Ramp secret sharing is a variant of secret sharing which can achieve better information ratio than perfect schemes by allowing some partial information on a secret to leak out. Strongly secure ramp schemes can control the amount of leaked information on the components of a secret. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two linear transformation methods to make a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previous methods which work for any linear ramp scheme are non-constructive. In addition, we present a novel application of strongly secure ramp schemes to symmetric PIR in a multi-user setting. Our solution is advantageous over those based on a non-strongly secure scheme in that it reduces the amount of communication between users and servers and also the amount of correlated randomness that servers generate in the setup.

We propose two secret sharing schemes realizing general access structures, which are based on unauthorized subsets. In the proposed schemes, shares are generated by Tassa's (k,n)-hierarchical threshold scheme instead of Shamir's (k,n)-threshold scheme. Consequently, the proposed schemes can reduce the number of shares distributed to each participant.

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].

It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)-threshold SSS by a modified cumulative map. However, such constructed SSSs are not efficient generally. In this paper, a new method is proposed to construct a SSS from a (t,m)-threshold scheme for any given general access structure. In the proposed method, integer programming is used to derive the optimal (t,m)-threshold scheme and the optimal distribution of the shares to minimize the average or maximum size of the distributed shares to participants. From the optimality, it can always attain lower coding rate than the cumulative maps because the cumulative maps cannot attain the optimal distribution in many cases. The same method is also applied to construct SSSs for incomplete access structures and/or ramp access structures.

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.

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.

In this paper, a new method is proposed to construct a visual secret sharing scheme with a general access structure for plural secret images. Although the proposed scheme can be considered as an extension of Droste's method that can encode only black-white images, it can encode plural gray-scale and/or color secret images.

In this letter we propose a new visual secret sharing scheme (VSSS) applicable to color images containing many colors such as photographs. In the proposed VSSS we can perceive a concealed secret image appearing on a reproduced image, which is obtained by stacking certain shares, according to the principle called the meanvalue-color mixing (MCM). First, we mathematically formulate the MCM and define a new parameter that determines the minimum quality of the reproduced secret image. Then, we explicitly construct the VSSS based on the MCM under general access structures. The construction is proved to be realistic by experiment under the (2,2)-threshold access structure.

This paper proposes a new construction of the visual secret sharing scheme for the (n,n)-threshold access structure applicable to color images. The construction uses matrices with n rows that can be identified with homogeneous polynomials of degree n. It is shown that, if we find a set of homogeneous polynomials of degree n satisfying a certain system of simultaneous partial differential equations, we can construct a visual secret sharing scheme for the (n,n)-threshold access structure by using the matrices corresponding to the homogeneous polynomials. The construction is easily extended to the cases of the (t,n)-threshold access structure and more general access structures.