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Digital Signature Scheme by an Elliptic Curve over a Field of Characteristic Three

COE2013-7. Digital Signature Scheme by an Elliptic Curve over a Field of Characteristic Three. Developers: Ms. Phisaknutcha Maneepradit 533040466-9 Mr. Yuthana Nanglah 533040468-5 Mentors: Assist. Prof. Bhichate Chiewthanakul Dr. Watis Leelapatra.

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Digital Signature Scheme by an Elliptic Curve over a Field of Characteristic Three

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  1. COE2013-7 Digital Signature Scheme by an Elliptic Curve over a Field of Characteristic Three Developers: Ms. Phisaknutcha Maneepradit 533040466-9 Mr. YuthanaNanglah533040468-5 Mentors: Assist. Prof. BhichateChiewthanakul Dr. WatisLeelapatra 188499 Computer EngineeringProject Dept. of Computer engineering, Faculty of Engineering, KhonKaen University

  2. Agenda

  3. Motivation

  4. Objective

  5. Relevant Theories

  6. What is RSA? • Public key cryptosystem for both encryption and authentication. • Based on the hardness of the problem of factorization.

  7. What is DSA? • DSA is a Digital Signature Algorithm. • Standard for signing the document.

  8. What is an ECC? • Standard Equation is • J. Hoffstein, J. Pipher and J. H. Silverman, An Introduction to Mathematical Cryptography,Springer-Verlag, 2004.

  9. Why ECDSA ? Prof. Bernhard Esslinger (co-author and editor) and the CrypTool Development Team, The CrypTool Script Cryptography, Mathematics and More 1998-2010.

  10. What is a digital signature? • Analogous to the purpose of a pen-and-ink signature on a physicaldocument. • Authentication • Intention to accept agreement.

  11. How does it work? Signed document Private Key (d) s(d,m) = (299044,197223) Signed Document Algorithm Electronics Document (m) Digital Signature s(d,m)

  12. How does it work? Verified Signature Public Key (e) Electronics Document (m) True, Signature Accepted Verified Signature Algorithm s(d,m) = (299044,197223) False, Signature Rejected Digital Signature s(d,m)

  13. Design • Create an Elliptic Curve. • Key creation. • Signing Digital Signature by an Elliptic Curve over a Field of Characteristic Three. • Verify Digital Signature by an Elliptic Curve over a Field of Characteristic Three.

  14. Test • Performance • Time

  15. Results • Create an Elliptic Curve.

  16. Results • Key creation. Average 0.07 s Max 0.08 s

  17. Results • Signing Digital Signature by an Elliptic Curve over a Field of Characteristic Three. Average 0.1 s Max 0.292 s

  18. Results • Verify Digital Signature by an Elliptic Curve over a Field of Characteristic Three. Average 0.146 s Max 0.148 s

  19. Test parameters

  20. Falsification • Forgery of documents • Forged signatures • Forged signatures and documents

  21. Test parameters

  22. Analysis Equations of elliptic curves and points on elliptic curves. No need to create a new page. Determining the quotient of the polynomial ring Enfield three characteristics. Users should determine the appropriate value. The digital signatures can be used with data compression to increase performance.

  23. Conclusion Algorithm designed can create a digital signature to sign electronic documents correctly. Since the generation of digital signatures make from calculation of elliptic curves inverse function is highly complex. To make highly secure digital signature.

  24. Digital Signature Scheme by an Elliptic Curve over a Field of Characteristic Three. Q & A

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