We construct a secure protocol for any multiparty functionality that remains secure (under a relaxed definition of security introduced by Prabhakaran and Sahai (STOC '04)) when executed concurrently with multiple copies of itself and other protocols, without any assumptions on existence of trusted parties, common reference string, honest majority or synchronicity of the network. The relaxation of security is obtained by allowing the ideal-model simulator to run in quasipolynomial (as opposed to polynomial) time. Quasipolynomial simulation suffices to ensure security for most applications of multiparty computation. Furthermore, Lindell (FOCS '03, TCC' 04) recently showed that such a protocol is impossible to obtain under the more standard definition of polynomial-time simulation by an ideal adversary. Our construction is the first such protocol under reasonably standard cryptographic assumptions (i.e., existence of a hash function collection that is collision resistent with respect to circuits of subexponential size, and existence of trapdoor permutations which are secure with respect to circuits of quasi-polynomial size). We introduce a new technique: "protocol condensing". That is, taking a protocol that has strong security properties but requires super-polynomial communication and computation, and then transforming it into a protocol with polynomial communication and computation, that still inherits the strong security properties of the original protocol. Our result is obtained by combining this technique with previous techniques of Canetti, Lindell, Ostrovsky, and Sahai (STOC '02) and Pass (STOC '04).
We construct a secure protocol for any multi-party functionality that remains secure (under a relaxed definition of security) when executed concurrently with multiple copies of itself and other protocols. We stress that we do not use any assumptions on existence of trusted parties, common reference string, honest majority or synchronicity of the network. The relaxation of security, introduced by Prabhakaran and Sahai (STOC ’04), is obtained by allowing the idealmodel simulator to run in quai-polynomial (as opposed to polynomial) time. Quasi-polynomial simulation suffices to ensure security for most applications of multi-party computation. Furthermore, Lindell (FOCS ’03, TCC ’ 04) recently showed that such a protocol is impossible to obtain under the more standard definition of polynomial-time simulation by an ideal adversary. Our construction is the first such protocol under reasonably standard cryptographic assumptions. That is, existence of a hash function collection that is collision resistent with respect to circuits of subexponential size, and existence of trapdoor permutations that are secure with respect to circuits of quasi-polynomial size. We introduce a new technique: “protocol condensing”. That is, taking a protocol that has strong security properties but requires super-polynomial communication and computation, and
We construct a protocol for general multi-party computation that remains secure even if executed concurrently with multiple copies of itself and of arbitrary other protocols. This is the first such construction that is based on standard cryptographic assumptions and does not require setup conditions such as the existence of a common reference string. Furthermore, our protocol utilizes only a constant number of communication rounds and remains secure also with respect to adaptive adversaries (without using memory erasures). The security of our protocol is demonstrated by a simulator with a quasi-polynomial simulation overhead, as opposed to the standard notion of polynomial simulation. However, quasipolynomial simulation still provides sufficient security for almost all applications. Furthermore, it was previously shown that there does not exist such a protocol with polynomial simulation
We show how to securely realize any multi-party functionality in a way that preserves security under an a-priori bounded number of concurrent executions, regardless of the number of corrupted parties. Previous protocols for the above task either rely on set-up assumptions such as a Common Reference String, or require an honest majority. Our constructions are in the plain model and rely on standard intractability assumptions (enhanced trapdoor permutations and collision resistant hash functions). Even though our main focus is on feasibility of concurrent multi-party computation we actually obtain a protocol using only a constant number of communication rounds. As a consequence our protocol yields the first construction of constant-round phstand-alone secure multi-party computation with a dishonest majority, proven secure under standard (polynomial-time) hardness assumptions; previous solutions to this task either require logarithmic round-complexity, or subexponential hardness assumptions. The core of our protocol is a novel construction of (concurrently) simulation-sound zero-knowledge protocols, which might be of independent interest. Finally, we extend the framework constructed to give a protocol for secure multi-party (and thus two-party) computation for any number of corrupted parties, which remains secure even when arbitrary subsets of parties concurrently execute the protocol, possibly with interchangeable roles. As far as we know, for the case of two-party or multi-party protocols with a dishonest majority, this is the first positive result for any non-trivial functionality which achieves this property in the plain model.
A protocol for computing a functionality is secure if an adversary in this protocol cannot cause more harm than in an ideal computation where parties give their inputs to a trusted party which returns the output of the functionality to all parties. In particular, in the ideal model such computation is fair -- all parties get the output. Cleve (STOC 1986) proved that, in general, fairness is not possible without an honest majority. To overcome this impossibility, Gordon and Katz (Eurocrypt 2010) suggested a relaxed definition -- 1/p-secure computation -- which guarantees partial fairness. For two parties, they construct 1/p-secure protocols for functionalities for which the size of either their domain or their range is polynomial (in the security parameter). Gordon and Katz ask whether their results can be extended to multiparty protocols. We study 1/p-secure protocols in the multiparty setting for general functionalities. Our main result is constructions of 1/p-secure protocols when the number of parties is constant provided that less than 2/3 of the parties are corrupt. Our protocols require that either (1) the functionality is deterministic and the size of the domain is polynomial (in the security parameter), or (2) the functionality can be randomized and the size of the range is polynomial. If the size of the domain is constant and the functionality is deterministic, then our protocol is efficient even when the number of parties is O(log log n) (where n is the security parameter). On the negative side, we show that when the number of parties is super-constant, 1/p-secure protocols are not possible when the size of the domain is polynomial.
