Secure two-party computation is a cryptographic tool that enables two parties to compute a function jointly without revealing their inputs. It is known that any function can be realized in the correlated randomness (CR) model, where a trusted dealer distributes input-independent CR to the parties beforehand. Sometimes we can construct more efficient secure two-party protocol for a function g than that for a function f, where g is a restriction of f. However, it is not known in which case we can construct more efficient protocol for domain-restricted function. In this paper, we focus on the size of CR. We prove that we can construct more efficient protocol for a domain-restricted function when there is a “good” structure in CR space of a protocol for the original function, and show a unified way to construct a more efficient protocol in such case. In addition, we show two applications of the above result: The first application shows that some known techniques of reducing CR size for domain-restricted function can be derived in a unified way, and the second application shows that we can construct more efficient protocol than an existing one using our result.

In this paper, we propose L0 norm optimization in a scrambled sparse representation domain and its application to an Encryption-then-Compression (EtC) system. We design a random unitary transform that conserves L0 norm isometry. The resulting encryption method provides a practical orthogonal matching pursuit (OMP) algorithm that allows computation in the encrypted domain. We prove that the proposed method theoretically has exactly the same estimation performance as the nonencrypted variant of the OMP algorithm. In addition, we demonstrate the security strength of the proposed secure sparse representation when applied to the EtC system. Even if the dictionary information is leaked, the proposed scheme protects the privacy information of observed signals.

Machine learning models inherently memorize significant amounts of information, and thus hiding not only prediction processes but also trained models, i.e., model obliviousness, is desirable in the cloud setting. Several works achieved model obliviousness with the MNIST dataset, but datasets that include complicated samples, e.g., CIFAR-10 and CIFAR-100, are also used in actual applications, such as face recognition. Secret sharing-based secure prediction for CIFAR-10 is difficult to achieve. When a deep layer architecture such as CNN is used, the calculation error when performing secret calculation becomes large and the accuracy deteriorates. In addition, if detailed calculations are performed to improve accuracy, a large amount of calculation is required. Therefore, even if the conventional method is applied to CNN as it is, good results as described in the paper cannot be obtained. In this paper, we propose two approaches to solve this problem. Firstly, we propose a new protocol named Batch-normalizedActivation that combines BatchNormalization and Activation. Since BatchNormalization includes real number operations, when performing secret calculation, parameters must be converted into integers, which causes a calculation error and decrease accuracy. By using our protocol, calculation errors can be eliminated, and accuracy degradation can be eliminated. Further, the processing is simplified, and the amount of calculation is reduced. Secondly, we explore a secret computation friendly and high accuracy architecture. Related works use a low-accuracy, simple architecture, but in reality, a high accuracy architecture should be used. Therefore, we also explored a high accuracy architecture for the CIFAR10 dataset. Our proposed protocol can compute prediction of CIFAR-10 within 15.05 seconds with 87.36% accuracy while providing model obliviousness.

In this paper, we propose a secure computation of sparse coding and its application to Encryption-then-Compression (EtC) systems. The proposed scheme introduces secure sparse coding that allows computation of an Orthogonal Matching Pursuit (OMP) algorithm in an encrypted domain. We prove theoretically that the proposed method estimates exactly the same sparse representations that the OMP algorithm for non-encrypted computation does. This means that there is no degradation of the sparse representation performance. Furthermore, the proposed method can control the sparsity without decoding the encrypted signals. Next, we propose an EtC system based on the secure sparse coding. The proposed secure EtC system can protect the private information of the original image contents while performing image compression. It provides the same rate-distortion performance as that of sparse coding without encryption, as demonstrated on both synthetic data and natural images.

In this paper, we propose secure dictionary learning based on a random unitary transform for sparse representation. Currently, edge cloud computing is spreading to many application fields including services that use sparse coding. This situation raises many new privacy concerns. Edge cloud computing poses several serious issues for end users, such as unauthorized use and leak of data, and privacy failures. The proposed scheme provides practical MOD and K-SVD dictionary learning algorithms that allow computation on encrypted signals. We prove, theoretically, that the proposal has exactly the same dictionary learning estimation performance as the non-encrypted variant of MOD and K-SVD algorithms. We apply it to secure image modeling based on an image patch model. Finally, we demonstrate its performance on synthetic data and a secure image modeling application for natural images.

