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Investigation into the Cryptographic Properties of Elliptic Curves Defined over a Prime Field by Adrian O'Gara

Investigation into the Cryptographic Properties of Elliptic Curves Defined over a Prime Field

by Adrian O'Gara
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Book cover type: Paperback
  • ISBN13: 9783656945628
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 44
  • Original Price: USD 25.5
  • Language: English
  • Edition: N/A
  • Item Weight: 68 grams
  • BISAC Subject(s): Networking / General and Security / General

Bachelor Thesis from the year 2014 in the subject Computer Science - IT-Security, grade: 90.00, course: Computer Security & Digital Forensics, language: English, abstract: Elliptic curves, as used in cryptography, are essentially points bounded by a finite prime field which display group properties that facilitate their usage in a cryptosystem. The Discrete Log Problem (DLP) - based on a large prime order subgroup of (Zp)* - constitutes the essence of Elliptic Curve Cryptography (ECC) and can be summed up as such; find an integer, k, such that Q = kP where k = logp(Q) and P, Q ∈ (Zp)*. Compared to the Integer Factorisation Problem - upon which RSA is constructed - the DLP achieves a greater level of complexity in terms of resistance to attack. This project seeks to describe the mathematical properties that enable ECC to outperform RSA, culminating in the construction of a software system to demonstrate ECC's ability to securely encipher and decipher files and text, according to the National Security Agency's (NSA) Cryptographic Interoperability Strategy (CIS) or Suite B Cryptography.

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