Roll Your Own

No shot I would get this. This challenge is based on the Paillier cryptosystem, an additive homomorphic cryptosystem. Paillier cryptosystem exploits the fact that certain discrete logarithms can be computed easily. Indeed, by binomial theorem: $$ (1 + n) ^ x = 1 + nx + {x \choose 2} n ^ 2 + \text{higher powers of n} $$ which, under modulo $n ^ 2$, leads to: $$ (1 + n) ^ x = 1 + nx \mod n^2 $$ This is the crux of the challenge....