The need for Cryptography arises out of the following fundamental question: can we perform useful computation while ensuring that an adversary does not learn anything about our private sensitive data? The notion of secure multiparty computation (MPC) \\cite{Yao82,GMW87} is a unifying framework for general secure protocols. MPC allows mutually distrusting parties to jointly evaluate any efficiently computable function on their private inputs in such a manner that each party does not learn anything beyond the output of the function. In this thesis, we study the question of building MPC protocols in various security models from standard cryptographic assumptions while minimizing the number of rounds of interaction amongst parties. In the first part of this thesis, (in a joint work with Vipul Goyal, Abhishek Jain, Yael Kalai, Dakshita Khurana and Amit Sahai, CRYPTO 2018) we construct the first round-optimal (i.e., four round) MPC protocol for general functions based on polynomially hard DDH (or QR or N
th-Residuosity) in the plain model where parties have access to no trusted setup. We further show how to overcome the four-round barrier for MPC by constructing a three-round protocol for ``list coin-tossing'' -- a slight relaxation of coin-tossing that suffices for most conceivable applications -- based on polynomially hard DDH (or QR or N
th-Residuosity). This result generalizes to randomized input-less functionalities. Previously, four round MPC protocols required sub-exponential-time hardness assumptions and no multi-party three-round protocols were known for any relaxed security notions with polynomial-time simulation against malicious adversaries. In order to build these protocols, we devise a new {\\em partitioned simulation} technique for MPC where the simulator uses different strategies for simulating the view of aborting adversaries and non-aborting adversaries. The protagonist of this technique is a new notion of {\\em promise zero knowledge} (ZK) where the ZK property only holds against non-aborting verifiers. We show how to realize promise ZK in three rounds in the simultaneous-message model assuming polynomially hard DDH (or QR or N
th-Residuosity). We also rely upon a new {\\em leveled rewinding security} technique that can be viewed as a polynomial-time alternative to leveled complexity leveraging for achieving ``non-malleability'' across different primitives. Then, we also we study the round complexity of concurrently secure multi-party computation (MPC) with super-polynomial simulation (SPS) in the plain model (in a joint work with Vipul Goyal, Abhishek Jain, Dakshita Khurana and Amit Sahai, TCC 2017). In the plain model, there are known explicit attacks that show that concurrently secure MPC with polynomial simulation is impossible to achieve; SPS security is the most widely studied model for concurrently secure MPC in the plain model. We construct a three-round concurrent MPC with SPS security against Byzantine adversaries, assuming sub-exponentially secure DDH and LWE. Prior to our work, the best known round complexity for SPS concurrent MPC was around twenty, although to the best of our knowledge, no previous work even gave an approximation of the constant round complexity that is sufficient for concurrent MPC.In the second part of the thesis, (in a joint work with Abhishek Jain, Rafail Ostrovsky and Ivan Visconti, ASIACRYPT 2018), we study the problem of non-interactive secure computation in the stateless hardware token model where parties have access to physical hardware as part of a trusted setup phase. The notion of non-interactive secure computation (NISC) first introduced in the work of Ishai et al. [EUROCRYPT 2011] studies the following problem: Suppose a receiver
R wishes to publish an encryption of her secret input
y so that any sender
S with input
x can then send a message
m that reveals
f(x,y) to
R (for some function
f). Here,
m can be viewed as an encryption of
f(x,y) that can be decrypted by
R. NISC requires security against both malicious senders and receivers, and also requires the receiver's message to be reusable across multiple computations (w.r.t. a fixed input of the receiver). All previous solutions to this problem necessarily rely upon OT (or specific number-theoretic assumptions) even in the common reference string model or the random oracle model or to achieve weaker notions of security such as super-polynomial-time simulation. In this work, we construct a NISC protocol based on the minimal assumption of one way functions, in the stateless hardware token model. Our construction achieves UC security and requires a single token sent by the receiver to the sender.
We consider the problem of constructing a general protocol for secure two-party computation in a way that preserves security under concurrent composition. In our treatment, we focus on the case where an a-priori bound on the number of concurrent sessions is specified before the protocol is constructed. (a.k.a. bounded concurrency). We make no setup assumptions. Lindel (STOC 2003) has shown that any protocol for bounded-concurrent secure two-party computation, whose security is established via black-box simulation, must have round complexity that is strictly larger than the bound on the number of concurrent sessions. In this paper, we construct a (non black-box) protocol for realizing bounded-concurrent secure two-party computation in a constant number of rounds. Our constructions rely on the existence of enhanced trapdoor permutations, as well as on the existence of hash functions that are collision-resistant against subexponential sized circuits.