Naively, when one applies rounding to a uniform random value one anticipates that the change is uniformly distributed. In lattice-based cryptography, is there a formal notion or proof of equivalence between learning with rounding and learning with uniform error schemes?
Secondly has anyone proposed a dynamic version of learning with rounding where the level of rounding is chosen to optimise the bandwidth savings in the rounded cryptogram. e.g. I might be prepared to round off the last three bits of a binary value 10001010100000000110 allowing me to round to nine significant figures whereas a binary value 1001001101010110101 might be rounded less.
