alexa Cryptographic Schemes Based on Elliptic Curves over the Ring Zp[i]

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Cryptographic Schemes Based on Elliptic Curves over the Ring Zp[i]

Elliptic Curve Cryptography recently gained a lot of attention in industry. The principal attraction of ECC compared to RSA is that it offers equal security for a smaller key size. The present paper includes the study of two elliptic curve Ea,b and Ea,-b defined over the ring Zp[i] where i2 = -1. After showing isomorphism between Ea,b and Ea,-b. We define a composition operation (in the form of a mapping) on their union set.

 
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