It is known that, using just a deck of cards, an arbitrary number of parties with private inputs can securely compute the output of any function of their inputs. In 2009, Mizuki and Sone constructed a six-card COPY protocol, a four-card XOR protocol, and a six-card AND protocol, based on a commonly used encoding scheme in which each input bit is encoded using two cards. However, up until now, there are no known results to construct a set of COPY, XOR, and AND protocols based on a two-card-per-bit encoding scheme, which all can be implemented using only four cards. In this paper, we show that it is possible to construct four-card COPY, XOR, and AND protocols using polarizing plates as cards and a corresponding two-card-per-bit encoding scheme. Our protocols use a minimum number of cards in the setting of two-card-per-bit encoding schemes since four cards are always required to encode the inputs. Moreover, we show that it is possible to construct two-card COPY, two-card XOR, and three-card AND protocols based on a one-card-per-bit encoding scheme using a common reference polarizer which is a polarizing material accessible to all parties.

Assume that Alice, Bob, and Carol, each of whom privately holds a one-bit input, want to learn the output of some Boolean function, say the majority function, of their inputs without revealing more of their own secret inputs than necessary. In this paper, we show that such a secure three-input function evaluation can be performed with a deck of real cards; specifically, the three players can learn only the output of the function using eight physical cards — four black and four red cards — with identical backs.

This paper deals with the information leakage measurement in a distributed computation protocol called SASC. The SASC protocol is a kind of two-party protocol between a client and a server. The computation for RSA cryptosystem is the target of this paper. This paper shows that a secure RSA-SASC protocol proposed recently could be changed to be insecure if the client which has secret information were to complain about the computation result. This paper first clarifies how to measure the information amount which leaks through the protocol. It, then, shows an attack procedure to make use of the client's complaint. Effectiveness of the attack procedure is measured by the information theoretic measure. By using the same measure, it is shown that some attacks do not work to derive the client's secret. It is also shown that a practical countermeasure to limit the number of incorrect computation allowed is effctive to limit the leakage of the secret information to some reasonable extent.

An extension of the notion of cryptographically strong pseudo-random generator to a distributed setting is proposed in this paper. Instead of a deterministic function to generate a pseudo-random bit string from a truly random shorter string, we have a deterministic secure protocol for a group of separate entities to compute a secretly shared pseudo-random string from a secretly shared and truly random shorter string. We propose a precise definition of this notion in terms of Yao's computational entropy and describe a concrete construction using Shamir's pseudo-random number generator. Several practical applications are also discussed.

Server aided secret computation (SASC) protocol also called the verifiable implicit asking protocol, is a protocol such that a powerful untrusted auxiliary device (server) can help a smart card (client) for computing a secret function efficiently. In this paper, we extend the concept of addition sequence to the secure addition sequence and develop an efficient algorithm to construct such sequence. By incorporating the secure addition sequence into the SASC protocol the performance of SASC protocol can be further enhanced.

In this paper, we discuss secure protocols for shared computation of algorithms associated with digital signature schemes based on discrete logarithms. Generic solutions to the problem of cooperatively computing arbitraty functions, though formally provable according to strict security notions, are inefficient in terms of communication--bits and rounds of interaction--; practical protocols for shared computation of particular functions, on the other hand, are often shown secure according to weaker notions of security. We propose efficient secure protocols to share the generation of keys and signatures in the digital signature schemes introduced by Schnorr (1989) and ElGamal (1985). The protocols are built on a protocol for non-interactive verifiable secret sharing (Feldman, 1987) and a novel construction for non-interactively multiplying secretly shared values. Together with the non-interactive protocols for shared generation of RSA signatures introduced by Desmedt and Frankel (1991), the results presented here show that practical signature schemes can be efficiently shared.