Randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information. This paper provides randomness extraction against quantum side information whose extractable key length is given by a quantum generalization of the collision entropy, which is smoothed and conditioned differently from how this is done in existing schemes. Based on the fact that the collision entropy is not subadditive, its optimization with respect to additional side information is introduced, and is shown to be asymptotically optimal. The lower bound derived there for general states is expressed as the difference between two unconditional entropies and its evaluation reduces to an eigenvalue problem of two states, which are the entire state and the marginal state of side information.

The aim of this paper is to maximize the range of the access control of visual secret sharing (VSS) schemes encrypting multiple images. First, the formulation of access structures for a single secret is generalized to that for multiple secrets. This generalization is maximal in the sense that the generalized formulation makes no restrictions on access structures; in particular, it includes the existing ones as special cases. Next, a sufficient condition to be satisfied by the encryption of VSS schemes realizing an access structure for multiple secrets of the most general form is introduced, and two constructions of VSS schemes with encryption satisfying this condition are provided. Each of the two constructions has its advantage against the other; one is more general and can generate VSS schemes with strictly better contrast and pixel expansion than the other, while the other has a straightforward implementation. Moreover, for threshold access structures, the pixel expansions of VSS schemes generated by the latter construction are estimated and turn out to be the same as those of the existing schemes called the threshold multiple-secret visual cryptographic schemes. Finally, the optimality of the former construction is examined, giving that there exist access structures for which it generates no optimal VSS schemes.

Secret sharing is a method of generating multiple shares from secret information so that only a qualified set of shares can be employed to recover this secret information. Visual secret sharing (VSS) is an example of secret sharing; its decryption can be performed by using human eyes without a computer. This paper provides a formulation of encryption for multiple secret images, which is a generalization of the existing ones, and also a general method of constructing VSS schemes encrypting multiple secret images.

Secret sharing is a method of encrypting a secret into multiple pieces called shares so that only qualified sets of shares can be employed to reconstruct the secret. Audio secret sharing (ASS) is an example of secret sharing whose decryption can be performed by human ears. This paper examines the security of an audio secret sharing scheme encrypting audio secrets with bounded shares, and optimizes the security with respect to the probability distribution used in its encryption.