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Distinguishability of Public Keys and Experimental Validation: The McEliece Public-Keyed Cryptosystem
Title
Distinguishability of Public Keys and Experimental Validation: The McEliece Public-Keyed Cryptosystem.
Creator
Pham, Hai, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
As quantum computers continue to develop, they pose a threat to cryptography since many popular cryptosystems will be rendered vulnerable. This is because the security of most currently used asymmetric systems requires the computational hardness of the integer factorization problem, the discrete logarithm or the elliptic curve discrete logarithm problem. However, there are still some cryptosystems that resist quantum computing. We will look at code-based cryptography in general and the...
Show moreAs quantum computers continue to develop, they pose a threat to cryptography since many popular cryptosystems will be rendered vulnerable. This is because the security of most currently used asymmetric systems requires the computational hardness of the integer factorization problem, the discrete logarithm or the elliptic curve discrete logarithm problem. However, there are still some cryptosystems that resist quantum computing. We will look at code-based cryptography in general and the McEliece cryptosystem specifically. Our goal is to understand the structure behind the McEliece scheme, including the encryption and decryption processes, and what some advantages and disadvantages are that the system has to offer. In addition, using the results from Courtois, Finiasz, and Sendrier's paper in 2001, we will discuss a digital signature scheme based on the McEliece cryptosystem. We analyze one classical algebraic attack against the security analysis of the system based on the distinguishing problem whether the public key of the McEliece scheme is generated from a generating matrix of a binary Goppa code or a random binary matrix. The idea of the attack involves solving an algebraic system of equations and we examine the dimension of the solution space of the linearized system of equations. With the assistance from a paper in 2010 by Faugere, Gauthier-Umana, Otmani, Perret, Tillich, we will see the parameters needed for the intractability of the distinguishing problem.
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Date Issued
2015
PURL
http://purl.flvc.org/fau/fd/FA00004535, http://purl.flvc.org/fau/fd/FA00004535
Subject Headings
Coding theory, Combinatorial analysis, Data encryption (Computer science), Data transmission systems -- Security measures, Information theory, McEliece, Robert J. -- Influence, Public key cryptography
Format
Document (PDF)
A Study on Partially Homomorphic Encryption Schemes
Title
A Study on Partially Homomorphic Encryption Schemes.
Creator
Mithila, Shifat P., Karabina, Koray, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
High processing time and implementation complexity of the fully homomorphic encryption schemes intrigued cryptographers to extend partially homomorphic encryption schemes to allow homomorphic computation for larger classes of polynomials. In this thesis, we study several public key and partially homomorphic schemes and discuss a recent technique for boosting linearly homomorphic encryption schemes. Further, we implement this boosting technique on CGS linearly homomorphic encryption scheme to...
Show moreHigh processing time and implementation complexity of the fully homomorphic encryption schemes intrigued cryptographers to extend partially homomorphic encryption schemes to allow homomorphic computation for larger classes of polynomials. In this thesis, we study several public key and partially homomorphic schemes and discuss a recent technique for boosting linearly homomorphic encryption schemes. Further, we implement this boosting technique on CGS linearly homomorphic encryption scheme to allow one single multiplication as well as arbitrary number of additions on encrypted plaintexts. We provide MAGMA source codes for the implementation of the CGS scheme along with the boosted CGS scheme.
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Date Issued
2017
PURL
http://purl.flvc.org/fau/fd/FA00004840, http://purl.flvc.org/fau/fd/FA00004840
Subject Headings
Computer networks--Security measures., Computer security., Computers--Access control--Code words., Cyberinfrastructure., Computer network architectures., Cryptography., Number theory--Data processing.
Format
Document (PDF)
Energy cost evaluation of a secure 802.11 wireless transmission using NS-2
Title
Energy cost evaluation of a secure 802.11 wireless transmission using NS-2.
Creator
Martins, Joao Marcelo Galindo., Florida Atlantic University, Mahgoub, Imad, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
Mobile devices capable of transmitting and receiving data over an 802.11 network have become very common gadgets in our society. Most small mobile devices available in the market today come with integrated 802.11 radio. The extraordinary growth of this technology has also introduced several worries regarding the vulnerabilities that exist by transmitting data over the air. In order to minimize such problems, encryption algorithms were added as an option to be used with 802.11. Unfortunately,...
Show moreMobile devices capable of transmitting and receiving data over an 802.11 network have become very common gadgets in our society. Most small mobile devices available in the market today come with integrated 802.11 radio. The extraordinary growth of this technology has also introduced several worries regarding the vulnerabilities that exist by transmitting data over the air. In order to minimize such problems, encryption algorithms were added as an option to be used with 802.11. Unfortunately, the usage of encryption algorithms also causes a faster depletion of the energy resources available to a mobile device. Depending on the encryption algorithm implementation, a greater number of packets may be required in order to transmit the same amount of data that would be transmitted with less packets over a non-encrypted channel. The objective of this research is to analyze and evaluate the affects that the encryption algorithms used by wireless security protocols can have during data transmission over a wireless medium.
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Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/13292
Subject Headings
Wireless communication systems--Security measurer--Evaluation, Coding theory--Evaluation, Computer architecture--Standards--Evaluation, IEEE 80211 (Standard), Mobile communication systems--Power supply--Evaluation
Format
Document (PDF)

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