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It turned out that the protocol I designed was good. Bob can't cheat because its impossible for him to discover $b$ because at every $\binom{1}{2}-OT$ iterations, Bob can only discover $b_i$ or $b_{i+1}$ for $i\geq1$ and $i=2k-1$ such that $1\leq k\leq\frac{n}{2}$ ($i$ is uneven). Alice has an exponentially small chance to cheat without getting caught ...