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Quantum Ramp Secret Sharing

Ryutaroh Matsumoto
(Tokyo Institute of Technology. Velux Visiting Professor at Aalborg University.)
Onsdag, 19 november, 2014, at 12:15-14:00, in Aud. G2 (1532-122)
It is well-known that the ramp (or non-perfect) secret sharing schemes
reduce share size.  This benefit also exists in the quantum ramp
secret sharing, in which secret and shares are quantum information.
The first and only quantum ramp secret sharing was proposed by Ogawa
et al., which encodes vector indices of quantum secret into
coefficients of a polynomial over a finite field $F_q$.  Ogawa et
al.'s scheme has two drawbacks, namely, (1) it does not control how
information is leaked to a non-qualified set of shares, and (2) the
dimension $q$ of quantum shares must be larger than the number of
shares, because a share is constructed by evaluation of a polynomial
at distinct non-zero elements in $F_q$. We propose new quantum ramp
schemes to overcome (1) and (2). To overcome (1), we introduce a
quantum version of the strong security proposed by H. Yamamoto for
classical ramp schemes, which ensures a non-qualified set of shares
has zero information about parts of secret, then we provide an
explicit construction of quantum strongly secure ramp schemes based on
the classical strongly secure ramp schemes. To overcome (2), we
provide a complete characterization of qualified, intermediate, and
forbidden sets of shares, when the quantum ramp secret sharing is the
Calderbank-Shor-Steane code for the quantum error correction.  The
first part is arXiv:1404.5749 and the second is arXiv:1405.0149.
Kontaktperson: Johan Peder Hansen