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Connections Among Algebra, Statistical Designs and Secret Sharing Schemes

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概要 Due to the recent development of computers and computer networks, huge amount of digital data can easily be transmitted or stored. But the transmitted data in networks or stored data in computers may ...easily be destroyed or substituted by enemies if the data are not enciphered by some cryptographic tools. So it is very important to restrict access of confidential information stored in a computer or in a certain nodes of a system. Access should be gained through a secret key, password or token. Again storing the secret key or password securely could be a problem. The best solution could be to memorize the secret key. But for large and complicated secret key, it is almost impossible to memorize the key. As a result, it should be stored safely. While storing data in a hard disk, the threats such as troubles of storage devices or attacks of destruction make the situation even worse. In order to prevent such attacks, we may make as many copies of the secret data as possible. But, if we have many copies of the secret data, the secret may be leaked out and hence the number of the copies should be as small as possible. Under this circumstances, it is desirable that the secret key should be governed by a secure key management scheme. If the key or the secret data is shared among several participants in such a way that the secret data can only be reconstructed by a significantly large and responsible group acting in agreement, then a high degree of security is attained. Shamir and Blakley, independently, addressed this problem in 1979 when they introduced the concept of a threshold secret sharing scheme. A (t,n)-threshold scheme is a method whereby n pieces of information, called shares, corresponding to the secret data or key K, are distributed to n participants so that the secret key can be reconstructed from the knowledge of any t or more shares and the secret key can not be reconstructed from the knowledge of fewer than t shares. This this we we further emphasize on a special type of secret sharing scheme known as visual secret sharing scheme. Visual cryptographic scheme, for a set P of n participants, is a cryptographic paradigm that enables us to split a secret image, which may be some handwritten note, printed text, picture, etc., into n shadow images called shares, where each participant in P receives one share. Certain qualified subsets of participants can "visually" recover the secret image with some loss of contrast, but other forbidden sets of participants have no information about the secret image. A "visual recovery" for a set X ⊆ P consists of photocopying the shares given to the participants in X onto the transparencies, and then stacking them. Since the reconstruction is done by human visual system, no computation is involved during decoding unlike traditional cryptographic schemes where a fair amount of computation is needed to reconstruct the plain text. In this talk, we shall describe how algebra and statistical designs play an important role in constructing visual cryptographic schemes.続きを見る

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登録日 2014.03.18
更新日 2023.10.05

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