scholarly journals Two-Party Secure Computation for Any Polynomial Function on Ciphertexts under Different Secret Keys

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Bingbing Jiang
Keyword(s):  
Polynomial Function ◽  
Homomorphic Encryption ◽  
Auxiliary Information ◽  
Secure Computation ◽  
Encryption Algorithm ◽  
Fully Homomorphic Encryption ◽  
Simple Scheme ◽  
Secret Keys ◽  
Learning With Errors ◽  
Multiple Keys

Multikey fully homomorphic encryption proposed by Lopez-Alt et al. (STOC12) is a significant primitive that allows one to perform computation on the ciphertexts encrypted by multiple different keys independently. Then, several schemes were constructed based on decisional small polynomial ratio or learning with errors. These schemes all require an expansion algorithm to transform a ciphertext under a single key into an encryption of the same message under a set of keys. To achieve the expansion algorithm without interaction with these key-keepers, their encryption algorithm not only outputs a ciphertext of a plaintext but also exports auxiliary information generated from the randomness used in the former encryption process. Beyond that, the size of the ciphertext encrypted by multiple keys increases linearly or quadratically in the number of participants. In this paper, we studied the problem whether someone can directly perform arbitrary computation on ciphertexts encrypted by different keys without any auxiliary information in the output of the encryption algorithm and an increase in the size of the ciphertext in the expansion algorithm. To this end, we proposed a novel and simple scheme of secure computation on ciphertexts under two different keys directly without any auxiliary information. In other words, each party just provides its own ciphertexts encrypted by the GSW scheme (CRYPTO13). In the procedure of executing evaluation on these ciphertexts, the size of the new ciphertext remains the same as that of the GSW ciphertext.

Computing Blindfolded on Data Homomorphically Encrypted under Multiple Keys: A Survey

2022 ◽  
Vol 54 (9) ◽  
pp. 1-37
Author(s):  
Asma Aloufi ◽  
Peizhao Hu ◽  
Yongsoo Song ◽  
Kristin Lauter
Keyword(s):  
Homomorphic Encryption ◽  
Lessons Learned ◽  
Secret Key ◽  
Sensitive Data ◽  
Encrypted Data ◽  
Outsourced Computation ◽  
Secret Keys ◽  
Comprehensive Survey ◽  
Multiple Keys ◽  
Cryptographic Techniques

With capability of performing computations on encrypted data without needing the secret key, homomorphic encryption (HE) is a promising cryptographic technique that makes outsourced computations secure and privacy-preserving. A decade after Gentry’s breakthrough discovery of how we might support arbitrary computations on encrypted data, many studies followed and improved various aspects of HE, such as faster bootstrapping and ciphertext packing. However, the topic of how to support secure computations on ciphertexts encrypted under multiple keys does not receive enough attention. This capability is crucial in many application scenarios where data owners want to engage in joint computations and are preferred to protect their sensitive data under their own secret keys. Enabling this capability is a non-trivial task. In this article, we present a comprehensive survey of the state-of-the-art multi-key techniques and schemes that target different systems and threat models. In particular, we review recent constructions based on Threshold Homomorphic Encryption (ThHE) and Multi-Key Homomorphic Encryption (MKHE). We analyze these cryptographic techniques and schemes based on a new secure outsourced computation model and examine their complexities. We share lessons learned and draw observations for designing better schemes with reduced overheads.

scholarly journals Blockchain-Based Secure Outsourcing of Polynomial Multiplication and Its Application in Fully Homomorphic Encryption

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Mingyang Song ◽  
Yingpeng Sang ◽  
Yuying Zeng ◽  
Shunchao Luo
Keyword(s):  
Homomorphic Encryption ◽  
Security Analysis ◽  
Secure Computation ◽  
Modular Exponentiation ◽  
Local Computation ◽  
Fully Homomorphic Encryption ◽  
Polynomial Multiplication ◽  
Secure Outsourcing ◽  
Cheating Detection ◽  
Constrained Devices

The efficiency of fully homomorphic encryption has always affected its practicality. With the dawn of Internet of things, the demand for computation and encryption on resource-constrained devices is increasing. Complex cryptographic computing is a major burden for those devices, while outsourcing can provide great convenience for them. In this paper, we firstly propose a generic blockchain-based framework for secure computation outsourcing and then propose an algorithm for secure outsourcing of polynomial multiplication into the blockchain. Our algorithm for polynomial multiplication can reduce the local computation cost to O n . Previous work based on Fast Fourier Transform can only achieve O n log n for the local cost. Finally, we integrate the two secure outsourcing schemes for polynomial multiplication and modular exponentiation into the fully homomorphic encryption using hidden ideal lattice and get an outsourcing scheme of fully homomorphic encryption. Through security analysis, our schemes achieve the goals of privacy protection against passive attackers and cheating detection against active attackers. Experiments also demonstrate our schemes are more efficient in comparisons with the corresponding nonoutsourcing schemes.

