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Public Key Cryptography - A Statistical Mechanics
Approach
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Introduction
Public Key Cryptography - A Statistical Mechanics Approach
An EPSRC funded project. This project is led by David Saad
working with Nikos Skantzos .
Jort van Mourik and Stephane Bounkong also contributed to some of the research
activities.The research aims at studying analytically and numerically
a new matrix-based cryptosystem. Insight gained from the analysis is
being used to devise improved constructions that will be efficient, secure
and practical.
Research Funding
EPSRC: 110,889 GBP
Duration
The project started in the February, 2001 and ended in 2003.
Project Background
The ever-increasing volume of sensitive data being transferred over the
internet requires the use of advanced public-key cryptosystems, authentication
methods and electronic signatures. Some of the leading methods suffer
from long decryption times, which indirectly reduce the cryptosystem's security
level.The new cryptosystem is based on insight gained from the analysis of
low-density parity-check codes, using methods of statistical physics.
The ciphertext is generated from modulo 2 sums of plaintext bits. These
are selected by employing two predetermined randomly constructed sparse matrices
and a single dense matrix. The generated ciphertext is then corrupted
by random flip noise of given probability. This probability, and the
choice of plaintext bits to be added, constitute the public key; the
detailed knowledge of the matrices used constitute the private key.
Decryption is carried out using methods of belief-propagation, which are
computationally economical.
Objectives
- Investigate both analytically and numerically the suggested cryptosystem
and related constructions using the methods of statistical physics.
- Exploit insight gained from the analysis for improving the current
framework, making it more appealing to practitioners.
Applet
This applet was prepared with the help of Christian
Rechberger
Further Information
We attempt to produce online versions of all relevant publications arising
from this project. You can see a list of all the available technical reports
by following the link below:
- Analysis of Common Attacks in LDPCC-Based Public-Key Cryptosystems
pdf ps
- Average and Reliability Error Exponents in Low-Density Parity-Check
Codes pdf ps
- Magnetization Enumerator of Real-Valued Symmetric Channels in Gallager
Error-Correcting Codes pdf ps
- Secure Low Density Parity Check Cryptosystem pdf ps
- Statistical Mechanics of Broadcast Channels Using Low Density ParityCheck
Codes pdf ps
- ICA for Watermarking
- Cryptographical Properties of Ising Spin Systems pdf ps
For additional papers in the areas of steganography and broadcasting please
search the NCRG archive http://www.ncrg.aston.ac.uk/Papers/index.html
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Aston University,
Aston Triangle, Birmingham B4 7ET, United Kingdom
telephone: +44 (0) 121 204 3000
- fax: +44 (0) 121 359 6350
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