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

Bachelor Thesis 2014 38 Pages

Computer Science - IT-Security

Summary

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.

Details

Pages
38
Year
2014
ISBN (Book)
9783656945628
File size
1.9 MB
Language
English
Catalog Number
v295698
Grade
90.00
Tags
investigation cryptographic properties elliptic curves defined prime field

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