scholarly journals An Effective NTRU-Based Fully Homomorphic Encryption Scheme

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiaoyue Qin ◽  
Ruwei Huang ◽  
Huifeng Fan
Keyword(s):  
Chinese Remainder Theorem ◽  
Homomorphic Encryption ◽  
Security Model ◽  
Storage Efficiency ◽  
Complex Matrix ◽  
Fully Homomorphic Encryption ◽  
Multiple Data ◽  
Learning With Errors ◽  
Matrix Vector ◽  
And Storage

Fully homomorphic encryption (FHE) supports arbitrary computations on ciphertexts without decryption to protect users’ privacy. However, currently, there are still some shortcomings in research studies on FHE. For example, the NTRU-based FHE scheme constructed using the approximate eigenvector method requires complex matrix multiplications, and the power-of-two cyclotomic ring cannot prevent subfield attacks. To address these problems, this paper proposed a NTRU-based FHE scheme constructed based on the power-of-prime cyclotomic ring and made the following improvements: (1) the power-of-prime cyclotomic ring is immune to subfield attacks; (2) complex matrix multiplications are replaced with matrix-vector multiplications to modify the ciphertext forms and decryption structures, so as to gain advantages in storage, transportation, and computations; (3) the single instruction multiple data (SIMD) technology is introduced, and homomorphic operations are executed through the Chinese remainder theorem, further improving the scheme computation and storage efficiency. The ciphertext of the scheme is in a form of a vector, and no key exchange is required for homomorphic operations. In addition, this scheme can eliminate the decisional small polynomial ratio (DSPR) assumption under certain conditions and only relies on the ring learning with errors (RLWE) assumption. The standard security model can prove that this scheme is secure against chosen-plaintext (IND-CPA) attacks. Compared with similar schemes, the proposed scheme improves the efficiency at least by a factor of l φ x / d +   1 and quadratically decreases the noise growth rate.

scholarly journals Two-Party Privacy-Preserving Set Intersection with FHE

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1339
Author(s):  
Yunlu Cai ◽  
Chunming Tang ◽  
Qiuxia Xu
Keyword(s):  
Private Information ◽  
Homomorphic Encryption ◽  
Bloom Filter ◽  
Cloud Service ◽  
Fully Homomorphic Encryption ◽  
Cloud Service Provider ◽  
Set Size ◽  
Set Intersection ◽  
Learning With Errors ◽  
Private Set Intersection

A two-party private set intersection allows two parties, the client and the server, to compute an intersection over their private sets, without revealing any information beyond the intersecting elements. We present a novel private set intersection protocol based on Shuhong Gao’s fully homomorphic encryption scheme and prove the security of the protocol in the semi-honest model. We also present a variant of the protocol which is a completely novel construction for computing the intersection based on Bloom filter and fully homomorphic encryption, and the protocol’s complexity is independent of the set size of the client. The security of the protocols relies on the learning with errors and ring learning with error problems. Furthermore, in the cloud with malicious adversaries, the computation of the private set intersection can be outsourced to the cloud service provider without revealing any private information.

A Key Management Scheme for Smart Grid Wireless Terminals

2013 ◽  
Vol 442 ◽  
pp. 501-506
Author(s):  
Bo Zhang ◽  
Yu Fei Wang ◽  
Tao Zhang ◽  
Yuan Yuan Ma
Keyword(s):  
Smart Grid ◽  
Power Systems ◽  
Key Management ◽  
Large Scale ◽  
Homomorphic Encryption ◽  
Symmetric Polynomial ◽  
Encryption Algorithm ◽  
Fully Homomorphic Encryption ◽  
Management Scheme ◽  
Key Management Scheme

With the large-scale construction of smart grid, smart grid terminals widely using wireless access technology to communicate to the power systems. For ensuring the communication security, pair-wise key pre-distribution scheme is widely used, however, which introduces the complexity of key management, and insufficient security problems. According to the smart grid terminals wireless communication features, proposes an intelligent grid wireless terminal online key management scheme, which is based on the t rank binary symmetric polynomial and fully homomorphic encryption algorithm. This scheme make the communication key could be established with a few parameters between the communicating parties, which reduces the complexity of key predistribution and the amount of calculation. Moreover, the whole process of the key generation is encrypted by fully homomorphic encryption algorithm, effectively enhances the security of the scheme.

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