▁ins u fficient ▁size ▁should ▁learn ▁nothing . ▁Secret ▁sharing ▁is ▁at ▁the ▁root ▁of ▁many ▁protocol s ▁for ▁secure ▁computation : ▁in ▁order ▁to ▁secure ly ▁compute ▁a ▁function ▁of ▁some ▁shared ▁input , ▁the ▁secret ▁shares ▁are ▁manip ulated ▁instead . ▁However , ▁if ▁shares ▁are ▁to ▁be ▁generated ▁by ▁mal icious ▁parties , ▁it ▁may ▁be ▁important ▁that ▁those ▁shares ▁can ▁be ▁checked ▁for ▁correct ness . ▁In ▁a ▁ver ifiable ▁secret ▁sharing ▁scheme , ▁the ▁distribution ▁of ▁a ▁secret ▁is ▁accompanied ▁by ▁commit ments ▁to ▁the ▁individual ▁shares . ▁The ▁commit ments ▁reve al ▁nothing ▁that ▁can ▁help ▁a ▁d ish on est ▁cab al , ▁but ▁the ▁shares ▁allow ▁each ▁individual ▁party ▁to ▁check ▁to ▁see ▁if ▁their ▁shares ▁are ▁correct . ▁ ▁Def ining ▁the ▁security ▁ ▁F ormal ▁definitions ▁of ▁commit ment ▁schemes ▁vary ▁strongly ▁in ▁notation ▁and ▁in ▁flav our . ▁The ▁first ▁such ▁flav our ▁is ▁whether ▁the ▁commit ment ▁scheme ▁provides ▁perfect ▁or ▁computational ▁security ▁with ▁respect ▁to ▁the ▁hiding ▁or ▁binding ▁properties . ▁ ▁Another ▁such ▁flav our ▁is ▁whether ▁the ▁commit ment ▁is ▁interactive , ▁i . e . ▁whether ▁both ▁the ▁commit ▁phase ▁and ▁the ▁reve al ▁phase ▁can ▁be ▁seen ▁as ▁being ▁executed ▁by ▁a ▁crypt ographic ▁protocol ▁or ▁whether ▁they ▁are ▁non - inter active , ▁consisting ▁of ▁two ▁algorithms ▁Comm it ▁and ▁Check Re ve al . ▁In ▁the ▁latter ▁case ▁Check Re ve al ▁can ▁often ▁be ▁seen ▁as ▁a ▁der andom ised ▁version ▁of ▁Comm