We study the communication complexity of the SHIFT (equivalently, SUM-INDEX) function in a 3-party simultaneous message model. Alice and Bob share an n-bit string x and Alice holds an index i and Bob an index j. They must send messages to a referee who knows only n, i and j, enabling him to determine x[(i+j) mod n]. Surprisingly, it is possible to achieve nontrivial savings even with such a strong restriction: Bob can now make do with only ceil(n/2) bits. Here we show that this bound is completely tight, for all n. This is an exact lower bound, with no asymptotics involved
