OT-Combiners via Secure Computation

349

352

Abstract. Secure multi-party computation has been considered by the cryptographic community for a number of years. Until recently it has been a purely theoretical area, with few implementations with which to test various ideas. This has led to a number of optimisations being proposed which are quite restricted in their application. In this paper we describe an implementation of the two-party case, using Yao's garbled circuits, and present various algorithmic protocol improvements. These optimisations are analysed both theoretically and empirically, using experiments of various adversarial situations. Our experimental data is provided for reasonably large circuits, including one which performs an AES encryption, a problem which we discuss in the context of various possible applications.

Section: Encryption Schemementioning

confidence: 99%

Secure Two-Party Computation Is Practical

Pinkas

Schneider

Smart

et al. 2009

349

352

“…For the inner protocol we use: GMW [GMW87] semi-honest secure protocol in F OT -hybrid. And the F OT instances are in turn obtained by using the constant-rate semi-honest OT combiner of Harnik et al [HIKN08].…”

Section: If the Receiver Uses Inputs Frommentioning

confidence: 99%

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

Kraschewski

Maji²,

Prabhakaran

et al. 2014

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].

“…Therefore, A(q) > 2d if q is (very) large. 7 The asymptotical result from [7] plays an important communication-saving role in two-party cryptography, see [23,24,18,22,13,21]. Often, the point is that terms in the communication analysis which would otherwise be logarithmic can be made constant using the [7] results.…”

Section: If the N-code C * I Is T-disconnected And If C * J Has (N − mentioning

confidence: 99%

“…A series of surprising results, concerning zero-knowledge for circuit satisfiability ("MPC in the Head"), two-party secure computation, OT-combiners, correlation extractors, and OT from noisy channels [23,24,18,22,13,21], has caused nothing less than a paradigm shift that perhaps appears even as counter-intuitive: secure multi-party computation is a very powerful abstract primitive for communication-efficient two-party cryptography. All these results use arithmetic secret sharing schemes, typically with d = 2 (see also [11] for an application with d > 2).…”

Section: Introductionmentioning

confidence: 99%

The Torsion-Limit for Algebraic Function Fields and Its Application to Arithmetic Secret Sharing

Cascudo

Cramer

Xing

2011

Abstract. An (n, t, d, n−t)-arithmetic secret sharing scheme (with uniformity) for F k q over Fq is an Fq-linear secret sharing scheme where the secret is selected from F k q and each of the n shares is an element of Fq. Moreover, there is t-privacy (in addition, any t shares are uniformly random in F t q ) and, if one considers the d-fold "component-wise" product of any d sharings, then the d-fold component-wise product of the d respective secrets is (n − t)-wise uniquely determined by it. Such schemes are a fundamental primitive in information-theoretically secure multi-party computation. Perhaps counter-intuitively, secure multi-party computation is a very powerful primitive for communication-efficient two-party cryptography, as shown recently in a series of surprising results from 2007 on. Moreover, the existence of asymptotically good arithmetic secret sharing schemes plays a crucial role in their communication-efficiency: for each d ≥ 2, if A(q) > 2d, where A(q) is Ihara's constant, then there exists an infinite family of such schemes over Fq such that n is unbounded, k = Ω(n) and t = Ω(n), as follows from a result at CRYPTO'06. Our main contribution is a novel paradigm for constructing asymptotically good arithmetic secret sharing schemes from towers of algebraic function fields. It is based on a new limit that, for a tower with a given Ihara limit and given positive integer , gives information on the cardinality of the -torsion sub-groups of the associated degree-zero divisor class groups and that we believe is of independent interest. As an application of the bounds we obtain, we relax the condition A(q) > 2d from the CRYPTO'06 result substantially in terms of our torsion-limit. As a consequence, this result now holds over nearly all finite fields Fq. For example, if d = 2, it is sufficient that q = 8, 9 or q ≥ 16.