Regarding Lattice atttacks on ECDSA with a portion of known bits of the nonce k
The constant is derived from the so-called Gaussian Heuristic, which is used to predict the expected length of the shortest vector of a random lattice. For the attack to work, one must ensure that the special vector that he is looking for will be the shortest, so that it can be found. We therefore compare the length of that to-be-found vector with the expected length of the shortest lattice vector.