Abstract
Quantum secret sharing (QSS) can usually realize unconditional security with entanglement of quantum systems. While the usual security proof has been established in theoretics, how to defend against the tolerable channel loss in practices is still a challenge. The traditional ( t , n ) threshold schemes are equipped in situation where all participants have equal ability to handle the secret. Here we propose an improved ( t , n ) threshold continuous variable (CV) QSS scheme using weak coherent states transmitting in a chaining channel. In this scheme, one participant prepares for a Gaussian-modulated coherent state (GMCS) transmitted to other participants subsequently. The remaining participants insert independent GMCS prepared locally into the circulating optical modes. The dealer measures the phase and the amplitude quadratures by using double homodyne detectors, and distributes the secret to all participants respectively. Special t out of n participants could recover the original secret using the Lagrange interpolation and their encoded random numbers. Security analysis shows that it could satisfy the secret sharing constraint which requires the legal participants to recover message in a large group. This scheme is more robust against background noise due to the employment of double homodyne detection, which relies on standard apparatuses, such as amplitude and phase modulators, in favor of its potential practical implementations.
Highlights
Secret sharing is a branch of cryptography [1], in which the dealer distributes a secret to all participants and only legitimate participants can reconstruct the shared secret in the cooperation fashion
Motivated by the elegant characteristics of the Gaussian-modulated coherent state (GMCS)-involved system, we suggest an approach for establishing the GMCS-based continuous variable QSS (CVQSS)
Because the secure key of CVQSS ought to secure against any group of t − 1 participants, the dealer needs to select the smallest one among secure key rates of legitimate participants and the dealer
Summary
Secret sharing is a branch of cryptography [1], in which the dealer distributes a secret to all participants and only legitimate participants can reconstruct the shared secret in the cooperation fashion. Supposing that the sequence of t participants is shown, the dealer randomly chooses a subset of the remained raw data and demands all participants except C12 to publish the corresponding Gaussian random numbers. The dealer selects the secure key rate R of the proposed protocol as the minimum of { R1j1 , R2j2 , · · · , Rtjt }, Rljl = R j [18] and sends them to all the participants according to the sequence of Clj. After affirming Clj has received the coding sequence, the dealer announces the initially inserted state and position of each decoy particles to Clj. { x j , f ( xljl )} becomes the private key of Clj. Legitimate participants restore the secret S by the Lagrange interpolation.
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