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Isogenies and cryptography

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Isogenies and cryptography

Kazmi, Raza Ali (2008) Isogenies and cryptography. Masters thesis, Concordia University.

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Abstract

This thesis explores the notion of isogenies and its applications to cryptography. Elliptic curve cryptography (ECC) is an efficient public cryptosystem with a short key size. For this reason it is suitable for implementing on memory-constraint devices such as smart cards, mobile devices, etc. However, these devices leak information about their private key through side channels (power consumption, electromagnetic radiation, timing etc) during cryptographic processing. In this thesis we have examined countermeasures against a specific side channel attack (power consumption) using isogeny, (a rational homomorphism between elliptic curves) and elliptic curve isomorphism. We found that these methods are an efficient way of securing cryptographic devices using ECC against power analysis attacks. We have also investigated the security and efficiency of implementation of a public key cryptosystem based on isogenies. We found that in order to implement the proposed cryptosystem one has to compute a root of the Hilbert polynomial H D ( X ) over F p . Since there is no known efficient way of achieving this calculation, the proposed cryptosystem cannot be used in practice.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Computer Science and Software Engineering
Item Type:Thesis (Masters)
Authors:Kazmi, Raza Ali
Pagination:x, 90 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:M. Comp. Sc.
Program:Computer Science and Software Engineering
Date:2008
Thesis Supervisor(s):Crépeau, Claude and Ford, David
ID Code:976070
Deposited By: Concordia University Library
Deposited On:22 Jan 2013 16:19
Last Modified:18 Jan 2018 17:41
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