Secret sharing - Size of the share I'm having some hard time understanding why the size of the share must be at least as large as the secret itself, why is this restriction imposed? What would happen if the share is smaller?
In Shamir's secret-sharing scheme, the secret and the shares of the secret all are elements of a finite field, and so necessarily have the same size. In the Reed-Solomon code based variant of Shamir's secret-sharing scheme proposed by the late Bob McEliece and myself (R.J. McEliece and D.V. Sarwate, "On sharing secrets and Reed-Solomon codes", Communications of the ACM, v. 24, Issue 9, Sep 1981), the $n$ shares are $\frac 1k$-th the size of the secret, but these schemes don't have the perfect information-theoretic security of Shamir's scheme. See this answer.