Alternative Implementations of Secure Real Numbers

Dimitrov, Vassil S.; Kerik, Liisi; Krips, Toomas; Randmets, Jaak; Willemson, Jan

doi:10.1145/2976749.2978348

Cited by 15 publications

(10 citation statements)

References 19 publications

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“…Along this line of research, [19] proposed in 2013 a similar secure floating-point computation scheme also based on a linear secret sharing framework. In 2016, [20] proposed other techniques for representing secure real numbers suitable for a secret sharing framework with their so-called golden-section and logarithmic number formats.…”

Section: State Of the Artmentioning

confidence: 99%

Privacy in Distributed Computations based on Real Number Secret Sharing

Tjell¹,

Wiśniewski²

2021

Preprint

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Privacy preservation in distributed computations is an important subject as digitization and new technologies enable collection and storage of vast amounts of data, including private data belonging to individuals. To this end, there is a need for a privacy preserving computation framework that minimises the leak of private information during computations while being efficient enough for practical usage. This paper presents a step towards such a framework with the proposal of a real number secret sharing scheme that works directly on real numbers without the need for conversion to integers which is the case in related schemes. The scheme offers computations like addition, multiplication, and division to be performed directly on secret shared data (the cipher text version of the data). Simulations show that the scheme is much more efficient in terms of accuracy than its counterpart version based on integers and finite field arithmetic. The drawback with the proposed scheme is that it is not perfectly secure. However, we provide a privacy analysis of the scheme, where we show that the leaked information can be upper bounded and asymptotically goes to zero. To demonstrate the scheme, we use it to perform Kalman filtering directly on secret shared data.

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Section: State Of the Artmentioning

confidence: 99%

Privacy in Distributed Computations based on Real Number Secret Sharing

Tjell¹,

Wiśniewski²

2021

Preprint

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“…Some works embed secure computations on real numbers into finite field operations by representing the real numbers as fixed or floating points numbers. This is for instance the case in the papers Catrina and Saxena (2010); Catrina and Dragulin (2009); Aliasgari et al (2013); Dimitrov et al (2016). One of the main challenges this approach faces is to carry out real number divisions in a secure way as division in a finite field and integer division are completely different.…”

Section: Mpcmentioning

confidence: 99%

Secure PAC Bayesian Regression via Real Shamir Secret Sharing

Gundersen¹,

Kuskonmaz²,

Wiśniewski³

2021

Preprint

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Common approach of machine learning is to generate a model by using huge amount of training data to predict the test data instances as accurate as possible. Nonetheless, concerns about data privacy are increasingly raised, but not always addressed. We present a secure protocol for obtaining a linear model relying on recently described technique called real number secret sharing. We take as our starting point the PAC Bayesian bounds and deduce a closed form for the model parameters which depends on the data and the prior from the PAC Bayesian bounds. To obtain the model parameters one need to solve a linear system. However, we consider the situation where several parties hold different data instances and they are not willing to give up the privacy of the data. Hence, we suggest to use real number secret sharing and multiparty computation to share the data and solve the linear regression in a secure way without violating the privacy of data. We suggest two methods; an inverse method and a Gaussian elimination method, and compare these methods at the end.

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“…They perform can perform exponentiation operations in about 164 ms (not amortized), whereas we can perform an exponentiation, with a known public base, in about 2.5 ms (under our 3 parties Shamir based setting). It is worth noting that Dimitrov et al [15] also provided implementations for the exponent function, using alternative ways to represent these rational numbers, using MPC. However, it is difficult to draw direct comparisons with this later work as they target passively secure MPC, whereas we focus on actively secure MPC.…”

Section: Exponentiation and Logarithmsmentioning

confidence: 99%

“…We see that, when Liedel's method can be applied then the performance is better, but the extra cost of our method in dealing with general inputs is only about a factor of two. Discussion: A recent implementation, with regards to the secure evaluation of square root functions on distributed environments, was introduced by Dimitrov et al [15]. These implementations where part of their work on alternative representations for real numbers.…”

mentioning

confidence: 99%

Benchmarking Privacy Preserving Scientific Operations

Aly

Smart

2019

Lecture Notes in Computer Science

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In this work, we examine the efficiency of protocols for secure evaluation of basic mathematical functions (sqrt, sin, arcsin, amongst others), essential to various application domains. e.g., Artificial Intelligence. Furthermore, we have incorporated our code in state-of-the-art Multiparty Computation (MPC) software, so we can focus on the algorithms to be used as opposed to the underlying MPC system. We make use of practical approaches that, although, some of them, theoretically can be regarded as less efficient, can, nonetheless, be implemented in such software libraries without further adaptation. We focus on basic scientific operations, and introduce a series of data-oblivious protocols based on fixed point representation techniques. Our protocols do not reveal intermediate values and do not need special adaptations from the underlying MPC protocols. We include extensive computational experimentation under various settings and MPC protocols.

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Alternative Implementations of Secure Real Numbers

Cited by 15 publications

References 19 publications

Privacy in Distributed Computations based on Real Number Secret Sharing

Privacy in Distributed Computations based on Real Number Secret Sharing

Secure PAC Bayesian Regression via Real Shamir Secret Sharing

Benchmarking Privacy Preserving Scientific Operations

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