Grade protocol

A group of k students (s₁ to s_k) is given each a secret grade g_i between 0 and m-1. The students want to compute the sum of their grades without disclosing them. To this aim they produce k random numbers between 0 and , such that the number r_i is known only to the students s_i and s_i. Then each student s_i declares a number , and the sum of all grades is equivalent to the sum of the declarations modulo n.

To prove the security of the protocol, and thus the secrecy of the grades, we need to show that the information the attacker gains by knowing the declarations and the sum is the same as the information he would gain by knowing only the sum. The leakage of the protocol for different numbers of students and grades is shown in the tables below; on the left the leakage of the Grade protocol and on the right the leakage of a protocol declaring only the final sum. The tables are identical, proving that the attacker that knowing the students declarations and the sum of the grades does not provide any more information to the attacker than just knowing the sum of the grades.