scholarly journals Algebraic Verification Algorithm

2018 ◽  
Vol 3 (1) ◽  
pp. 7
Author(s):  
Areej M Abduldaim
Keyword(s):  
Algebraic Structure ◽  
Ring Theory ◽  
Authentication Scheme ◽  
Cryptographic Protocol ◽  
Zero Knowledge ◽  
Additional Information ◽  
Verification Algorithm ◽  
Public Networks ◽  
Armendariz Rings ◽  
Soundness And Completeness

Authentication over insecure public networks or with untrusted servers raises more concerns in privacy and security.Modern algebra is one of the significantfields of mathematics. It is a combination of techniques used for a variety of applications including the process of the manipulation of the mathematical categories. In addition,modern algebra deals in depth with the study of abstractions such as groups, rings and fields,the main objective of this article is to provide a novel algebraic verification protocol using ring theory. The protocol is blind, meaning that it detects only the identity, and no additional information will be known anything about the prover (the biometric) to the authenticating server or vice-versa. More officially a blind authentication scheme is a cryptographic protocol that comprises of two parties, a user (the prover) that wants to achieve having signs on her messages, and a signer (the verifier) that is in ownership of his secret signing key. In this paper, we employ the algebraic structure called central Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.This method gave two important properties for the central Armendariz zero knowledge protocol compared with other known protocols.

scholarly journals A study of universal zero-knowledge proof circuit-based virtual machines that validate general operations & reduce transaction validation

2021 ◽  
Vol 18 (2) ◽  
pp. 481-497
Author(s):  
Soonhyeong Jeong ◽  
Byeongtae Ahn
Keyword(s):  
Virtual Machine ◽  
Virtual Machines ◽  
Key Generation ◽  
Zero Knowledge ◽  
Verification Algorithm ◽  
Blockchain Technology ◽  
General Operation ◽  
Zero Knowledge Proof

Recently, blockchain technology accumulates and stores all transactions. Therefore, in order to verify the contents of all transactions, the data itself is compressed, but the scalability is limited. In addition, since a separate verification algorithm is used for each type of transaction, the verification burden increases as the size of the transaction increases. Existing blockchain cannot participate in the network because it does not become a block sink by using a server with a low specification. Due to this problem, as the time passes, the data size of the blockchain network becomes larger and it becomes impossible to participate in the network except for users with abundant resources. Therefore, in this paper, we studied the zero knowledge proof algorithm for general operation verification. In this system, the design of zero-knowledge circuit generator capable of general operation verification and optimization of verifier and prover were also conducted. Also, we developed an algorithm for optimizing key generation. Based on all of these, the zero-knowledge proof algorithm was applied to and tested on the virtual machine so that it can be used universally on all blockchains.

scholarly journals A Novel Blockchain Identity Authentication Scheme Implemented in Fog Computing

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Huijuan Wang ◽  
Yong Jiang
Keyword(s):  
Elliptic Curves ◽  
Fog Computing ◽  
Key Distribution ◽  
Identity Authentication ◽  
Ring Theory ◽  
Authentication Scheme ◽  
Consensus Algorithm ◽  
Computing Environment ◽  
Cryptographic Scheme

In a fog computing environment, lots of devices need to be authenticated in order to keep the platform being secured. To solve this problem, we turn to blockchain techniques. Unlike the identification cryptographic scheme based on elliptic curves, the proposed 2-adic ring identity authentication scheme inherits the high verification efficiency and high key distribution of sequence ciphers of 2-adic ring theory, and this algorithm adds identity hiding function and trading node supervision function by design. The main designed application scenario of this solution is applicable to the consortium blockchain, and the master nodes are mutually trusting cooperative relations. The node transaction verification and block generation consensus algorithm designed in this solution can be implemented in a set of algorithms, which has higher verification efficiency and easier to be deployed than other solutions. This scheme can be widely used in the fog computing environment.

scholarly journals A note on almost prime submodule of CSM module over principal ideal domain

2021 ◽  
Vol 2106 (1) ◽  
pp. 012011
Author(s):  
I G A W Wardhana ◽  
N D H Nghiem ◽  
N W Switrayni ◽  
Q Aini
Keyword(s):  
Prime Ideal ◽  
Algebraic Structure ◽  
Principal Ideal ◽  
Ring Theory ◽  
Principal Ideal Domain ◽  
Module Theory ◽  
Ideal Domain ◽  
Multiplication Operation ◽  
Prime Submodule ◽  
Almost Prime

Abstract An almost prime submodule is a generalization of prime submodule introduced in 2011 by Khashan. This algebraic structure was brought from an algebraic structure in ring theory, prime ideal, and almost prime ideal. This paper aims to construct similar properties of prime ideal and almost prime ideal from ring theory to module theory. The problem that we want to eliminate is the multiplication operation, which is missing in module theory. We use the definition of module annihilator to bridge the gap. This article gives some properties of the prime submodule and almost prime submodule of CMS module over a principal ideal domain. A CSM module is a module that every cyclic submodule. One of the results is that the idempotent submodule is an almost prime submodule.

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