Abstract-Information-theoretically secure string oblivious transfer (OT) can be constructed based on discrete memoryless channel (DMC). The oblivious transfer capacity of a channel characterizes -similarly to the (standard) information capacity -how efficiently it can be exploited for secure oblivious transfer of strings. The OT capacity of a Generalized Erasure Channel (GEC) -which is a combination of a (general) DMC with the erasure channel -has been established by Ahlswede and Csizar at ISIT'07 in the case of passive adversaries. In this paper, we present the protocol that achieves this capacity against malicious adversaries for GEC with erasure probability at least 1/2. Our construction is based on the protocol of Crépeau and Savvides from Eurocrypt'06 which uses interactive hashing (IH). We solve an open question posed by the above paper, by basing it upon a constant round IH scheme (previously proposed by Ding et al at TCC'04). As a side result, we show that Ding et al IH protocol can deal with transmission errors.

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Committed Oblivious Transfer (COT) is a two-party primitive that combines one-out-of-two oblivious transfer with bit commitment. In the beginning of COT, a sender is committed to bits b0, b1 and a receiver to a choice bit c. In the end, the receiver is committed to bc without learning anything about b1-c, while the sender learns nothing about c. This primitive implies secure multi-party computation assuming that a broadcast channel is available. In this paper, we introduce the first universally composable unconditionally secure committed oblivious transfer protocol based on a Trusted Initializer (TI), which pre-distributes data to the parties. Our protocol builds on simple bit commitment and oblivious transfer protocols, using XOR commitments to prove simple relations in zero-knowledge. Besides providing very high security guarantees, our protocols are significantly simpler and more efficient than previous results, since they rely on pre-computed operations distributed by the TI.