Visible to the public A new elliptic curve cryptographic system over the finite fields

TitleA new elliptic curve cryptographic system over the finite fields
Publication TypeConference Paper
Year of Publication2017
AuthorsPriyatharsan, U., Rupasinghe, P. L., Murray, I.
Conference Name2017 6th National Conference on Technology and Management (NCTM)
KeywordsCayley Hamilton theorem, cryptographic protocols, cryptosystems, cyber security, Diffie Hellman protocol, discrete logarithms, Discrete Logarithms Problems, ECC, ElGamal, elliptic curve cryptographic system, Elliptic curve cryptography, Elliptic curves, Encryption, finite fields, invertible matrix, key exchange authentication, Mathematical model, matrix algebra, Menezes Qu Vanstone encryption protocols, message authentication, Metrics, network communications, private key cryptography, private key matrices, Protocols, pubcrawl, public key cryptography, public key vectors, Resiliency, Scalability, secure communication, security, square matrices
Abstract

Security of the information is the main problem in network communications nowadays. There is no algorithm which ensures the one hundred percent reliability of the transmissions. The current society uses the Internet, to exchange information such as from private images to financial data. The cryptographic systems are the mechanisms developed to protect and hide the information from intruders. However, advancing technology is also used by intruders to breach the security of the systems. Hence, every time cryptosystems developed based on complex Mathematics. Elliptic curve cryptography(ECC) is one of the technique in such kind of cryptosystems. Security of the elliptic curves lies in hardness of solving the discrete logarithms problems. In this research, a new cryptographic system is built by using the elliptic curve cryptography based on square matrices to achieve a secure communication between two parties. First, an invertible matrix is chosen arbitrarily in the the field used in the system. Then, by using the Cayley Hamilton theorem, private key matrices are generated for both parties. Next, public key vectors of the both parties are generated by using the private keys of them and arbitrary points of the given elliptic curve. Diffie Hellman protocol is used to authenticate the key exchange. ElGamal plus Menezes Qu Vanstone encryption protocols are used to encrypt the messages. MATLAB R2015a is used to implement and test the proper functioning of the built cryptosystem.

URLhttps://ieeexplore.ieee.org/document/7872847
DOI10.1109/NCTM.2017.7872847
Citation Keypriyatharsan_new_2017