scholarly journals Towards the Construction of Reed-Muller Code Based Symmetric Key FHE

2021 ◽  
Vol 26 (6) ◽  
pp. 585-590
Author(s):  
Ratnakumari Challa ◽  
VijayaKumari Gunta
Keyword(s):  
Structural Properties ◽  
Experimental Evaluation ◽  
Coding Theory ◽  
Homomorphic Encryption ◽  
Cryptographic Primitives ◽  
Correctness Proof ◽  
Security Applications ◽  
Unlimited Number ◽  
Multiplication Operation ◽  
Symmetric Key

Homomorphic encryption (HE) schemes became popular cryptographic primitives and very useful in variety of security applications. Homomorphic encryption based on coding theory have the advantages of faster computations due to the structural properties of the codes used. Several schemes are supporting unlimited Mod2 addition operations in literature. The present paper introduces Reed-Muller (RM) code based Mod2 multiplication operation thereby making RM code based HE scheme fully homomorphic. The representation of the codeword with necessary adaption to support unlimited number of Mod2​ multiplication operations is presented along with the scheme first. The correctness proof of the homomorphic operations along with experimental evaluation is also presented to demonstrate the practical aspects of the proposal.

scholarly journals A Modified Symmetric Key Fully Homomorphic Encryption Scheme Based on Read-Muller Code

2021 ◽  
Vol 18 (2(Suppl.)) ◽  
pp. 0899
Author(s):  
RatnaKumari Challa ◽  
VijayaKumari Gunta
Keyword(s):  
Coding Theory ◽  
Homomorphic Encryption ◽  
Security Analysis ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
Chosen Plaintext Attack ◽  
Security Proof ◽  
Expansion Technique ◽  
Cryptographic Primitive ◽  
Symmetric Key

Homomorphic encryption became popular and powerful cryptographic primitive for various cloud computing applications. In the recent decades several developments has been made. Few schemes based on coding theory have been proposed but none of them support unlimited operations with security.   We propose a modified Reed-Muller Code based symmetric key fully homomorphic encryption to improve its security by using message expansion technique. Message expansion with prepended random fixed length string provides one-to-many mapping between message and codeword, thus one-to many mapping between plaintext and ciphertext. The proposed scheme supports both (MOD 2) additive and multiplication operations unlimitedly.   We make an effort to prove the security of the scheme under indistinguishability under chosen-plaintext attack (IND-CPA) through a game-based security proof. The security proof gives a mathematical analysis and its complexity of hardness. Also, it presents security analysis against all the known attacks with respect to the message expansion and homomorphic operations.

Architecture of ASIP Crypto-Processor for Dynamic Runtime Security Applications

2016 ◽  
Vol 4 (2) ◽  
pp. 412
Author(s):  
Mahaba Saad ◽  
Khalid Youssef ◽  
Mohamed Tarek ◽  
Hala Abdel-Kader
Keyword(s):  
Quantitative Analysis ◽  
High Speed ◽  
Reference Model ◽  
Power Performance ◽  
Security Applications ◽  
Logical Operations ◽  
Symmetric Key ◽  
Encryption Algorithms ◽  
Security Operations ◽  
The Masses

<p>Nowadays, demands of data security are increasing, especially after introduction of wireless communications to the masses. Cryptographic algorithms are mainly used to obtain confidentiality and integrity of data in communication. There are a variety of encryption algorithms have been developed. This paper provides quantitative analysis and comparison of some symmetric key cryptographic ciphers (DES, 3DES, AES, Blowfish, RC5, and RC6).  The quantitative analysis approach is a step towards optimizing the security operations for an efficient next generation family of network processors with enhanced speed and power performance. A framework will be proposed as a reference model for quantitative analysis of security algorithm mathematical and logical operations. This paper also provides a dynamic crypto processor used for selected symmetric key cryptographic ciphers   and  provides an implementation of 16bit cryptographic processor that performs logical operations and arithmetic operations like rotate shift left, modular addition 2^16, S_box operation, and key expansion operation  on spartan6 lower power, xc6slx150L-1lfgg676 FPGA. Simulation results show that developed processor working with high Speed, low power, and low delay time. </p>

