The complexity of promise problems with applications to public-key cryptography

Comparing entropies in statistical zero knowledge with applications to the structure of SZK

“…I follows. 1 A promise problem is a pair of disjoint sets of strings, corresponding to yes and no instances, respectively [9].…”

A thirty Year old conjecture about promise problems

“…We say that a set S is a separator for (A, B) if B ⊆ S and A ⊆ S. We now state the original conjecture of Even, Selman, and Yacobi [ESY84].…”

“…Even, Selman and Yacobi [ESY84,SY82] conjectured that there do not exist certain promise problems all of whose solutions are NP-hard. Specifically, there do not exist disjoint NP-pairs all of whose separators are NP-hard.…”

Survey of Disjoint NP-pairs and Relations to Propositional Proof Systems

“…Although we are primarily interested in the question of whether there exist many-one complete pairs, let's pause for a moment to consider the question of whether there exist Turingcomplete pairs. Even, Selman, and Yacobi [ESY84] conjectured that DisjNP does not contain a disjoint pair all of whose separators are NP-hard (i.e., ≤ p T -hard for NP.) The conjecture has strong consequences, for it implies that NP = coNP, NP = UP, and no public-key cryptosystem is NP-hard to crack [ESY84,GS88].…”

“…Even, Selman, and Yacobi [ESY84] conjectured that DisjNP does not contain a disjoint pair all of whose separators are NP-hard (i.e., ≤ p T -hard for NP.) The conjecture has strong consequences, for it implies that NP = coNP, NP = UP, and no public-key cryptosystem is NP-hard to crack [ESY84,GS88]. For example, if NP = coNP, then for every NP-complete S, the pair (S, S) is in DisjNP and all of its separators are NP-hard (since S is the only separator).…”