"A study on security of quantum cryptograph"

Securty of cryptography being used now depends on computationally intractable problems such as Factoring problem or Discrete logarithm problem. When it comes to be able to solve these problems by the advancement of the computer at the polynomial time, the safety of a present cryptography cannot be guaranteed. Especially, the achievement of the quantum computer is a threat. Because it has already been proven to be able to do factorization into prime factors with a quantum computer at the polynomial time.
Then, the quantum is remarkable in recent years. This is because of the safety of the quantum cryptography are based on the law of not the computational complexity but the quantum mechanics. This enables us to design systems that are unconditionally secure, i.e. systems that are even secure in the presence of an eavesdropper with unlimited computational power.
The law of the quantum mechanics is an indeterminacy principle chiefly and no-cloning theorem. The physical quantity that cannot be measured at the same time exists with the indeterminacy principle. In other words, it is shown that former state breaks when measuring it once. When what state of the quantum prepared is not understood, the No-cloning theorem shows that an accurate copy cannot be done. Because the existence can be discovered even if the wiretapper exists from these two laws, the quantum cryptgraphy is safe.
The research on a variety of quantum cryptgraphy is done now. The quantum key distribution, the quantum bit commitment, and the quantum secret sharing and quantum oblivious transfer, etc. are enumerated assuming that it is the main. In this research, the quantum secret sharing schemes (QSSS) are especially paid to attention.
It explains secret sharing schemea before it explains quantum secret sharing schemes. Secret Sharing Schemes (SSS) was a method of dividing, and sharing the confidential information in two or more division information (share), and it was independently proposed by Shamir and Blakely. There is a (k,n) threshold scheme in one of SSS. In a (k,n) threshold scheme,any k of the n users can reconstruct the secret, while a set of less than k users has no information about secret at all. The set that can reconstruct the secret is called and authorized set and the set that cannot be reconstruct are called unauthorized set. SSS with only authorized set and unauthorized set is called perfect. Moreover, the family of authorized set is called an access structure.
In general, the one that is called QSSS is divided into two. One shares classics information by using the state of the quantum. Another shares the state of the quantum treated by this research. The purpose of QSSS is toshare "Important state of the quantum" as it is. Presumption and the measurement are finally done to the state of the quantum. However, "Important state of the quantum" indicates the state of the quantum before the measurement of the operation result of the quantum computer etc. is done here.
For instance, it thinks about the quantum calculation. In the quantum calculation, it thinks the unitary transformation by the space that N bit tensor product puts to be a calculation by making it correspond to 0 and 1 by using the orthogonalization of two semi-place system. The function as do not provide the Entangled quantum state of N bit that appears by the process so far is offered. The Entangled quantum various states that appear during the calculation are preserved in the memory of the quantum computer. However, it can be superposition various possibilities to a final solution and exists. Therefore, it is unknown. It can be said that the QSSS are the important field of researchs for preservation and sharing in the state of the quantum that will become important by the development such as the quantum computers in the future.
The QSSS were proposed by Hillery for the first time in 1999. This protocol is called HBB QSSS, and is ((n,n)) threshold scheme that uses the state of GHZ in the state of Entangled more than three particles. The condition concerning QSSS were shown by Cleve and Gottesman. In addtion, it proposed the technique for which Smith used MSP(Monotone Span Programs) for the protocol and it proposed the technique for which Bnadyopadhyay used the quantum teleportation.
In this research, it proposes the protocol that shares two or more confidential information based on the protocol that uses MSP that Smith proposed. Moreover, this protocol shows that only the provided confidential information is reconstructed according to authorized set.

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