A collection of K random variables are called (K,n)-MDS if any n of the
K variables are independent and determine all remaining variables. In the MDS
variable generation problem, K users wish to generate variables that are
(K,n)-MDS using a randomness variable owned by each user. We show that to
generate 1 bit of (K,n)-MDS variables for each nβ{1,2,β―,K},
the minimum size of the randomness variable at each user is 1+1/2+β―+1/K bits.
An intimately related problem is secure summation with user selection, where
a server may select an arbitrary subset of K users and securely compute the
sum of the inputs of the selected users. We show that to compute 1 bit of an
arbitrarily chosen sum securely, the minimum size of the key held by each user
is 1+1/2+β―+1/(Kβ1) bits, whose achievability uses the generation
of (K,n)-MDS variables for nβ{1,2,β―,Kβ1}