to multiple secrets linked by linear computations, widening the set of vulnerable code parameters.
The paper extends a randomized subfield-subcode construction of linear exact repair scheme (LERS)-derived leakage attacks to settings where N secrets include linearly computed values. It analyzes addition first, then generalizes to arbitrary linear computations on K linearly independent inputs. The analysis applies to general linear codes of length n+1 and dimension k over F_q^m with k <= Nn/(Km), relaxing the previous bound of k <= n/m - 1. Simulations show identical leakage functions can arise for certain linear relations, yielding a more realistic yet still powerful attack model.
- Leakage attacks extended to N secrets with K linearly independent inputs and linear computations.
- Applicable code dimension bound improved from k <= n/m - 1 to k <= Nn/(Km).
- Identical leakage functions for certain linear relations create a more realistic attack model.
From the original article
1 min read at arxiv.orgLeakage attacks on secret sharing schemes exploit partial information about individual shares to recover the underlying secret. In coding theory, linear exact repair schemes (LERSs) enable the recovery of one codeword symbol from a small amount of information obtained from the remaining symbols, provided that the code has sufficiently low rate.
By Nadja Aoutouf · arxiv.org
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