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].

In 1987, Ito, Saito and Nishizeki proposed a secret sharing scheme realizing general access structures, called the multiple assignment secret sharing scheme (MASSS). In this paper, we propose new MASSS's which are perfect secret sharing schemes and include Shamir's (k,n)-threshold schemes as a special case. Furthermore, the proposed schemes are more efficient than the original MASSS from the viewpoint of the number of shares distributed to each participant.