# Choosing the Bernoulli distribution for LPN encryption scheme

The symmetric-key encryption scheme from  is based on the LPN (learning parity with noise) problem. The definition of the problem is, informally, that the adversary cannot recover $$\mathbf{s}$$ from $$\mathbf{A} \cdot \mathbf{s} \oplus \mathbf{e}$$ given $$\mathbf{A}$$, where $$\mathbf{A}, \mathbf{s}$$ and $$\mathbf{e}$$ are some random (public) matrix, the secret and the noise vector, respectively. The noise $$\mathbf{e}$$ is sampled from a Bernoulli distribution with parameter $$\eta$$.

My understanding is that typically $$0 < \eta < 1/2$$. But the lower $$\eta$$ is, the easier it is to break LPN (when $$\eta$$ is 0 LPN can be solved using Gaussian elimination). Suppose I need a security level of, for example, 80 bits, how do I select the value of $$\eta$$ if other parameters are fixed? I understand  provides some concrete parameters, but it's unclear to me how to calculate the security level from a concrete value of $$\eta$$.