▁the ▁secret . ▁The ▁secret ▁can ▁be ▁re construct ed ▁only ▁when ▁a ▁sufficient ▁number ▁of ▁shares , ▁of ▁possibly ▁different ▁types , ▁are ▁combined ▁together ; ▁individual ▁shares ▁are ▁of ▁no ▁use ▁on ▁their ▁own . ▁A ▁secret ▁sharing ▁scheme ▁is ▁perfect ▁if ▁every ▁collection ▁of ▁participants ▁that ▁does ▁not ▁meet ▁the ▁criteria ▁for ▁obtain ing ▁the ▁secret , ▁has ▁no ▁additional ▁knowledge ▁of ▁what ▁the ▁secret ▁is ▁than ▁does ▁an ▁individual ▁with ▁no ▁share . ▁ ▁In ▁one ▁type ▁of ▁secret ▁sharing ▁scheme ▁there ▁is ▁one ▁deal er ▁and ▁n ▁players . ▁The ▁deal er ▁gives ▁shares ▁of ▁a ▁secret ▁to ▁the ▁players , ▁but ▁only ▁when ▁specific ▁conditions ▁are ▁ful filled ▁will ▁the ▁players ▁be ▁able ▁to ▁re construct ▁the ▁secret . ▁The ▁deal er ▁accomplish es ▁this ▁by ▁giving ▁each ▁player ▁a ▁share ▁in ▁such ▁a ▁way ▁that ▁any ▁group ▁of ▁t ▁( for ▁threshold ) ▁or ▁more ▁players ▁can ▁together ▁re construct ▁the ▁secret ▁but ▁no ▁group ▁of ▁fewer ▁than ▁t ▁players ▁can . ▁Such ▁a ▁system ▁is ▁called ▁a ▁( t ,   n )- th reshold ▁scheme . ▁ ▁A ▁t -( v , ▁n ▁+ ▁ 1 , ▁ 1 ) ▁orthogonal ▁array ▁may ▁be ▁used ▁to ▁construct ▁a ▁perfect ▁( t , ▁n )- th reshold ▁scheme . ▁ ▁Let ▁A ▁be ▁the ▁orthogonal ▁array . ▁The ▁first ▁n ▁columns ▁will ▁be ▁used ▁to ▁provide ▁shares ▁to ▁the ▁players , ▁while ▁the ▁last ▁column ▁represents ▁the ▁secret ▁to ▁be ▁shared . ▁If ▁the ▁deal