ECvisual: a visualization tool for elliptic curve based ciphers

Authors:
Jun Tao;Jun Ma;Melissa Keranen;Jean Mayo;Ching-Kuang Shene
Affiliations:
Michigan Technological University, Houghton, MI, USA;Michigan Technological University, Houghton, MI, USA;Michigan Technological University, Houghton, MI, USA;Michigan Technological University, Houghton, MI, USA;Michigan Technological University, Houghton, MI, USA
Venue:
Proceedings of the 43rd ACM technical symposium on Computer Science Education
Year:
2012

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Abstract

This paper describes a visualization tool ECvisual that helps students understand and instructors teach elliptic curve based ciphers. This tool permits the user to visualize elliptic curves over the real field and over a finite field of prime order, perform arithmetic operations, do encryption and decryption, and convert plaintext to a point on an elliptic curve. The demo mode of ECvisual can be used for classroom presentation and self-study. With the practice mode, the user may go through steps in finite field computations, encryption, decryption and plaintext conversion. The user may compute the output for each operation check each answer for correctness. This helps students understand the primitive operations and how they are used in an elliptic curve cipher. The opportunity for self-study provides an instructor greater flexibility in selecting a lecture pace for this detail-filled material. Classroom evaluation was positive and very encouraging.