6 Secret sharing at Hogwarts1 Hogwarts teachers found a secr

6. [Secret sharing at Hogwarts^1] Hogwarts teachers found a secret spell that reprograms the Golden Snitch if it is acting strangely in a Quidditch match. They represented the secret spell as an integer and decided to use a secret sharing scheme to distribute it to all Quidditch players. There are four Quidditch teams at Hogwarts, with seven players on each team. However, the teachers realized that the standard secret sharing scheme will not work because they have the following unusual requirement: A subset of the players should be able to recover the secret if and only if it contains majorities (at least four out of seven) of at least three of the teams. Explain how to modify the polynomial secret sharing scheme to achieve this requirement. Hint: Try a two-level scheme, one level for teams, the other for players on each team.

Solution

There are seven players each in 4 teams thus 28 players.

This scret can be recovered only if min 4 out of 7 or at least 3 teams

i.e. 12 members should be present out of 28.

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