They are generally esoteric conjectures similar in spirit to P != NP. For example, the third paper uses the assumption "E requires exponential circuits". Here E

They are generally esoteric conjectures similar in spirit to P != NP. For example, the third paper uses the assumption "E requires exponential circuits". Here E is the class of problems solvable in exponential time, or 2^O(n) time, on a Turing Machine. Another model of computation besides Turing Machines are Boolean circuits, i.e. AND, OR, and NOT gates. The conjecture is that not every problem in E can be solved by "small" (subexponential-sized) circuits. The basic idea of the work is that if these problems are hard, then we can use them to build pseudorandom generators that are "just as good" as true random, which we can use to turn truly random algorithms into pseudorandom algorithms with the same performance.