On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment
on Weakened Security Assumptions
Ivan B. Damgård December 1998 |

## Abstract:We consider the problem of basing Oblivious Transfer (OT) and
Bit Commitment (BC), with information theoretic security, on seemingly weaker
primitives. We introduce a general model for describing such primitives,
called We give a precise characterization for when one can base OT on WOT. When the deviation of the WOT from the ideal is above a certain threshold, we show that no information-theoretic reductions from OT (even against passive adversaries) and BC exist; when the deviation is below this threshold, we give a reduction from OT (and hence BC) that is information-theoretically secure against active adversaries. For unfair noisy channels we show a similar threshold phenomenon for bit commitment. If the upper bound on the noise is above a threshold (given as function of the lower bound) then no information-theoretic reduction from OT (even against passive adversaries) or BC exist; when it is below this threshold we give a reduction from BC. As a partial result, we give a reduction from OT to UNC for smaller noise intervals
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