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.
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Leakage 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. This can be interpreted as recovering the secret from partial information, namely subfield symbols, of the shares. Recently, a randomized construction based on subfield subcodes was proposed for constructing LERS-derived leakage attacks against Massey secret sharing schemes based on general linear codes. We extend this framework to multiple shared secrets whose corresponding shares are related through linear computations, with leakage also allowed on the computation outcomes. More precisely, we consider N secrets, of which K $\le$ N are linearly independent input values and the remaining N -K secrets are determined by linear computations on these inputs. We analyse the existence of LERS-derived leakage that exploits this structure. We first study the case of addition and then generalize our construction to arbitrary linear computations. Our analysis applies to general linear codes of length n+1 and dimension k over F\_{q^m} with k $\le$ N n/(Km), and supports arbitrary linear computations, whereas the previous subfield subcode construction only applies to k $\le$ n/m -1. Consequently, exploiting the linear relations enables LERS based leakage which extend the range of code parameters vulnerable to such attacks. Finally, identical leakage functions can arise for certain linear relations, making this a more realistic yet still potentially powerful attack model. Finally, simulations indicate that identical leakage functions can be used for certain linear relations, yielding a more realistic attack model.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.19929