Abstract
In the paper, we propose three threshold secret sharing schemes that are based on difference equations. The first scheme is a (t,n) −threshold scheme which is an ideal perfect secure. The other two schemes add the restricted order structure to the set of shadows and the access structure of secret sharing policy. The basis of the access structure of one scheme allows that only subsets that contain consecutive shadows can compute the broken secret, but no other subset of shadows can do so. The basis of the access structure of the other scheme allows that shadow subsets contain an imperfect consecutive shadow subset that has one gap of size 1, and can compute the original secret.
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References
Shamir, A.: how to share a secret. Communications of the ACM 22, 612–613 (1979)
Stinson, D.R.: cryptography–theory and practice. CRC Press, Boca Raton, London, Tokyo (1995)
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© 2007 Springer-Verlag Berlin Heidelberg
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Chan, CW., Chang, CC. (2007). A New (t,n) −Threshold Scheme Based on Difference Equations. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_9
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DOI: https://doi.org/10.1007/978-3-540-74450-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74449-8
Online ISBN: 978-3-540-74450-4
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