Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Protocols and Hardness Results for the Two-Player
  Cryptogenography Problem   The cryptogenography problem, introduced by Brody, Jakobsen, Scheder, and
Winkler (ITCS 2014), is to collaboratively leak a piece of information known to
only one member of a group (i)~without revealing who was the origin of this
information and (ii)~without any private communication, neither during the
process nor before. Despite several deep structural results, even the smallest
case of leaking one bit of information present at one of two players is not
well understood. Brody et al.\ gave a 2-round protocol enabling the two players
to succeed with probability $1/3$ and showed the hardness result that no
protocol can give a success probability of more than~$3/8$.
  In this work, we show that neither bound is tight. Our new hardness result,
obtained by a different application of the concavity method used also in the
previous work, states that a success probability better than 0.3672 is not
possible. Using both theoretical and numerical approaches, we improve the lower
bound to $0.3384$, that is, give a protocol leading to this success
probability. To ease the design of new protocols, we prove an equivalent
formulation of the cryptogenography problem as solitaire vector splitting game.
Via an automated game tree search, we find good strategies for this game. We
then translate the splits that occurred in this strategy into inequalities
relating position values and use an LP solver to find an optimal solution for
these inequalities. This gives slightly better game values, but more
importantly, it gives a more compact representation of the protocol and a way
to easily verify the claimed quality of the protocol.
  These improved bounds, as well as the large sizes and depths of the improved
protocols we find, suggests that finding good protocols for the
cryptogenography problem as well as understanding their structure are harder
than what the simple problem formulation suggests.

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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin