# Is that simple additive homomorphic scheme secure?

I am doing a little cryptography research and stuck with question.

Suppose $\bar m$ is a vector of 64-bit numbers. And i want to have an additive homomorphic encryption over them. I choose large (2048 bit) prime $n$, large not prime $s$ and vector $\bar r$ of large random numbers, with size of vector equal to vector $\bar m$. Finaly, encryption function $Enc$ looks like that: $$Enc(m_i) = (r_i,m_i+r_i\cdot s\mod n)$$ where $Enc$ yields an ordered pair of numbers. So the number $n$ with encrypted vector $c=Enc(m)$ goes to the opponent, but $s$ keeps secret.

Sum of an encrypted values is just sum of pairs (all operations are modulo $n$): $$Sum(c_i,c_j) = (c_i.first+c_j.first,c_i.second+c_j.second)$$ $$or$$ $$(a,b)+(c,d)=(a+c,b+d)$$ where $c_i.first$ is the first element of pair $c_i$ and $c_i.second$ is the second.

Decryption looks like that: $$Dec(c_i) = c_i.second - c_i.first\cdot s$$

Intuitively, i think, that this scheme is vulnerable, but i can't see why. I will be glad to have a hint to understanding this problem.

Many thanks in advance to your great community!
(sorry for any grammar mistakes, English is not my native language)

It is not semantically secure. If the adversary asks for the encryption of message $0$ then it gets $r_i,r_i*s$, so it recovers the secret key $s$ and breaks the security game.