Post-Quantum Secure Feldman's Verifiable Secret Sharing has Timing Side-Channels in Matrix Operations

Post-Quantum Secure Feldman's Verifiable Secret Sharing provides a Python implementation of Feldman's Verifiable Secret Sharing (VSS) scheme. In versions 0.8.0b2 and prior, the feldman_vss library contains timing side-channel vulnerabilities in its matrix operations, specifically within the _find_secure_pivot function and potentially other parts of _secure_matrix_solve. These vulnerabilities are due to Python's execution model, which does not guarantee constant-time execution. An attacker with the ability to measure the execution time of these functions (e.g., through repeated calls with carefully crafted inputs) could potentially recover secret information used in the Verifiable Secret Sharing (VSS) scheme. The _find_secure_pivot function, used during Gaussian elimination in _secure_matrix_solve, attempts to find a non-zero pivot element. However, the conditional statement if matrix[row][col] != 0 and row_random < min_value: has execution time that depends on the value of matrix[row][col]. This timing difference can be exploited by an attacker. The constant_time_compare function in this file also does not provide a constant-time guarantee. The Python implementation of matrix operations in the _find_secure_pivot and _secure_matrix_solve functions cannot guarantee constant-time execution, potentially leaking information about secret polynomial coefficients. An attacker with the ability to make precise timing measurements of these operations could potentially ex…