Homomorphic Public Key Cryptosystem Research Articles

Encrypted images-based reversible data hiding in Paillier cryptosystem

Homomorphic public key technology effectively protects privacy, allowing algebraic operations directly in the cipher-text. Therefore, it has been extensively studied in the field of cloud computing. In this study, an encrypted image-based data hiding (EIRDH) algorithm with homomorphic public key cryptosystem is presented. The key contributions are these two sides. (1) An improved fast Paillier homomorphic public key cryptosystem system is proposed for encrypting image. It improves the efficiency of encryption operations greatly. (2) A difference expansion (DE) scheme is developed by exploiting the cover pixel to construct a new pair of pixels for data hiding. Compared with other methods, the experimental results show that, the proposed method has larger payload and higher stego-image quality. It accomplishes the image quality’s increasing instead of general decreasing.

Prediction error expansion‐based reversible data hiding in encrypted images with public key cryptosystem

Advances in signal processing in the encrypted domain and cloud computing have given rise to privacy-preserving technologies. In recent years, reversible data hiding in encrypted images (RDH-EI) has received attention from the research community because additional data can be embedded into an encrypted image without accessing its original content, and the encrypted image can be losslessly recovered after extracting the embedded data. Although the recent development of RDH-EI compatible with homomorphic public key cryptosystems has intensified research interest, most of the existing mature RDH schemes cannot be transplanted to the encrypted domain due to the limitations of the underlying cryptosystems. In this paper, prediction error expansion based RDH-ED using probabilistic and homomorphic properties of the Paillier cryptosystem is presented. This work implements non-integer mean value computation in the encrypted domain without any interactive protocol between the content owner and the cloud server. This work presents mathematical detail of pixel prediction (mean), prediction error, error expansion and data embedding in the encrypted domain and data extraction and content recovery in the plain domain. Experimental results from standard test images reveal that the proposed scheme outperforms other state-of-the-art encrypted domain schemes.

New Approach to Set Representation and Practical Private Set-Intersection Protocols

Private set intersection (PSI) is a fundamental cryptographic protocol, which has many important applications, such as personal properties matching, data sharing, or data mining. PSI has been widely studied in the literature, and many PSI protocols have been presented; however, today, many real-world applications do not use a secure PSI protocol, mainly because current PSI protocols have two issues: the insufficient efficiency and not considering the secure storage of users’ datasets. Without using the PSI protocols, users of the real-world applications will sacrifice their privacy. In this paper, we propose a new approach for sets representation, which denotes sets by bit vectors and naturally hides the cardinality of a set. The new approach is particularly suitable to cloud computing environments. Then, we present two practical PSI and PSI cardinality protocols based on an additive homomorphic public-key cryptosystem (PKC). The new protocols enjoy two main advantages: 1) they are more efficient than other related protocols, especially when the set size is less than 212 and 2) the approach used in our protocols provides a good solution to securely store users’ datasets, and the encrypted datasets could be used as protocols’ messages directly without any additional computations. Finally, we implement our PSI and PSI cardinality protocols with Paillier PKC and ElGamal PKC in Java .

Dual protocols for private multi-party matrix multiplication and trust computations

This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on a weighted average protocol, in order to securely compute a dot-product with a quadratic volume of communications and linear number of rounds. We also propose two dual protocols with five communication rounds, using a Paillier-like underlying homomorphic public key cryptosystem, which is secure in the semi-honest model or secure with high probability in the malicious adversary model. Using cryptographic protocol verification tools, we are able to check the security of both protocols and provide a countermeasure for each attack found by the tools. We also give a generic randomization method to avoid collusion attacks. As an application, we show that this protocol enables a distributed and secure evaluation of trust relationships in a network, for a large class of trust evaluation schemes.

On the existence of provably secure cloud computing systems

We study a formal model of cloud computing systems with auxiliary cryptoservers. Assuming an existence of a secure threshold somewhat homomorphic public key cryptosystem we show how to build a cloud computing system secure in this model.

Logsum using Garbled Circuits.

Secure multiparty computation allows for a set of users to evaluate a particular function over their inputs without revealing the information they possess to each other. Theoretically, this can be achieved using fully homomorphic encryption systems, but so far they remain in the realm of computational impracticability. An alternative is to consider secure function evaluation using homomorphic public-key cryptosystems or Garbled Circuits, the latter being a popular trend in recent times due to important breakthroughs. We propose a technique for computing the logsum operation using Garbled Circuits. This technique relies on replacing the logsum operation with an equivalent piecewise linear approximation, taking advantage of recent advances in efficient methods for both designing and implementing Garbled Circuits. We elaborate on how all the required blocks should be assembled in order to obtain small errors regarding the original logsum operation and very fast execution times.

Key Technologies and Applications of Secure Multiparty Computation

With the advent of the information age, the network security is particularly important. The secure multiparty computation is a very important branch of cryptography. It is a hotspot in the field of information security. It expanded the scope of the traditional distributed computing and information security, provided a new computing model for the network collaborative computing. First we introduced several key technologies of secure multiparty computation: secret sharing and verifiable secret sharing, homomorphic public key cryptosystem, mix network, zero knowledge proof, oblivious transfer, millionaire protocol. Second we discussed the applications of secure multiparty computation in electronic voting, electronic auctions, threshold signature, database queries, data mining, mechanical engineering and other fields. DOI: http://dx.doi.org/10.11591/telkomnika.v11i7.2827

Cryptanalysis of a homomorphic public-key cryptosystem over a finite group

The paper cryptanalyses a public-key cryptosystem recently proposed by Grigoriev and Ponomarenko, which encrypts an element from a fixed finite group defined in terms of generators and relations to produce a ciphertext from . The paper presents a heuristic method for recovering the secret key from the public key, and so this cryptosystem should not be used in practice.

On non-Abelian homomorphic public-key cryptosystems

An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems, which are (secret) epimorphisms f : G → H, where G and H are (publically known) groups and H is finite. A letter of a message to be encrypted is an element h ∈ H, while its encryption is an element g ∈ G such that f(g) = h. A homomorphic cryptosystem allows one to perform computations (in the group G) with encrypted information (without knowing the original message over H).In this paper, homomorphic cryptosystems are constructed for the first time for non-Abelian groups H (earlier, homomorphic cryptosystems were known only in the Abelian case). In fact, we present such a system for any (fixed) solvable group H. Bibliography: 24 titles.

An Anonymous Fingerprinting Scheme Based on Additively Homomorphic Public Key Cryptosystem

This paper proposes an anonymous fingerprinting scheme based on the additively homomorphic public key cryptosystems. The proposed fingerprinting scheme enables the merchant to identify the illegal distributors without the help of a trusted third party when he/she finds an illegally redistributed fingerprinted copy. Furthermore, it allows two-party trials, i.e. there is no need for the accused (and possibly innocent) buyer to take part in the dispute resolution protocol and reveal his/her secrets. In addition, the problem of how to construct the anonymous public key and private key pairs is also addressed in the scheme. The security analysis shows that the proposed scheme is secure for both seller and buyer, and has the properties of anonymity and unlinkability for the buyer.