Efficient Unconditional Oblivious Transfer from Almost Any Noisy Channel

Crépeau, Claude; Morozov, Kirill; Wolf, Stefan

doi:10.1007/978-3-540-30598-9_4

Cited by 70 publications

(61 citation statements)

References 16 publications

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“…Motivated by our results from Sect. 6 and Sect. 7, we categorize correlated equilibria payoffs using the terminology of Impagliazzo [11].…”

Section: Computational Cheap Talk Simultaneous Move Gamesmentioning

confidence: 95%

“…It follows from the seminal work of Impagliazzo and Luby [12] that weak coin-flip implies one-way functions. 6 Consider the CTSM game specified by Γ = (A 1 , A 2 ), where A 1 = {c, d}, A 2 = {C, D}, and the utility function u is given in Fig. 3 is a convex hull NE achieving the utility profile (2, 2).…”

Section: Implementing All Minicrypt Payoffs Implies One-way Functionsmentioning

confidence: 99%

“…We use the result of Crépeau, Morozov and Wolf [6] that any non-trivial Discrete Memoryless Channel implies OT. Thus, it suffices to show that there are some correlation devices that can be used to simulate a non-trivial DMC; the existence of any such correlation device would consequently imply the existence of OT.…”

Section: Perfectly Implementing Any Ce Outside Chne Implies Unconditimentioning

confidence: 99%

“…Definition 7.4 (Crépeau et al [6]). We call a channel P Y |X trivial if there exist, after removal of all redundant input symbols, partitions of the (remaining) ranges X of X and …”

Section: Definition 73 (Discrete Memoryless Channel)mentioning

confidence: 99%

“…The following theorem characterizes DMCs with respect to the possibility of their use to create unconditional OT: Theorem 7.8 (Crépeau et al [6]). Let two players A and B be connected by a non-trivial channel P Y |X .…”

Section: Definition 73 (Discrete Memoryless Channel)mentioning

confidence: 99%

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Limits on the Power of Cryptographic Cheap Talk

Hubáček

Nielsen

Rosen

2013

Advances in Cryptology – CRYPTO 2013

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We revisit the question of whether cryptographic protocols can replace correlated equilibria mediators in two-player strategic games. This problem was first addressed by Dodis, Halevi and Rabin (CRYPTO 2000), who suggested replacing the mediator with a secure protocol and proved that their solution is stable in the Nash equilibrium (NE) sense, provided that the players are computationally bounded.We show that there exist two-player games for which no cryptographic protocol can implement the mediator in a sequentially rational way; that is, without introducing empty threats. This explains why all solutions so far were either sequentially unstable, or were restricted to a limited class of correlated equilibria (specifically, those that do not dominate any NE, and hence playing them does not offer a clear advantage over playing any NE).In the context of computational NE, we classify necessary and sufficient cryptographic assumptions for implementing a mediator that allows to achieve a given utility profile of a correlated equilibrium. The picture that emerges is somewhat different than the one arising in semi-honest secure two-party computation. Specifically, while in the latter case every functionality is either "complete" (i.e., implies Oblivious Transfer) or "trivial" (i.e., can be securely computed unconditionally), in the former there exist some "intermediate" utility profiles whose implementation is equivalent to the existence of one-way functions.

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“…Motivated by our results from Sect. 6 and Sect. 7, we categorize correlated equilibria payoffs using the terminology of Impagliazzo [11].…”

Section: Computational Cheap Talk Simultaneous Move Gamesmentioning

confidence: 95%

Section: Implementing All Minicrypt Payoffs Implies One-way Functionsmentioning

confidence: 99%

Section: Perfectly Implementing Any Ce Outside Chne Implies Unconditimentioning

confidence: 99%

“…Definition 7.4 (Crépeau et al [6]). We call a channel P Y |X trivial if there exist, after removal of all redundant input symbols, partitions of the (remaining) ranges X of X and …”

Section: Definition 73 (Discrete Memoryless Channel)mentioning

confidence: 99%

Section: Definition 73 (Discrete Memoryless Channel)mentioning

confidence: 99%

See 3 more Smart Citations

Limits on the Power of Cryptographic Cheap Talk

Hubáček

Nielsen

Rosen

2013

Advances in Cryptology – CRYPTO 2013

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New Monotones and Lower Bounds in Unconditional Two-Party Computation

Wolf

Wullschleger

2005

Advances in Cryptology – CRYPTO 2005

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Since bit and string oblivious transfer and commitment, two primitives of paramount importance in secure two-and multi-party computation, cannot be realized in an unconditionally secure way for both parties from scratch, reductions to weak information-theoretic primitives as well as between different variants of the functionalities are of great interest. In this context, we introduce three independent monotones-quantities that cannot be increased by any protocol-and use them to derive lower bounds on the possibility and efficiency of such reductions. An example is the transition between different versions of oblivious transfer, for which we also propose a new protocol allowing to increase the number of messages the receiver can choose from at the price of a reduction of their length. Our scheme matches the new lower bound and is, therefore, optimal.

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