Security Assessment of Brute-Force Attack to Subset Sum-Based Verifiable Secret Sharing Scheme

The integration of subset sum in the verifiable secret sharing scheme provides added security measure for a multiparty computation such as immediate identification of and removal of an imposter, avoidance or discourages man-in-the-middle attack and lattice-based attack, and lessens dealer's burden on processing monitoring the integrity of shareholders. This study focuses on the security assessment of a brute-force attack on the subset sum-based verifiable secret sharing scheme. With the simulation done using a generator of all possible fixed-length partition (which is k=3 as the least possible) summing up to the sum of the original subset generated by the dealer, it shows that it will already took 11,408 years to brute-force all possible values even on a small 32-bit-length value and 3.8455 years for a 128-bit length value thus proving that the resiliency on brute attack on the subset sum based VSSS can be discounted despite simplicity of the implementation. Zero knowledge on the number of threshold will also multiply to the impossibility of the brute force attack.