A new fully homomorphic encryption over the integers using smaller public key

2016 ◽  
Vol 8 (4) ◽  
pp. 303
Author(s):  
Yeluripati Govindha Ramaiah ◽  
Gunta Vijaya Kumari
Keyword(s):  
Homomorphic Encryption ◽  
Public Key ◽  
Fully Homomorphic Encryption

scholarly journals LWR-Based Fully Homomorphic Encryption, Revisited

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Fucai Luo ◽  
Fuqun Wang ◽  
Kunpeng Wang ◽  
Jie Li ◽  
Kefei Chen
Keyword(s):  
Tensor Product ◽  
Gaussian Noise ◽  
Homomorphic Encryption ◽  
Matrix Multiplication ◽  
Public Key ◽  
Multiparty Computation ◽  
Secret Key ◽  
Fully Homomorphic Encryption ◽  
Private Key ◽  
Modulus Problem

Very recently, Costache and Smart proposed a fully homomorphic encryption (FHE) scheme based on the Learning with Rounding (LWR) problem, which removes the noise (typically, Gaussian noise) sampling needed in the previous lattices-based FHEs. But their scheme did not work, since the noise of homomorphic multiplication is complicated and large, which leads to failure of decryption. More specifically, they chose LWR instances as a public key and the private key therein as a secret key and then used the tensor product to implement homomorphic multiplication, which resulted in a tangly modulus problem. Recall that there are two moduli in the LWR instances, and then the moduli will tangle together due to the tensor product. Inspired by their work, we built the first workable LWR-based FHE scheme eliminating the tangly modulus problem by cleverly adopting the celebrated approximate eigenvector method proposed by Gentry et al. at Crypto 2013. Roughly speaking, we use a specific matrix multiplication to perform the homomorphic multiplication, hence no tangly modulus problem. Furthermore, we also extend the LWR-based FHE scheme to the multikey setting using the tricks used to construct LWE-based multikey FHE by Mukherjee and Wichs at Eurocrypt 2016. Our LWR-based multikey FHE construction provides an alternative to the existing multikey FHEs and can also be applied to multiparty computation with higher efficiency.

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.

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.

scholarly journals A Multi-Bit Fully Homomorphic Encryption With Shorter Public Key From LWE

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 50588-50594 ◽  
Author(s):  
Xinxia Song ◽  
Zhigang Chen ◽  
Liang Chen
Keyword(s):  
Homomorphic Encryption ◽  
Public Key ◽  
Fully Homomorphic Encryption

scholarly journals Cryptanalysis of Enhanced More

2019 ◽  
Vol 73 (1) ◽  
pp. 163-178
Author(s):  
Damian Vizár ◽  
Serge Vaudenay
Keyword(s):  
Homomorphic Encryption ◽  
Public Key ◽  
Linear Transformations ◽  
Original Design ◽  
Fully Homomorphic Encryption ◽  
Matrix Operation ◽  
Research Topics ◽  
Public Key Cryptosystems ◽  
Highly Efficient ◽  
The Matrix

Abstract Fully homomorphic encryption (FHE) has been among the most popular research topics of the last decade. While the bootstrapping-based, public key cryptosystems that follow Gentry’s original design are getting more and more efficient, their performance is still far from being practical. This leads to several attempts to construct symmetric FHE schemes that would not be as inefficient as their public key counterparts. Unfortunately, most such schemes were also based on (randomized) linear transformations, and shown to be completely insecure. One such broken scheme was the Matrix Operation for Randomization and Encryption (MORE). In a recent paper, Hariss, Noura and Samhat propose Enhanced MORE, which is supposed to improve over MORE’s weaknesses. We analyze Enhanced MORE, discuss why it does not improve over MORE, and show that it is even less secure by presenting a highly efficient ciphertext-only decryption attack. We implement the attack and confirm its correctness.

Fully Homomorphic Encryption with Matrix based Public Key Crypto Systems

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Addepalli VN Krishna ◽  
Addepalli Hari Narayana ◽  
Kokk Madhura Vani
Keyword(s):  
Prime Number ◽  
Homomorphic Encryption ◽  
Public Key ◽  
Generator Matrix ◽  
Fully Homomorphic Encryption ◽  
Asymmetric Mode ◽  
Cipher Text ◽  
Global Variables ◽  
Key Length ◽  
Sufficient Strength

In this work, a novel mechanism is considered for asymmetric mode of encrypting data. A generator matrix is used to generate a field with a large prime number. The generator matrix, prime number and quaternary vector are used as global variables. Those global variables are used to calculate public key and also sub keys which in turn are used in the ElGamal mode of encryption. The decryption of data is done with Private Key. The proposed algorithm supports the features like authenticity of users, security & confidentiality of data transmitted. The mechanism can well be used in homomorphic encryption where computations are carried out on cipher text and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintext. Going by the construction of the algorithm, encryption is being done on blocks of data for which it consumes less computing resources. Going by complexity of the algorithm, the key length needed is much less to provide sufficient strength against crypto analysis.

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