The Analysis of Constructing Fully Homomorphic Encryption over Integers

2014 ◽  
Vol 989-994 ◽  
pp. 4780-4784
Author(s):  
Lei Jin ◽  
Xin Xia Song
Keyword(s):  
Quadratic Form ◽  
Linear Form ◽  
Homomorphic Encryption ◽  
Random Oracle ◽  
Public Key ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
Compression Technique ◽  
The Public ◽  
Approximate Gcd

Fully homomorphic encryption has long been regarded as cryptography’s prized “holy grail”–extremely useful yet rather elusive. At 2010 van Dijk et al. described a fully homomorphic encryption scheme over theintegers. The main appeal of this scheme is its conceptual simplicity. This simplicity comes at the expense of a public key size inÕ(λ10) which is too large for any practical system. The construction is based on the hardness of the approximate-GCD problem. At 2011 Coron et al. reduced the public key size to about Õ(λ7) by encrypting with a quadratic form in the public key elements, instead of a linear form. This scheme is based on a stronger variant of the approximate-GCD problem. An implementation of the full scheme was obtained with a 802MB public key. At 2012 Coron et al. described a compression technique that reduces the public key size to aboutÕ(λ5). This variant remains semantically secure, but in the random oracle model.A level of efficiency very similar to above scheme was obtained but with a 10.1MB public key instead of a 802MB one.Coron et al. also described a new modulus switching technique for the DGHV scheme that enables to use the new FHE framework without bootstrapping from Brakerski, Gentry and Vaikuntanathan with theDGHV scheme. At present asymptotics of FHE over integers are much better.

An Improvement for Fully Homomorphic Encryption over Integers with Shorter Public Keys

2014 ◽  
Vol 989-994 ◽  
pp. 4326-4331
Author(s):  
Ze Tao Jiang ◽  
Xiao Te Huang
Keyword(s):  
Quadratic Form ◽  
Homomorphic Encryption ◽  
Public Key ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
The Public ◽  
Cubic Form ◽  
Public Keys ◽  
Subset Sum ◽  
Approximate Gcd

This paper puts forward a more efficient fully homomorphic encryption scheme with a view to improving the oversized public key based on the Dijk’s scheme.Encrypted with a cubic form in the public key elements instead of quadratic form by adopting Gentry’s fully homomorphic techonology.The results show that the public key size reduce from to compared to the Coron’s scheme.The security of the proposed scheme is based on both the approximate GCD problem and the sparse-subset sum problem.

An Additively Homomorphic Encryption over Large Message Space

2015 ◽  
Vol 10 (3) ◽  
pp. 82-102 ◽  
Author(s):  
Hu Chen ◽  
Yupu Hu ◽  
Zhizhu Lian ◽  
Huiwen Jia ◽  
Xu An Wang
Keyword(s):  
Homomorphic Encryption ◽  
Prime Numbers ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
The Public ◽  
Real World Applications ◽  
Encryption Schemes ◽  
Setting Parameters ◽  
Message Space ◽  
The Ideal

Fully homomorphic encryption schemes available are not efficient enough to be practical, and a number of real-world applications require only that a homomorphic encryption scheme is somewhat homomorphic, even additively homomorphic and has much larger message space for efficiency. An additively homomorphic encryption scheme based heavily on Smart-Vercauteren encryption scheme (SV10 scheme, PKC 2010) is put forward, where both schemes each work with two ideals I and J. As a contribution of independent interest, a two-element representation of the ideal I is given and proven by factoring prime numbers in a number field. This two-element representation serves as the public key. The authors' scheme allows working over much larger message space than that of SV10 scheme by selecting the ideal I with larger decryption radius to generate public/private key pair, instead of choosing the ideal J as done in the SV10 scheme. The correctness and security of the scheme are shown, followed by setting parameters and computational results. The results indicate that this construction has much larger message space than SV10 scheme.

scholarly journals Privacy-Preserving Oriented Floating-Point Number Fully Homomorphic Encryption Scheme

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Shuangjie Bai ◽  
Geng Yang ◽  
Jingqi Shi ◽  
Guoxiu Liu ◽  
Zhaoe Min
Keyword(s):  
Homomorphic Encryption ◽  
Privacy Preserving ◽  
Expansion Ratio ◽  
Public Key ◽  
Floating Point ◽  
Encryption Scheme ◽  
Cloud Environment ◽  
Fully Homomorphic Encryption ◽  
Point Number ◽  
Floating Point Number

The issue of the privacy-preserving of information has become more prominent, especially regarding the privacy-preserving problem in a cloud environment. Homomorphic encryption can be operated directly on the ciphertext; this encryption provides a new method for privacy-preserving. However, we face a challenge in understanding how to construct a practical fully homomorphic encryption on non-integer data types. This paper proposes a revised floating-point fully homomorphic encryption scheme (FFHE) that achieves the goal of floating-point numbers operation without privacy leakage to unauthorized parties. We encrypt a matrix of plaintext bits as a single ciphertext to reduce the ciphertext expansion ratio and reduce the public key size by encrypting with a quadratic form in three types of public key elements and pseudo-random number generators. Additionally, we make the FFHE scheme more applicable by generalizing the homomorphism of addition and multiplication of floating-point numbers to analytic functions using the Taylor formula. We prove that the FFHE scheme for ciphertext operation may limit an additional loss of accuracy. Specifically, the precision of the ciphertext operation’s result is similar to unencrypted floating-point number computation. Compared to other schemes, our FFHE scheme is more practical for privacy-preserving in the cloud environment with its low ciphertext expansion ratio and public key size, supporting multiple operation types and high precision.

scholarly journals BESTIE: Broadcast Encryption Scheme for Tiny IoT Equipment

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1389
Author(s):  
Jiwon Lee ◽  
Jihye Kim ◽  
Hyunok Oh
Keyword(s):  
The Other ◽  
Public Key ◽  
Broadcast Encryption ◽  
Encryption Scheme ◽  
The Public ◽  
Private Key ◽  
Diffie Hellman ◽  
The Standard Model ◽  
Encryption Decryption ◽  
Subset Difference

In public key broadcast encryption, anyone can securely transmit a message to a group of receivers such that privileged users can decrypt it. The three important parameters of the broadcast encryption scheme are the length of the ciphertext, the size of private/public key, and the performance of encryption/decryption. It is suggested to decrease them as much as possible; however, it turns out that decreasing one increases the other in most schemes. This paper proposes a new broadcast encryption scheme for tiny Internet of Things (IoT) equipment (BESTIE), minimizing the private key size in each user. In the proposed scheme, the private key size is O(logn), the public key size is O(logn), the encryption time per subset is O(logn), the decryption time is O(logn), and the ciphertext text size is O(r), where n denotes the maximum number of users, and r indicates the number of revoked users. The proposed scheme is the first subset difference-based broadcast encryption scheme to reduce the private key size O(logn) without sacrificing the other parameters. We prove that our proposed scheme is secure under q-Simplified Multi-Exponent Bilinear Diffie-Hellman (q-SMEBDH) in the standard model.

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