Elliptic Curve Cryptography Lab Report

Multi-keyed algorithm of Elliptic Curve Cryptography L.K. Suresh Kumar, Supriya Akkirala, Saritha Ramavath, Poonam Loya

Department of Computer Science and Engineering, University College of Engineering,

Osmania University, Hyderabad.

Email: suresh.lokhande, poonamloya0414, supriyaakkirala03,saritharathod311 {@gmail.com}

Abstract — Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC requires smaller keys compared to non-ECC cryptography (based on plain Galo fields) to provide equivalent security. The major advantage of elliptic curve cryptography is that it offers equal security for a smaller key-size when compared to its

Thus this curve is symmetric about the x-axis. Key Generation by Key size

PROPOSED METHOD Let the communicating parties be called Alice and Bob.They agree upon an elliptic curve Ep(a,b) where p is a prime number and a,b are curve parameters. Next they choose a point G on the curve which is usually the generating point of the curve. Communication between Alice and Bob begins with exchange of keys. Alice selects a large random number nA which is less than the order of the curve Ep(a,b) and any two points P , Q on the curve. nA , P , Q being her private keys she computes her public keys A1 , A2 , A3 . Similarly Bob also selects a large random number nB less than the order of the curve and any two points R , S on the curve. Stating nB , R , S private Bob computes his public keys B1 , B2 , B3 . After calculating their public keys , they both compute specific public keys AB , BA for each other. Alice calculates AB for Bob and Bob calculates BA for Alice. The above computations takes place as shown below

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