Two-party computation allows two clients to jointly compute an arbitrary function of their inputs without revealing these inputs to each other. In this study, we adopt a server-aided model, in which a set of computing servers performs computation using the inputs of two clients. In the (k, n) threshold secret sharing scheme, input s is divided into n shares and can be recovered from k shares, where k is a threshold. Typically, the multiplication of shares increases the polynomial's degree from (k-1) to (2k-2), thus increasing the number of shares required from k to 2k-1. Because each server typically holds only one share, the number of servers required also increases to 2k-1. Therefore, a set of n servers can compute multiplication securely only if the adversary corrupts at most k-1 <; n/2 servers. In this study, we differentiate N, which is the number of required servers, and n, which is the parameter of the (k, n) threshold secret sharing scheme. We propose a method of multiplication by using only N ≥ k servers. This is implemented by sending two shares of the same input to each server. In a “normal” method, sending multiple shares to one server violates security because k shares can be leaked from k-1 servers. We overcome this by implementing a different functionality, where each share is first encrypted with a different random number (encrypted share) before being sent to a server. Instead of the “normal shares” of ab, our protocol computes the encrypted shares of ab using the encrypted shares of a and b. We show that the proposed method is secure against a non-colluding semi-honest adversary. Moreover, we implement our method in MATLAB and show its efficiency.Two-party computation allows two clients to jointly compute an arbitrary function of their inputs without revealing these inputs to each other. In this study, we adopt a server-aided model, in which a set of computing servers performs computation using the inputs of two clients. In the (k, n) threshold secret sharing scheme, input s is divided into n shares and can be recovered from k shares, where k is a threshold. Typically, the multiplication of shares increases the polynomial's degree from (k-1) to (2k-2), thus increasing the number of shares required from k to 2k-1. Because each server typically holds only one share, the number of servers required also increases to 2k-1. Therefore, a set of n servers can compute multiplication securely only if the adversary corrupts at most k-1 <; n/2 servers. In this study, we differentiate N, which is the number of required servers, and n, which is the parameter of the (k, n) threshold secret sharing scheme. We propose a method of multiplication by using only N ≥ k servers. This is implemented by sending two shares of the same input to each server. In a “normal” method, sending multiple shares to one server violates security because k shares can be leaked from k-1 servers. We overcome this by implementing a different functionality, where each share is first encrypted with a different random number (encrypted share) before being sent to a server. Instead of the “normal shares” of ab, our protocol computes the encrypted shares of ab using the encrypted shares of a and b. We show that the proposed method is secure against a non-colluding semi-honest adversary. Moreover, we implement our method in MATLAB and show its efficiency.

IEEE AccessJan 1, 202111 citations

Secure Computation from Random Error Correcting Codes

Hao Chen, Ronald Cramer, Shafi Goldwasser +2 more

Lecture notes in computer scienceJan 1, 2007128 citations

Verifiable Secret Sharing as Secure Computation

Rosario Gennaro, Silvio M. Micali

Lecture notes in computer scienceJan 1, 199534 citations

Communication-Efficient Secure Computation of Encrypted Inputs using (k, n) Threshold Secret Sharing

Keiichi Iwamura, Ahmad Akmal Aminuddin Mohd Kamal

Advancements in Internet of Things devices allow for the collection and analysis of big data. Moreover, cloud computing has emerged as an ideal platform for big data analysis because it quickly provides computing resources for analysis at scale. However, concerns exist regarding the privacy and security of this information. Secure computation is a technology that enables computation while maintaining data encryption. In this study, we present a new secure computation based on a client-server model, in which a set of servers perform computations using the inputs of multiple clients. We adopt the $(k, n)$ threshold secret sharing approach, where an input $s$ is divided into $n$ shares and can be recovered from shares with a threshold $k$ . However, conventional secure computation using $(k,n)$ threshold secret sharing generally requires the condition $n \geq 2k-1$ and communication among multiple servers for each multiplication. To the best of our knowledge, no previous study has solved this problem completely. We demonstrate that processes that require communication can be concentrated in the preprocessing phase and propose a secure computation using $(k,n)$ threshold secret sharing that does not require communication during the secure computation phase, even when multiplication is performed. Moreover, we show that the number of communications does not depend on the number of multiplications, unlike in conventional methods. As communication often requires more processing time than the actual secure computation, our method makes it possible to realize faster overall processing than conventional methods. We also present an extensive security analysis and experimental simulation of the proposed method. Our proposed method achieves information-theoretic security against semi-honest adversaries under certain conditions with $n < 2k-1$ .Advancements in Internet of Things devices allow for the collection and analysis of big data. Moreover, cloud computing has emerged as an ideal platform for big data analysis because it quickly provides computing resources for analysis at scale. However, concerns exist regarding the privacy and security of this information. Secure computation is a technology that enables computation while maintaining data encryption. In this study, we present a new secure computation based on a client-server model, in which a set of servers perform computations using the inputs of multiple clients. We adopt the$(k, n)$threshold secret sharing approach, where an input$s$is divided into$n$shares and can be recovered from shares with a threshold$k$. However, conventional secure computation using$(k,n)$threshold secret sharing generally requires the condition$n \geq 2k-1$and communication among multiple servers for each multiplication. To the best of our knowledge, no previous study has solved this problem completely. We demonstrate that processes that require communication can be concentrated in the preprocessing phase and propose a secure computation using$(k,n)$threshold secret sharing that does not require communication during the secure computation phase, even when multiplication is performed. Moreover, we show that the number of communications does not depend on the number of multiplications, unlike in conventional methods. As communication often requires more processing time than the actual secure computation, our method makes it possible to realize faster overall processing than conventional methods. We also present an extensive security analysis and experimental simulation of the proposed method. Our proposed method achieves information-theoretic security against semi-honest adversaries under certain conditions with$n < 2k-1$.

IEEE AccessJan 1, 202314 citations

(k, n)

threshold secret sharing approach, where an input

s

is divided into

n

shares and can be recovered from shares with a threshold

k

. However, conventional secure computation using

(k,n)

threshold secret sharing generally requires the condition

n \geq 2k-1

and communication among multiple servers for each multiplication. To the best of our knowledge, no previous study has solved this problem completely. We demonstrate that processes that require communication can be concentrated in the preprocessing phase and propose a secure computation using

(k,n)

threshold secret sharing that does not require communication during the secure computation phase, even when multiplication is performed. Moreover, we show that the number of communications does not depend on the number of multiplications, unlike in conventional methods. As communication often requires more processing time than the actual secure computation, our method makes it possible to realize faster overall processing than conventional methods. We also present an extensive security analysis and experimental simulation of the proposed method. Our proposed method achieves information-theoretic security against semi-honest adversaries under certain conditions with

n < 2k-1