Cheating-immune secret sharing schemes from codes and cumulative arrays

A cheating-immune secret sharing scheme prevents a cheater, who submits a corrupted share, from gaining an advantage in knowing the secret over the honest participants. We revisit two methods, that uses linear codes, to construct Boolean functions satisfying multiple cryptographic criteria. We show that these methods can be used to build new cheating-immune (n, n)-secret sharing schemes. We also revisit two general constructions of secret sharing schemes using cumulative arrays and apply them to build cheating-immune (t, n)-threshold secret sharing schemes.