The extended Euclidean Algorithm made easy

2016 ◽  
Vol 100 (547) ◽  
pp. 147-149
Author(s):  
Paul Levrie ◽  
Rudi Penne
Keyword(s):  
Euclidean Algorithm ◽  
Extended Euclidean Algorithm

scholarly journals GCD of Aunu Binary Polynomials of Cardinality Seven Using Extended Euclidean Algorithm

2021 ◽  
Vol 09 (09) ◽  
Author(s):  
Ibrahim A. A. ◽  
Keyword(s):  
Finite Fields ◽  
Coding Theory ◽  
Error Correcting Codes ◽  
Euclidean Algorithm ◽  
Greatest Common Divisor ◽  
Algebraic Structures ◽  
Extended Euclidean Algorithm ◽  
Encryption Schemes ◽  
Theory Error

Finite fields is considered to be the most widely used algebraic structures today due to its applications in cryptography, coding theory, error correcting codes among others. This paper reports the use of extended Euclidean algorithm in computing the greatest common divisor (gcd) of Aunu binary polynomials of cardinality seven. Each class of the polynomial is permuted into pairs until all the succeeding classes are exhausted. The findings of this research reveals that the gcd of most of the pairs of the permuted classes are relatively prime. This results can be used further in constructing some cryptographic architectures that could be used in design of strong encryption schemes.

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

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