The Edwards-curve Digital Signature Algorithm (EdDSA) was proposed to perform fast public-key digital signatures and thus replace the Elliptic-Curve Digital Signature Algorithm. Its key advantages over the latter include higher performance and straightforward, secure implementation for embedded devices. EdDSA algorithm is implemented over Galois Field. The operations like addition and multiplication in Galois field are different compared to normal addition and multiplication. Hence implementing EdDSA over Galois field provides more security compared to the conventional EdDSA signature. The basics of Galois Field and its application to store data is introduced. The finite field GF (pm) is an indispensable mathematical tool for some research fields such as information coding, cryptology, theory and application of network coding.