Algebraic (Trapdoor) One-Way Functions and Their Applications

Catalano, Dario; Fiore, Dario; Gennaro, Rosario; Vamvourellis, Konstantinos

doi:10.1007/978-3-642-36594-2_38

Cited by 46 publications

(32 citation statements)

References 35 publications

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“…The subject became popular more recently, due to an important application of homomorphic signatures to linear network coding. Efficient schemes of this primitive have been proposed both in the random oracle [10,27,12,17] and in the standard model [1,2,18,19,23,3]. Realizations for more complex functionalities (i.e., beyond linear) have been proposed only very recently [11,28,16,4].…”

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confidence: 99%

Generalizing Homomorphic MACs for Arithmetic Circuits

Catalano

Fiore

Gennaro

et al. 2014

Public-Key Cryptography – PKC 2014

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Abstract. Homomorphic MACs, introduced by Gennaro and Wichs in 2013, allow anyone to validate computations on authenticated data without knowledge of the secret key. Moreover, the secret-key owner can verify the validity of the computation without needing to know the original (authenticated) inputs. Beyond security, homomorphic MACs are required to produce short tags (succinctness) and to support composability (i.e., outputs of authenticated computations should be re-usable as inputs for new computations).At Eurocrypt 2013, Catalano and Fiore proposed two realizations of homomorphic MACs that support a restricted class of computations (arithmetic circuits of polynomial degree), are practically efficient, but fail to achieve both succinctness and composability at the same time.In this paper, we generalize the work of Catalano and Fiore in several ways. First, we abstract away their results using the notion of encodings with limited malleability, thus yielding new schemes based on different algebraic settings. Next, we generalize their constructions to work with graded encodings, and more abstractly with k-linear groups. The main advantage of this latter approach is that it allows for homomorphic MACs which are (somewhat) composable while retaining succinctness. Interestingly, our construction uses graded encodings in a generic way. Thus, all its limitations (limited composability and non-constant size of the tags) solely depend on the fact that currently known multilinear maps share similar constraints. This means, for instance, that our scheme would support arbitrary circuits (polynomial depth) if we had compact multilinear maps with an exponential number of levels.

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confidence: 99%

Generalizing Homomorphic MACs for Arithmetic Circuits

Catalano

Fiore

Gennaro

et al. 2014

Public-Key Cryptography – PKC 2014

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“…However, since then, most works focus solely on linear functions, mainly because of the important application to network coding [14]. Several efficient schemes for linear functions have been proposed both in the random oracle model [14,29,16,18] and in the standard model [1,5,19,20,26,6,7]. Three more recent works consider the case of larger classes of functions [15,30,17].…”

Section: Related Workmentioning

confidence: 99%

“…As we mentioned earlier, the problem considered by our work and addressed via homomorphic authenticators is related to the notion of verifiable computation for which there exits a vast literature, ranging from works for arbitrary computations [36,40,32,27,21,2,47,28,46] to works for specific classes of computations [11,25,43,18]. In verifiable computation, a client wants to delegate a computationally heavy task to a remote server while being able to verify the result in a very efficient way.…”

Section: Related Workmentioning

confidence: 99%

Verifiable delegation of computation on outsourced data

Backes

Fiore

Reischuk

2013

Proceedings of the 2013 ACM SIGSAC Conference on Computer &Amp; Communications Security - CCS '13

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162

134

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Abstract. We address the problem in which a client stores a large amount of data with an untrusted server in such a way that, at any moment, the client can ask the server to compute a function on some portion of its outsourced data. In this scenario, the client must be able to efficiently verify the correctness of the result despite no longer knowing the inputs of the delegated computation, it must be able to keep adding elements to its remote storage, and it does not have to fix in advance (i.e., at data outsourcing time) the functions that it will delegate. Even more ambitiously, clients should be able to verify in time independent of the input-size -a very appealing property for computations over huge amounts of data.In this work we propose novel cryptographic techniques that solve the above problem for the class of computations of quadratic polynomials over a large number of variables. This class covers a wide range of significant arithmetic computations -notably, many important statistics. To confirm the efficiency of our solution, we show encouraging performance results, e.g., correctness proofs have size below 1 kB and are verifiable by clients in less than 10 milliseconds.

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“…In verifiable computation [30,26,22,2,41,40,24,18,21], a client outsources a computationally intensive task to a server and verifies its results in an efficient manner upon its completion. The basic question was formulated in work on interactive proofs (IP) [8,31], efficient arguments based on probabilistically checkable proofs (PCP) [35,36], and computationally sound (CS) proofs [38].…”

Section: Related Workmentioning

confidence: 99%

Efficient Secure and Verifiable Outsourcing of Matrix Multiplications

Zhang

Blanton

2014

Lecture Notes in Computer Science

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With the emergence of cloud computing services, a resource-constrained client can outsource its computationally-heavy tasks to cloud providers. Because such service providers might not be fully trusted by the client, the need to verify integrity of the returned computation result arises. The ability to do so is called verifiable delegation or verifiable outsourcing. Furthermore, the data used in the computation may be sensitive and it is often desired to protect it from the cloud throughout the computation. In this work, we put forward solutions for verifiable outsourcing of matrix multiplications that favorably compare with the state of the art. Our goal is to minimize the cost of verifying the result without increasing overhead associated with other aspects of the scheme. In our scheme, the cost of verifying the result of computation uses only a single modulo exponentiation and the number of modulo multiplications linear in the size of the output matrix. This cost can be further reduced to avoid all cryptographic operations if the cloud is rational. A rational cloud is neither honest nor arbitrarily malicious, but rather economically motivated with the sole purpose of maximizing its monetary reward. We extend our core constructions with several desired features such as data protection, public verifiability, and computation chaining.

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Algebraic (Trapdoor) One-Way Functions and Their Applications

Cited by 46 publications

References 35 publications

Generalizing Homomorphic MACs for Arithmetic Circuits

Generalizing Homomorphic MACs for Arithmetic Circuits

Verifiable delegation of computation on outsourced data

Efficient Secure and Verifiable Outsourcing of Matrix Multiplications

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