Let s be a secret that is an integer between 0 and q .

Bob designed an (n,n) secret sharing scheme using the addition operation. It works in the following way:

• To share the secret, the dealer chooses n 1 uniformly random number between 0 to q , d₁, ... , d_n1. The dealer computes the last share d_n = s + d₁ + d₂ + d_n1. The dealer gives d_i to the ith party.
• To reconstruct the secret, compute s' = d_n d₁ d₂ -d_n1.

True/False, this addition based secret sharing scheme is perfectly secure, i.e. no information is leaked about the secret from any proper subset of the shares?