In secret sharing schemes for general access structures, an important issue is the number of shares distributed to each participant. However, in general, the existing schemes are impractical in this respect when the size of the access structure is very large. In 2015, a secret sharing scheme that can reduce the number of shares distributed to specified participants was proposed (the scheme A of T15). In this scheme, we can select a subset of participants and reduce the number of shares distributed to any participant who belongs to the selected subset though this scheme cannot reduce the number of shares distributed to every participant. In other words, this scheme cannot reduce the number of shares distributed to each participant who does not belong to the selected subset. In this paper, we modify the scheme A of T15 and propose a new secret sharing scheme realizing general access structures. The proposed scheme can reduce the number of shares distributed to each participant who does not belong to the selected subset as well. That is, the proposed scheme is more efficient than the scheme A of T15.

We propose two multiple assignment secret sharing schemes realizing general access structures. One is always more efficient than the secret sharing scheme proposed by Ito, Saito and Nishizeki [5] from the viewpoint of the number of shares distributed to each participant. The other is also always more efficient than the scheme I of [7].

We propose efficient secret sharing schemes realizing general access structures. Our proposed schemes are perfect secret sharing schemes and include Shamir's (k, n)-threshold schemes as a special case. Furthermore, we show that a verifiable secret sharing scheme for general access structures is realized by one of the proposed schemes.