The development and growth of Internet technology has made digital signature in the convenient and helpful manner for electronic transaction security and business applications. Digital signature is largely used because of its data integrity, protecting the data, privacy and authenticity assets. Digital signatures are mostly used in financial transaction, credential identify and software distribution, where it is indispensable to detect forgery or tampering of data. Digital signatures based on elliptic curves are more secure, reliable and suitable for constrained environments like wireless sensor networks because of its reduced processing overhead. This paper discusses the principles of Digital Signatures, their applications based on Elliptic Curve Digital Signature (ECDSA) scheme using asymmetrical cryptography along with Galois Field. Finally, a practical elliptic curve digital signature system using Galois Field is implemented and its time complexity is analyzed. The time complexity results validation claim that the proposed ECDSA is suitable for use in real time environments like WSN and smart cards. The proposed technique is based on mathematical model used in ECC with Galois Field along with the secure hash function. Programming language Python is used to realize the algorithm used.

Digital Signatures, DSA, ECC, Galois Field, ECDSA, Encryption using asymmetric cryptography, Hash Functions, SHA 512

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