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Finite Field Arithmetic Comparison over GF (p) and GF (2m)

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Abstract:
Due to the increase in the use of internet over the shared system, cryptography plays an important role in securing the information. Secure data transfer over the internet requires public key cryptosystem where it uses a secret key during the encryption of data. The two mostly secured public key cryptosystems are RSA and ECC. The advantage which is offered by Elliptic curve cryptosystem (ECC) is more security per key bit. The finite field arithmetic over the Galois field includes modular addition, subtraction multiplication, inversion and division. This paper compares the finite arithmetic architecture (modular inversion) of GF(p) and GF(2m) and focus at the FPGA implementation.
Keywords:GF(p) and GF(2m) Arithmetic Operations, Elliptic Curve Cryptography.

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