1 July 2009 Fast-weighted secret image sharing
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Optical Engineering, 48(7), 077008 (2009). doi:10.1117/1.3168644
Thien and Lin [Comput. and Graphics 26(5), 765-770 (2002)] proposed a threshold scheme to share a secret image among n shadows: any t of the n shadows can recover the secret, whereas t-1 or fewer shadows cannot. However, in real life, certain managers probably play key roles to run a company and thus need special authority to recover the secret in managers' meeting. (Each manager's shadow should be more powerful than an ordinary employee's shadow.) In Thien and Lin's scheme, if a company has less than t managers, then manager's meeting cannot recover the secret, unless some managers were given multiple shadows in advance. But this compromise causes managers inconvenience because too many shadows were to be kept daily and carried to the meeting. To solve this dilemma, a weighted sharing method is proposed: each of the shadows has a weight. The secret is recovered if and only if the total weights (rather than the number) of received shadows is at least t. The properties of GF(2r) are utilized to accelerate sharing speed. Besides, the method is also a more general approach to polynomial-based sharing. Moreover, for convenience, each person keeps only one shadow and only one shadow index.
Sian-Jheng Lin, Lee Shu-Teng Chen, Ja-Chen Lin, "Fast-weighted secret image sharing," Optical Engineering 48(7), 077008 (1 July 2009). https://doi.org/10.1117/1.3168644


Geometry of a spherical image
Proceedings of SPIE (June 23 1993)

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