scholarly journals Privacy Preserving Using Extended Euclidean Algorithm Applied To RSA-Homomorphic Encryption Technique

2019 ◽  
Vol 8 (10) ◽  
pp. 3175-3179
Keyword(s):  
Homomorphic Encryption ◽  
Euclidean Algorithm ◽  
Sensitive Information ◽  
Brute Force ◽  
Confidential Information ◽  
Security Applications ◽  
Private Key ◽  
Extended Euclidean Algorithm ◽  
Cryptographic Algorithms ◽  
Important Challenge

Communication of confidential information over Internet is the key aspect of security applications. Providing protection to sensitive information is of major concern. Many cryptographic algorithms have been in use for providing security of confidential information. Providing security for data has become major challenge in this era. Classical cryptography is playing a major role in providing security for applications. In modern days securing confidential information in the cloud is considered as an important challenge. Homomorphic Encryption technique is one of the best solutions that provide security in the cloud[1]. In this paper, Extended Euclidean Algorithm is used for generating keys. This technique follows RSA Homomorphic encryption technique. .RSA Homomorphic encryption using Extended Euclidean algorithm (RSA-HEEEA) is secure when compared to RSA as it based on the generation of private key which makes the algorithm complex .This technique of using Extended Euclidean Algorithm(EEA) is fast and secure when compared to RSA homomorphic encryption technique. The encryption process utilizes modulo operator which gives security as well.The beauty of this algorithm is in generation of private key which uses Extended Euclidean Algorithm (EEA) that helps in avoiding brute force attacks. Also, this technique uses Homomorphic operations which gives enhance security to confidential information in the cloud

scholarly journals A Note on the Computation of the Modular Inverse for Cryptography

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 116
Author(s):  
Michele Bufalo ◽  
Daniele Bufalo ◽  
Giuseppe Orlando
Keyword(s):  
Periodic Solution ◽  
Computational Cost ◽  
Euclidean Algorithm ◽  
Extended Euclidean Algorithm ◽  
Modulo Operation ◽  
Cryptographic Algorithms ◽  
Naive Algorithm ◽  
Positive Integers

In literature, there are a number of cryptographic algorithms (RSA, ElGamal, NTRU, etc.) that require multiple computations of modulo multiplicative inverses. In this paper, we describe the modulo operation and we recollect the main approaches to computing the modulus. Then, given a and n positive integers, we present the sequence (zj)j≥0, where zj=zj−1+aβj−n, a<n and GCD(a,n)=1. Regarding the above sequence, we show that it is bounded and admits a simple explicit, periodic solution. The main result is that the inverse of a modulo n is given by a−1=⌊im⌋+1 with m=n/a. The computational cost of such an index i is O(a), which is less than O(nlnn) of the Euler’s phi function. Furthermore, we suggest an algorithm for the computation of a−1 using plain multiplications instead of modular multiplications. The latter, still, has complexity O(a) versus complexity O(n) (naive algorithm) or complexity O(lnn) (extended Euclidean algorithm). Therefore, the above procedure is more convenient when a<<n (e.g., a<lnn).

scholarly journals Improved Algorithm of Steganography Combined with Cryptography

2021 ◽  
Vol 9 (VI) ◽  
pp. 3793-3804
Author(s):  
Anees Banu
Keyword(s):  
Information Security ◽  
Multimedia Information ◽  
Secret Data ◽  
Confidential Information ◽  
Additional Layer ◽  
Confidential Data ◽  
The World ◽  
Cryptographic Algorithms ◽  
Written Form ◽  
Improved Algorithm

When it comes to preventing unauthorised access to, destruction of, or inspection of confidential data, information security has always been a major factor. Multimedia information is now used in every field throughout the world. The confidential information that is used in these areas must be kept secure. There are a variety of methods for keeping data secure. One of these is steganography, which is concealing information within other data into a format that the cover information remains unchanged. Cryptography, an encryption process that scrambles data into a written form that is sometimes referred to as a hash, is an auxiliary approach for securing information. Steganography and cryptography each have their own set of benefits and drawbacks. Even though both technologies give security, it is usually a good practise to combine Cryptographic algorithms to create additional layers of security. When cryptographic with steganography are combined, a multi-layer security paradigm is created. The proposed work's main goal is to add an additional layer of protection by using cryptography and steganography to encrypt and embed secret data conveyed across an insecure channel.

scholarly journals Survey on Asymmetric Key Cryptographic Algorithms

2020 ◽  
pp. 404-408
Author(s):  
Sabitha S ◽  
Binitha V Nair
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
The Public ◽  
Private Key ◽  
Design And Implementation ◽  
Diffie Hellman ◽  
Encryption And Decryption ◽  
Cryptographic Algorithms ◽  
Symmetric Key ◽  
Symmetric Key Cryptography

Cryptography is an essential and effective method for securing information’s and data. Several symmetric and asymmetric key cryptographic algorithms are used for securing the data. Symmetric key cryptography uses the same key for both encryption and decryption. Asymmetric Key Cryptography also known as public key cryptography uses two different keys – a public key and a private key. The public key is used for encryption and the private key is used for decryption. In this paper, certain asymmetric key algorithms such as RSA, Rabin, Diffie-Hellman, ElGamal and Elliptical curve cryptosystem, their security aspects and the processes involved in design and implementation of these algorithms are examined.

scholarly journals Privacy-Preserved Approximate Classification Based on Homomorphic Encryption

2019 ◽  
Vol 24 (4) ◽  
pp. 92 ◽  
Author(s):  
Xiaodong Xiao ◽  
Ting Wu ◽  
Yuanfang Chen ◽  
Xingyue Fan
Keyword(s):  
Time Complexity ◽  
Homomorphic Encryption ◽  
Classification Problem ◽  
Sensitive Information ◽  
Cloud Infrastructure ◽  
Crucial Issue ◽  
Computational Overhead ◽  
Computation Formula ◽  
Online Prediction ◽  
Real World Problems

Privacy is a crucial issue for outsourcing computation, which means that clients utilize cloud infrastructure to perform online prediction without disclosing sensitive information. Homomorphic encryption (HE) is one of the promising cryptographic tools resolving privacy issue in this scenario. However, a bottleneck in application of HE is relatively high computational overhead. In this paper, we study the privacy-preserving classification problem. To this end, we propose a novel privacy-preserved approximate classification algorithm. It exploits a set of decision trees to reduce computational complexity during homomorphic evaluation computation formula, the time complexity of evaluating a polynomial is degraded from O n to O log n . As a result, for an MNIST dataset, the Micro- f 1 score of the proposed algorithm is 0 . 882 , compared with 0 . 912 of the standard method. For the Credit dataset, the algorithm achieves 0 . 601 compared with 0 . 613 of the method. These results show that our algorithm is feasible and practical in real world problems.

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.

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