(GAP question) The league club Crawlers United has six senior board members. Each year the club...

 

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(GAP question) The league club Crawlers United has six senior board members. Each year the club holds an anniversary day, and on this day the senior board members have a duty to open the club vault, take out the club's meager collection of trophies, and put them on display. According to a clause in the club's constitution any four of them are allowed to open the vault. The club set up a Shamir's threshold access secret sharing scheme for facilitating this clause with the secret password being an element of Z97. According to this scheme the administrator issued electronic cards to the senior board members as required. Suppose that three senior board members are gathered to open the vault with the following cards: 1 Z(97)37 2 Z(97)7 4 6 Z(97) 24 Z(97)27 (a) Show how the secret password can be calculated. (b) Which cards were given to the two remaining senior board members? Hint: Use commands InterpolatedPolynomial and Value. (GAP question) The league club Crawlers United has six senior board members. Each year the club holds an anniversary day, and on this day the senior board members have a duty to open the club vault, take out the club's meager collection of trophies, and put them on display. According to a clause in the club's constitution any four of them are allowed to open the vault. The club set up a Shamir's threshold access secret sharing scheme for facilitating this clause with the secret password being an element of Z97. According to this scheme the administrator issued electronic cards to the senior board members as required. Suppose that three senior board members are gathered to open the vault with the following cards: 1 Z(97)37 2 Z(97)7 4 6 Z(97) 24 Z(97)27 (a) Show how the secret password can be calculated. (b) Which cards were given to the two remaining senior board members? Hint: Use commands InterpolatedPolynomial and Value.