Binary extension and prime field-based elliptic curves are used in Elliptic curve cryptography (ECC). From the performance point of view, ECC using Binary field are faster and easy to compute on hardware platforms than the prime field. However, ECC using prime field is in use extensively and many standards and many new elliptic curves are in place. Why is that? Does ECC over the prime field more secure than the binary field or for any other pertinent reasons?
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