This system is based on a type of knapsack problem. Specifically, the underlying problem is this: given integers c,n,p and v0,...,vn, find a vector such that
The idea here is that when the vi are relatively prime and much smaller than the modulus p this problem can be solved easily. It is this observation which allows decryption.
Read more about this topic: Naccache–Stern Knapsack Cryptosystem
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