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On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions
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On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions
Ivan Damgård5  , Joe Kilian6 and Louis Salvail5
| (5) |
BRICS, Basic Research in Computer Science, center of the Danish National Research Foundation, Department of Computer Science, University of Århus, Ny Munkegade, DK-8000 Århus C, Denmark |
| (6) |
NEC Research Institute, 4 Independence Way, Princeton, NJ, 08540, Denmark |
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 Weak Generic Transfer (WGT). This model includes as important special cases Weak Oblivious Transfer (WOT), where both the sender and receiver may learn too much about the other party’s input, and a new, more realistic model
of noisy channels, called unfair noisy channels. An unfair noisy channel has a known range of possible noise levels; protocols must work for any level within this range
against adversaries who know the actual noise level.
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 a 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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