Completeness Theorems with Constructive Proofs for Finite Deterministic 2-Party Functions

Kraschewski, Daniel; Müller-Quade, Jörn

doi:10.1007/978-3-642-19571-6_22

Cited by 18 publications

(14 citation statements)

References 27 publications

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“…Using the normal form described above, we show that, unless a functionality is passive-complete, it is isomorphic to one with symmetric output. This generalizes an analogous result of [9] for non-reactive functionalities.…”

Section: Passive-trivial; and 2 F Is Passive-complete If And Only Ifsupporting

confidence: 86%

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Characterizing the Cryptographic Properties of Reactive 2-Party Functionalities

Jeffs

Rosulek

2013

Theory of Cryptography

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Abstract. In secure multi-party computation, a reactive functionality is one which maintains persistent state, takes inputs, and gives outputs over many rounds of interaction with its parties. Reactive functionalities are fundamental and model many interesting and natural cryptographic tasks; yet their security properties are not nearly as well-understood as in the non-reactive case (known as secure function evaluation).We present new combinatorial characterizations for 2-party reactive functionalities, which we model as finite automata. We characterize the functionalities that have passive-secure protocols, and those which are complete with respect to passive adversaries. Both characterizations are in the information-theoretic setting.

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Section: Passive-trivial; and 2 F Is Passive-complete If And Only Ifsupporting

confidence: 86%

“…Kilian [6] was the first to characterize completeness for 2-party SFE functionalities. The result was later generalized to functionalities with possibly different outputs to the two parties [9]. As before, we strongly leverage the well-known characterization for the SFE case in our own result for the reactive case.…”

Section: Introductionmentioning

confidence: 76%

Characterizing the Cryptographic Properties of Reactive 2-Party Functionalities

Jeffs

Rosulek

2013

Theory of Cryptography

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“…Kilian vastly generalized this by giving several completeness characterizations: active-complete deterministic asymmetric functions, passive-complete symmetric functions and passive-complete asymmetric functions [Kil00]. Kilian's result for active-completeness was extended in two different directions by subsequent work: Crépeau, Morozov and Wolf [CMW04] considered "channel functions" which are randomized asymmetric functions (only one party has output), but with the additional restriction that only one party has input; Kraschewski and Müller-Quade [KM11] considered functions in which both parties can have inputs and outputs, but restricted to deterministic functions.…”

Section: Connections To Circuitmentioning

confidence: 99%

A Full Characterization of Completeness for Two-Party Randomized Function Evaluation

Kraschewski

Maji²,

Prabhakaran

et al. 2014

Lecture Notes in Computer Science

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We settle a long standing open problem which has pursued a full characterization of completeness of (potentially randomized) finite functions for 2-party computation that is secure against active adversaries. Since the first such complete function was discovered [Kilian, FOCS 1988], the question of which finite 2-party functions are complete has been studied extensively, leading to characterization in many special cases. In this work, we completely settle this problem.We provide a polynomial time algorithm to test whether a 2-party finite secure function evaluation (SFE) functionality (possibly randomized) is complete or not. The main tools in our solution include:• A formal linear algebraic notion of redundancy in a general 2-party randomized function.• A notion of statistically testable games. A kind of interactive proof in the information-theoretic setting where both parties are computationally unbounded but differ in their knowledge of a secret.• An extension of the (weak) converse of Shannon's channel coding theorem, where an adversary can adaptively choose the channel based on it view.We show that any function f , if complete, can implement any (randomized) circuit C using only O(|C| + κ) calls to f , where κ is the statistical security parameter. In particular, for any two-party functionality g, this establishes a universal notion of its quantitative "cryptographic complexity" independent of the setup and has close connections to circuit complexity. * This paper is the result of merger of two independent works. One of these works is available online as [Kra13].

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“…(Converting the erasure channel to F OT requires interaction.) The way [KM11] handles active corruption using cut-and-choose checks is highly interactive and again inadequate for our purposes.…”

Section: Our Techniquesmentioning

confidence: 99%

“…This rather enigmatic protocol does invoke F with fixed roles, but is not useful for showing impossibility of concurrent secure protocol for F, because it is modestly interactive (two steps which should occur one after the other) and more importantly, because it yields only an erasure channel and not a 2 1 -OT. 10 The only known substitute for this protocol, by [KM11], is much more interactive, involving several rounds of communication in both directions, apart from the invocation of F. Our challenge is to devise an asynchronous non-interactive protocol which uses F with fixed-roles and directly yields 2 1 -OT. Being non-interactive and asynchronous requires that all the sessions are invoked together by an honest party, but the adversary is allowed to schedule them adaptively, and base its inputs for later sessions based on the outputs from earlier sessions (rushing adversary).…”

Section: Output Idealmentioning

confidence: 99%

New Impossibility Results for Concurrent Composition and a Non-interactive Completeness Theorem for Secure Computation

Agrawal

Goyal

Jain

et al. 2012

Lecture Notes in Computer Science

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We consider the client-server setting for the concurrent composition of secure protocols: in this setting, a single server interacts with multiple clients concurrently, executing with each client a specified protocol where only the client should receive any nontrivial output. Such a setting is easily motivated from an application standpoint. There are important special cases for which positive results are known -such as concurrent zero knowledge protocols -and it has been an open question explicitly asked, for instance, by Lindell [J. Cryptology'08] -whether other natural functionalities such as Oblivious Transfer (OT) are possible in this setting.In this work:• We resolve this open question by showing that unfortunately, even in this very limited concurrency setting, broad new impossibility results hold, ruling out not only OT, but in fact all nontrivial asymmetric functionalities. Our new negative results hold even if the inputs of all honest parties are fixed in advance, and the adversary receives no auxiliary information.• Along the way, we establish a new unconditional completeness result for asymmetric functionalities, where we characterize functionalities that are non-interactively complete secure against active adversaries. When we say that a functionality F is non-interactively complete, we mean that every other asymmetric functionality can be realized by parallel invocations of several copies of F, with no other communication in any direction. Our result subsumes a completeness result of Kilian [STOC'00] that uses protocols which require additional interaction in both directions. * UCLA.

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Completeness Theorems with Constructive Proofs for Finite Deterministic 2-Party Functions

Cited by 18 publications

References 27 publications

Characterizing the Cryptographic Properties of Reactive 2-Party Functionalities

Characterizing the Cryptographic Properties of Reactive 2-Party Functionalities

A Full Characterization of Completeness for Two-Party Randomized Function Evaluation

New Impossibility Results for Concurrent Composition and a Non-interactive Completeness Theorem for Secure Computation

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