3,497 research outputs found
Secure Grouping Protocol Using a Deck of Cards
We consider a problem, which we call secure grouping, of dividing a number of
parties into some subsets (groups) in the following manner: Each party has to
know the other members of his/her group, while he/she may not know anything
about how the remaining parties are divided (except for certain public
predetermined constraints, such as the number of parties in each group). In
this paper, we construct an information-theoretically secure protocol using a
deck of physical cards to solve the problem, which is jointly executable by the
parties themselves without a trusted third party. Despite the non-triviality
and the potential usefulness of the secure grouping, our proposed protocol is
fairly simple to describe and execute. Our protocol is based on algebraic
properties of conjugate permutations. A key ingredient of our protocol is our
new techniques to apply multiplication and inverse operations to hidden
permutations (i.e., those encoded by using face-down cards), which would be of
independent interest and would have various potential applications
The Landscape of Computing Symmetric -Variable Functions with Cards
Secure multi-party computation using a physical deck of cards, often called
card-based cryptography, has been extensively studied during the past decade.
Many card-based protocols to securely compute various Boolean functions have
been developed. As each input bit is typically encoded by two cards, computing
an -variable Boolean function requires at least cards. We are
interested in optimal protocols that use exactly cards. In particular, we
focus on symmetric functions, where the output only depends on the number of 1s
in the inputs. In this paper, we formulate the problem of developing -card
protocols to compute -variable symmetric Boolean functions by classifying
all such functions into several NPN-equivalence classes. We then summarize
existing protocols that can compute some representative functions from these
classes, and also solve some of the open problems by developing protocols to
compute particular functions in the cases , , , and
AND Protocols Using Only Uniform Shuffles
Secure multi-party computation using a deck of playing cards has been a
subject of research since the "five-card trick" introduced by den Boer in 1989.
One of the main problems in card-based cryptography is to design
committed-format protocols to compute a Boolean AND operation subject to
different runtime and shuffle restrictions by using as few cards as possible.
In this paper, we introduce two AND protocols that use only uniform shuffles.
The first one requires four cards and is a restart-free Las Vegas protocol with
finite expected runtime. The second one requires five cards and always
terminates in finite time.Comment: This paper has appeared at CSR 201
Using Five Cards to Encode Each Integer in
Research in secure multi-party computation using a deck of playing cards,
often called card-based cryptography, dates back to 1989 when Den Boer
introduced the "five-card trick" to compute the logical AND function. Since
then, many protocols to compute different functions have been developed. In
this paper, we propose a new encoding scheme using five cards to encode each
integer in . Using this encoding scheme, we develop
protocols that can copy a commitment with 13 cards, add two integers with 10
cards, and multiply two integers with 16 cards. All of our protocols are the
currently best known protocols in terms of the required number of cards. Our
encoding scheme can also be generalized to encode integers in
for other values of as well
Card-Based ZKP Protocols for Takuzu and Juosan
International audienc
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