## Compressing and Disguising Elements in Discrete Logarithm Cryptography (2008)

### BibTeX

@MISC{Nicholas08compressingand,

author = {Philip Nicholas and James Eagle},

title = {Compressing and Disguising Elements in Discrete Logarithm Cryptography},

year = {2008}

}

### OpenURL

### Abstract

In the modern world, the ubiquity of digital communication is driven by the constantly evolving world of cryptography. Consequently one must efficiently implement asymmetric cryptography in environments which have limited resources at their disposal, such as smart–cards, ID cards, vehicular microchips and many more. It is the primary purpose of this thesis to investigate methods for reducing the bandwidth required by these devices. Part I of this thesis considers compression techniques for elliptic curve cryptography (ECC). We begin this by analysing how much data is actually required to establish domain parameters for ECC. Following the widely used cryptographic standards (for example: SEC 1), we show that naïvely implemented systems use extensively more data than is actually required and suggest a flexible and compact way to better implement these. This is especially of use in a multi–curve environment. We then investigate methods for reducing the inherent redundancy in the point representation of Koblitz systems; a by–product of the best known Pollard–ρ based attacks by Wiener & Zuccherato and Gallant, Lambert & Vanstone. We present methods which allow such systems to operate (with a high confidence) as efficiently as generic ones whilst maintaining all of their com-