scholarly journals polarRLCE: A New Code-Based Cryptosystem Using Polar Codes

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jingang Liu ◽  
Yongge Wang ◽  
Zongxiang Yi ◽  
Zhiqiang Lin
Keyword(s):  
Coding Theory ◽  
Public Key ◽  
Security Level ◽  
Polar Codes ◽  
Encryption Scheme ◽  
Cryptographic Primitives ◽  
The Public ◽  
Security Challenges ◽  
High Security Level ◽  
Code Based Cryptography

Security challenges brought about by the upcoming 5G era should be taken seriously. Code-based cryptography leverages difficult problems in coding theory and is one of the main techniques enabling cryptographic primitives in the postquantum scenario. In this work, we propose the first efficient secure scheme based on polar codes (i.e., polarRLCE) which is inspired by the RLCE scheme, a candidate for the NIST postquantum cryptography standardization in the first round. In addition to avoiding some weaknesses of the RLCE scheme, we show that, with the proper choice of parameters, using polar codes, it is possible to design an encryption scheme to achieve the intended security level while retaining a reasonably small public key size. In addition, we also present a KEM version of the polarRLCE scheme that can attain a negligible decryption failure rate within the corresponding security parameters. It is shown that our proposal enjoys an apparent advantage to decrease the public key size, especially on the high-security level.

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

On the exact decryption range for Gentry–Halevi's implementation of fully homomorphic encryption

2014 ◽  
Vol 8 (3) ◽  
Author(s):  
Masaya Yasuda ◽  
Kazuhiro Yokoyama ◽  
Takeshi Shimoyama ◽  
Jun Kogure ◽  
Takeshi Koshiba
Keyword(s):  
Upper Bound ◽  
Experimental Evaluation ◽  
Homomorphic Encryption ◽  
Euclidean Norm ◽  
Fully Homomorphic Encryption ◽  
Ideal Lattices ◽  
Noise Density ◽  
Original Scheme ◽  
Somewhat Homomorphic Encryption ◽  
Noise Management

AbstractIn this paper, we revisit the fully homomorphic encryption (FHE) scheme implemented by Gentry and Halevi, which is just an instantiation of Gentry's original scheme based on ideal lattices. Their FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, and its decryption range is deeply related with the FHE construction. Gentry and Halevi gave an experimental evaluation of the decryption range, but theoretical evaluations have not been given so far. Moreover, we give a theoretical upper bound, and reconsider suitable parameters for theoretically obtaining an FHE scheme. In particular, while Gentry and Halevi use the Euclidean norm evaluation in the noise management of ciphertexts, our theoretical bound enables us to use the ∞-norm evaluation, and hence it helps to lower the difficulty of controlling the noise density of ciphertexts.

scholarly journals A Verifiable Fully Homomorphic Encryption Scheme for Cloud Computing Security

Technologies ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 21
Author(s):  
Ahmed EL-YAHYAOUI ◽  
Mohamed Dafir ECH-CHERIF EL KETTANI
Keyword(s):  
Cloud Computing ◽  
Homomorphic Encryption ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
Sensitive Data ◽  
Verifiable Computation ◽  
Multiplication Operation ◽  
Matrix Operations ◽  
Encryption Schemes ◽  
Simple Matrix

