Non-interactive Proofs for Integer Multiplication

Damgård, Ivan; Thorbek, Rune

doi:10.1007/978-3-540-72540-4_24

Cited by 39 publications

(21 citation statements)

References 25 publications

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“…We use Pseudo-random Replicated Secret Sharing (PRSS) [6] to generate without interaction shared random values in F with uniform distribution and random sharings of zero. Also, we use the integer variant of PRSS (RISS) [10] to generate shared random integers in a given interval, and the ideas in [11] for bit-share conversions (e.g., BitF2MtoZQ converts bit shares from F 2 8 to Z q ).…”

Section: Building Blocksmentioning

confidence: 99%

Secure Computation with Fixed-Point Numbers

Catrina

Saxena

2010

Lecture Notes in Computer Science

185

179

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Abstract. Secure computation is a promising approach to business problems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that support all the primitive data types and allow secure protocol composition and efficient application development. Secure computation with rational numbers has been a challenging problem. We present in this paper a family of protocols for multiparty computation with rational numbers using fixed-point representation. This approach offers more efficient solutions for secure computation than other usual representations.

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Section: Building Blocksmentioning

confidence: 99%

Secure Computation with Fixed-Point Numbers

Catrina

Saxena

2010

Lecture Notes in Computer Science

185

179

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“…Also, we use the integer variant RISS [8] to generate shared random integers in a given interval and the ideas in [9] for share conversions. To enable these techniques, we assume that numbers are encoded in Z q and q > 2 k+κ+ν+1 , where k is the required integer bit-length, κ is the security parameter, ν = ⌈log( n t )⌉, n is the number of parties, and t is the corruption threshold.…”

Section: Core Protocolsmentioning

confidence: 99%

Secure Multiparty Linear Programming Using Fixed-Point Arithmetic

Catrina

Hoogh

2010

Lecture Notes in Computer Science

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Abstract. Collaborative optimization problems can often be modeled as a linear program whose objective function and constraints combine data from several parties. However, important applications of this model (e.g., supply chain planning) involve private data that the parties cannot reveal to each other. Traditional linear programming methods cannot be used in this case. The problem can be solved using cryptographic protocols that compute with private data and preserve data privacy. We present a practical solution using multiparty computation based on secret sharing. The linear programming protocols use a variant of the simplex algorithm and secure computation with fixed-point rational numbers, optimized for this type of application. We present the main protocols as well as performance measurements for an implementation of our solution.

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“…The notion of security is such that the state of the adversary returned by those simulators is statistically indistinguishable from the state of the adversary in the real-life model. A different kind of scheme for proof of knowledge named Public Key Encryption with Non-interactive Openning (PKENO) in standard model [4][5][6]11] has been proposed, which is more efficient than the known NIZK proofs in standard model. For proving the knowledge, a verifier needs to know the (ciphertext, proof, plaintext)-tuple.…”

Section: Threshold Two-party Computationmentioning

confidence: 99%

Efficient Privacy-Preserving Data Mining in Malicious Model

Emura

Miyaji

Rahman

2010

Advanced Data Mining and Applications

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Abstract. In many distributed data mining settings, disclosure of the original data sets is not acceptable due to privacy concerns. To address such concerns, privacy-preserving data mining has been an active research area in recent years. While confidentiality is a key issue, scalability is also an important aspect to assess the performance of a privacypreserving data mining algorithms for practical applications. With this in mind, Kantarcioglu et al. proposed secure dot product and secure setintersection protocols for privacy-preserving data mining in malicious adversarial model using zero knowledge proofs, since the assumption of semi-honest adversary is unrealistic in some settings. Both the computation and communication complexities are linear with the number of data items in the protocols proposed by Kantarcioglu et al. In this paper, we build efficient and secure dot product and set-intersection protocols in malicious model. In our work, the complexity of computation and communication for proof of knowledge is always constant (independent of the number of data items), while the complexity of computation and communication for the encrypted messages remains the same as in Kantarcioglu et al.'s work (linear with the number of data items). Furthermore, we provide the security model in Universal Composability framework.

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Non-interactive Proofs for Integer Multiplication

Cited by 39 publications

References 25 publications

Secure Computation with Fixed-Point Numbers

Secure Computation with Fixed-Point Numbers

Secure Multiparty Linear Programming Using Fixed-Point Arithmetic

Efficient Privacy-Preserving Data Mining in Malicious Model

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