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Distinguishability of Public Keys and Experimental Validation: The McEliece Public-Keyed Cryptosystem

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Date Issued:
2015
Summary:
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 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.
Title: Distinguishability of Public Keys and Experimental Validation: The McEliece Public-Keyed Cryptosystem.
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Name(s): Pham, Hai, author
Steinwandt, Rainer, Thesis advisor
Florida Atlantic University, Degree grantor
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2015
Date Issued: 2015
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 45 p.
Language(s): English
Summary: 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 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.
Identifier: FA00004535 (IID)
Degree granted: Thesis (M.S.)--Florida Atlantic University, 2015.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Coding theory
Combinatorial analysis
Data encryption (Computer science)
Data transmission systems -- Security measures
Information theory
McEliece, Robert J. -- Influence
Public key cryptography
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Links: http://purl.flvc.org/fau/fd/FA00004535
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00004535
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.