Secret Sharing, Zero Sum Sets, and Hamming Codes
Keyword(s):
A (t,n)-secret sharing scheme is a method of distribution of information among n participants such that any t>1 of them can reconstruct the secret but any t−1 cannot. A ramp secret sharing scheme is a relaxation of that protocol that allows that some (t−1)-coalitions could reconstruct the secret. In this work, we explore some ramp secret sharing schemes based on quotients of polynomial rings. The security analysis depends on the distribution of zero-sum sets in abelian groups. We characterize all finite commutative rings for which the sum of all elements is zero, a result of independent interest. When the quotient is a finite field, we are led to study the weight distribution of a coset of shortened Hamming codes.
2021 ◽
Vol 6
(3)
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pp. 6-13
Keyword(s):
2016 ◽
Vol 27
(05)
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pp. 595-605
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Keyword(s):
2015 ◽
Vol 11
(1)
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pp. 15
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2019 ◽
Vol 2
(2)
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pp. 81
2005 ◽
Vol 5
(1)
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pp. 68-79
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2007 ◽
Vol 44
(3)
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pp. 297-306
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