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Software Implementations and Applications of Elliptic Curve Cryptography

Kultinov, Kirill
http://rave.ohiolink.edu/etdc/view?acc_num=wright1559232475298514

Abstract Details

2019, Master of Science in Cyber Security (M.S.C.S.), Wright State University, Computer Science.
Elliptic Curve Cryptography (ECC) is a public-key cryptography system. Elliptic Curve Cryptography (ECC) can achieve the same level of security as the public-key cryptography system, RSA, with a much smaller key size. It is a promising public key cryptography system with regard to time efficiency and resource utilization. This thesis focuses on the software implementations of ECC over finite field GF(p) with two distinct implementations of the Big Integer classes using character arrays, and bit sets in C++ programming language. Our implementation works on the ECC curves of the form y^2 = x^3 + ax + b (mod p). The point addition operation and the scalar multiplication are implemented on a real SEC (Standards for Efficient Cryptography) ECC curve over a prime field with two different implementations. The Elliptic Curve Diffie-Hellman key exchange, the ElGamal encryption/decryption system, and the Elliptic Curve Digital Signature Algorithm (ECDSA) on a real SEC ECC curve with two different implementations of the big integer classes are tested, and validated. The performances of the two different implementations are compared and analyzed.
Meilin Liu, Ph.D. (Advisor)
Junjie Zhang, Ph.D. (Committee Member)
Keke Chen, Ph.D. (Committee Member)
88 p.
Computer Science; Information Technology
Elliptic Curve Cryptography; ECC; software implementation of ECC; ECC over finite fields; ECDH; ECDSA; ECC ElGamal; ECC applications

Recommended Citations

Citations

  • Kultinov, K. (2019). Software Implementations and Applications of Elliptic Curve Cryptography [Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1559232475298514

    APA Style (7th edition)

  • Kultinov, Kirill. Software Implementations and Applications of Elliptic Curve Cryptography. 2019. Wright State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright1559232475298514.

    MLA Style (8th edition)

  • Kultinov, Kirill. "Software Implementations and Applications of Elliptic Curve Cryptography." Master's thesis, Wright State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=wright1559232475298514

    Chicago Manual of Style (17th edition)

wright1559232475298514
677
© 2019, all rights reserved.
This open access ETD is published by Wright State University and OhioLINK.