I recently encountered a breakthrough in FHE crypto, which claims to have a literally quasi-linear time FHE without any "lambda" factor in the keys and no noise in the cipher-text.
This fully homomorphic encryption works like for addition like $E(m_1)·E(m_2) = E(m_1+m_2)$ and for multiplication like $E(m_1)^{m_2} = E(m_1·m_2)$ ; they say they achieved it using p-adic exponential.
My Question is: What is exactly p-adic exponential?