Strong Conditional Oblivious Transfer and Computing on Intervals

We consider the problem of securely computing the Greater Than (GT) predicate and its generalization – securely determining membership in a union of intervals. We approach these problems from the point of view of Q-Conditional Oblivious Transfer (Q-COT), introduced by Di Crescenzo, Ostrovsky and Rajagopalan [4]. Q-COT is an oblivious transfer that occurs iff predicate Q evaluates to true on the parties’ inputs. We are working in the semi-honest model with computationally unbounded receiver. In this paper, we propose: (i) a stronger, simple and intuitive definition of COT, which we call strong COT, or Q-SCOT. (ii) A simpler and more efficient one-round protocol for securely computing GT and GTSCOT. (iii) A simple and efficient modular construction reducing SCOT based on membership in a union of intervals (UI-SCOT) to GT-SCOT, producing an efficient one-round UI-SCOT.