Performing smart computations in a context of cloud computing and big data is highly appreciated today. It allows customers to fully benefit from cloud computing capacities (such as processing or storage) without losing confidentiality of sensitive data. Fully homomorphic encryption (FHE) is a smart category of encryption schemes that enables working with the data in its encrypted form. It permits us to preserve confidentiality of our sensible data and to benefit from cloud computing capabilities. While FHE is combined with verifiable computation, it offers efficient procedures for outsourcing computations over encrypted data to a remote, but non-trusted, cloud server. The resulting scheme is called Verifiable Fully Homomorphic Encryption (VFHE). Currently, it has been demonstrated by many existing schemes that the theory is feasible but the efficiency needs to be dramatically improved in order to make it usable for real applications. One subtle difficulty is how to efficiently handle the noise. This paper aims to introduce an efficient and symmetric verifiable FHE based on a new mathematic structure that is noise free. In our encryption scheme, the noise is constant and does not depend on homomorphic evaluation of ciphertexts. The homomorphy of our scheme is obtained from simple matrix operations (addition and multiplication). The running time of the multiplication operation of our encryption scheme in a cloud environment has an order of a few milliseconds.

scholarly journals Algorithms for CRT-variant of Approximate Greatest Common Divisor Problem

2020 ◽  
Vol 14 (1) ◽  
pp. 397-413
Author(s):  
Jung Hee Cheon ◽  
Wonhee Cho ◽  
Minki Hhan ◽  
Jiseung Kim ◽  
Changmin Lee
Keyword(s):  
Time Complexity ◽  
Chinese Remainder Theorem ◽  
Homomorphic Encryption ◽  
Divisor Problem ◽  
Greatest Common Divisor ◽  
Fully Homomorphic Encryption ◽  
Cryptographic Primitives ◽  
Multiple Messages ◽  
Polynomial Factor ◽  
Parameter Condition

AbstractThe approximate greatest common divisor problem (ACD) and its variants have been used to construct many cryptographic primitives. In particular, the variants of the ACD problem based on Chinese remainder theorem (CRT) are being used in the constructions of a batch fully homomorphic encryption to encrypt multiple messages in one ciphertext. Despite the utility of the CRT-variant scheme, the algorithms that secures its security foundation have not been probed well enough.In this paper, we propose two algorithms and the results of experiments in which the proposed algorithms were used to solve the variant problem. Both algorithms take the same time complexity $\begin{array}{} \displaystyle 2^{\tilde{O}(\frac{\gamma}{(\eta-\rho)^2})} \end{array}$ up to a polynomial factor to solve the variant problem for the bit size of samples γ, secret primes η, and error bound ρ. Our algorithm gives the first parameter condition related to η and γ size. From the results of the experiments, it has been proved that the proposed algorithms work well both in theoretical and experimental terms.

scholarly journals Using Simon's algorithm to attack symmetric-key cryptographic primitives

2017 ◽  
Vol 17 (1&2) ◽  
pp. 65-78
Author(s):  
Thomas Santoli ◽  
Christian Schaffner
Keyword(s):  
Quantum Information ◽  
Cryptographic Primitives ◽  
Forgery Attack ◽  
Security Proofs ◽  
Symmetric Key ◽  
Quantum Oracle ◽  
Independent Work ◽  
Oracle Access

We present new connections between quantum information and the field of classical cryptography. In particular, we provide examples where Simon’s algorithm can be used to show insecurity of commonly used cryptographic symmetric-key primitives. Specifically, these examples consist of a quantum distinguisher for the 3-round Feistel network and a forgery attack on CBC-MAC which forges a tag for a chosen-prefix message querying only other messages (of the same length). We assume that an adversary has quantum-oracle access to the respective classical primitives. Similar results have been achieved recently in independent work by Kaplan et al. [KLLNP16]. Our findings shed new light on the post-quantum security of cryptographic schemes and underline that classical security proofs of cryptographic constructions need to be revisited in light of quantum attackers.

scholarly journals On Constructing Homomorphic Encryption Schemes from Coding Theory

2011 ◽  
pp. 23-40 ◽  
Author(s):  
Frederik Armknecht ◽  
Daniel Augot ◽  
Ludovic Perret ◽  
Ahmad-Reza Sadeghi
Keyword(s):  
Coding Theory ◽  
Homomorphic Encryption ◽  
Encryption Schemes
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