On Secret Sharing Schemes from Nonlinear Codes

In a secret sharing scheme, a secret is divided into shares and then distributed among participants. The legitimate sets of participants that can recover the secret is called the access structure of the secret sharing scheme. The existing constructions of secret sharing schemes are primarily based on linear error correcting codes. These schemes are however susceptible to “Tompa-Woll attack”. Recently, secret sharing schemes have been designed based on nonlinear error correcting codes to resist “Tompa-Woll attack”. In this paper, we determine the access structure of several nonlinear codes and examine its performance against “Tompa-Woll attack”. We explained that access structure based on nonlinear code is obtained from it’s formally dual code. We also explain the idea of finding the access structure of secret sharing scheme of shortened and punctured code from the access structure of secret sharing scheme of their parental code.