On beating the hybrid argument

The hybrid argument allows one to relate the distinguishability of a distribution (from uniform) to the predictability of individual bits given a prefix. The argument incurs a loss of a factor k equal to the bit-length of the distributions: ϵ-distinguishability implies ϵ/k-predictability. This paper studies the consequences of avoiding this loss -- what we call “beating the hybrid argument” -- and develops new proof techniques that circumvent the loss in certain natural settings. Our main results are: