Improved Upper Bounds for the Information Rates of the Secret Sharing Schemes Induced by the Vamos Matroid

Details Improved Upper Bounds for the Information Rates of the Secret Sharing Schemes Induced by the Vamos Matroid Improved Upper Bounds for the Information Rates of the Secret Sharing Schemes Induced by the Vamos Matroid

2008-09-17

arxiv.org/abs/0809.3010v1

Computer Science

Cryptography and Security

Scientific paper

An access structure specifying the qualified sets of a secret sharing scheme must have information rate less than or equal to one. The Vamos matroid induces two non-isomorphic access structures V1 and V6, which were shown by Marti-Farre and Padro to have information rates of at least 3/4. Beimel, Livne, and Padro showed that the information rates of V1 and V6 are bounded above by 10/11 and 9/10 respectively. Here we improve those upper bounds to 19/21 for V1 and 17/19 for V6.

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