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A Survey on IQ Cryptography
 In Proceedings of Public Key Cryptography and Computational Number Theory
, 2001
"... This paper gives a survey on cryptographic primitives based on class groups of imaginary quadratic orders (IQ cryptography, IQC). We present IQC versions of several well known cryptographic primitives, and we explain, why these primitives are secure if one assumes the hardness of the underlying p ..."
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This paper gives a survey on cryptographic primitives based on class groups of imaginary quadratic orders (IQ cryptography, IQC). We present IQC versions of several well known cryptographic primitives, and we explain, why these primitives are secure if one assumes the hardness of the underlying problems. We give advice on the selection of the cryptographic parameters and show the impact of this advice on the eciency of some IQ cryptosystems.
IKE Authentication Using ECDSA
, 2001
"... This document is an InternetDraft and is in full conformance with all provisions of Section 10 of RFC2026. InternetDrafts are working documents of the Internet Engineering Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as Internet ..."
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This document is an InternetDraft and is in full conformance with all provisions of Section 10 of RFC2026. InternetDrafts are working documents of the Internet Engineering Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as InternetDrafts. InternetDrafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use InternetDrafts as reference material or to cite them other than as "work in progress." The list of current InternetDrafts can be accessed at
November 2000 CSTR00017
, 2001
"... We compare the method of Weil descent for solving the ECDLP against the standard method of parallelised Pollard rho. We give details of a theoretical and practical comparison and then use this to analyse the di#culty of actually solving the ECDLP for curves of the size needed in a practical cryp ..."
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We compare the method of Weil descent for solving the ECDLP against the standard method of parallelised Pollard rho. We give details of a theoretical and practical comparison and then use this to analyse the di#culty of actually solving the ECDLP for curves of the size needed in a practical cryptographic systems. In particular we examine the elliptic curves proposed in the Oakley key determination protocol.
Compressing and Disguising Elements in Discrete Logarithm Cryptography
, 2008
"... 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 microchi ..."
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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
A comparison of different finite field . . .
 UNIVERSITY OF BRISTOL, DEPARTMENT OF COMPUTER SCIENCE
, 2000
"... We examine the relative efficiency of four methods for finite field representation in the context of elliptic curve cryptography (ECC). We conclude that a set of fields called the Optimized Extension Fields (OEFs) give greater performance, even when used with affine coordinates, when compared ag ..."
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We examine the relative efficiency of four methods for finite field representation in the context of elliptic curve cryptography (ECC). We conclude that a set of fields called the Optimized Extension Fields (OEFs) give greater performance, even when used with affine coordinates, when compared against the type of fields recommended in the emerging ECC standards. Although this performance advantage is only marginal and hence there is probably no need to change the current standards to allow OEF fields in standards compliant implementations.