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- Title
- An algebraic attack on block ciphers.
- Creator
- Matheis, Kenneth., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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The aim of this work is to investigate an algebraic attack on block ciphers called Multiple Right Hand Sides (MRHS). MRHS models a block cipher as a system of n matrix equations Si := Aix = [Li], where each Li can be expressed as a set of its columns bi1, . . . , bisi . The set of solutions Ti of Si is dened as the union of the solutions of Aix = bij , and the set of solutions of the system S1, . . . , Sn is dened as the intersection of T1, . . . , Tn. Our main contribution is a hardware...
Show moreThe aim of this work is to investigate an algebraic attack on block ciphers called Multiple Right Hand Sides (MRHS). MRHS models a block cipher as a system of n matrix equations Si := Aix = [Li], where each Li can be expressed as a set of its columns bi1, . . . , bisi . The set of solutions Ti of Si is dened as the union of the solutions of Aix = bij , and the set of solutions of the system S1, . . . , Sn is dened as the intersection of T1, . . . , Tn. Our main contribution is a hardware platform which implements a particular algorithm that solves MRHS systems (and hence block ciphers). The case is made that the platform performs several thousand orders of magnitude faster than software, it costs less than US$1,000,000, and that actual times of block cipher breakage can be calculated once it is known how the corresponding software behaves. Options in MRHS are also explored with a view to increase its efficiency.
Show less - Date Issued
- 2010
- PURL
- http://purl.flvc.org/FAU/2976444
- Subject Headings
- Ciphers, Cryptography, Data encryption (Computer science), Computer security, Coding theory, Integrated circuits, Design and construction
- Format
- Document (PDF)
- 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.
Show less - 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)
- Title
- Elliptic curves: identity-based signing and quantum arithmetic.
- Creator
- Budhathoki, Parshuram, Steinwandt, Rainer, Eisenbarth, Thomas, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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Pairing-friendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identity-based signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identity-based signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In...
Show morePairing-friendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identity-based signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identity-based signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In addition to faster signing, for batch signing the signature size can be reduced, and if multiple signatures for the same identity need to be verified, the verification can be accelerated. Neither the signing nor the verification algorithm rely on the availability of a (pseudo)random generator, and we give a provable security reduction in the random oracle model to the (`-)Strong Diffie-Hellman problem. Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor’s algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. Our Python software generates circuit descriptions that, without increasing the number of qubits or T-depth, involve less than 39% of the number of T-gates in the best previous construction. The software also optimizes the (CNOT) depth for F2-linear operations by means of suitable graph colorings.
Show less - Date Issued
- 2014
- PURL
- http://purl.flvc.org/fau/fd/FA00004182, http://purl.flvc.org/fau/fd/FA00004182
- Subject Headings
- Coding theory, Computer network protocols, Computer networks -- Security measures, Data encryption (Computer science), Mathematical physics, Number theory -- Data processing
- Format
- Document (PDF)
- Title
- Implementation and comparison of the Golay and first order Reed-Muller codes.
- Creator
- Shukina, Olga., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
In this project we perform data transmission across noisy channels and recover the message first by using the Golay code, and then by using the first-order Reed- Muller code. The main objective of this thesis is to determine which code among the above two is more efficient for text message transmission by applying the two codes to exactly the same data with the same channel error bit probabilities. We use the comparison of the error-correcting capability and the practical speed of the Golay...
Show moreIn this project we perform data transmission across noisy channels and recover the message first by using the Golay code, and then by using the first-order Reed- Muller code. The main objective of this thesis is to determine which code among the above two is more efficient for text message transmission by applying the two codes to exactly the same data with the same channel error bit probabilities. We use the comparison of the error-correcting capability and the practical speed of the Golay code and the first-order Reed-Muller code to meet our goal.
Show less - Date Issued
- 2013
- PURL
- http://purl.flvc.org/fcla/dt/3362579
- Subject Headings
- Error-correcting codes (Information theory), Coding theory, Computer algorithms, Digital modulation
- Format
- Document (PDF)
- Title
- New Results in Group Theoretic Cryptology.
- Creator
- Sramka, Michal, Florida Atlantic University, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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With the publication of Shor's quantum algorithm for solving discrete logarithms in finite cyclic groups, a need for new cryptographic primitives arose; namely, for more secure primitives that would prevail in the post-quantum era. The aim of this dissertation is to exploit some hard problems arising from group theory for use in cryptography. Over the years, there have been many such proposals. We first look at two recently proposed schemes based on some form of a generalization of the...
Show moreWith the publication of Shor's quantum algorithm for solving discrete logarithms in finite cyclic groups, a need for new cryptographic primitives arose; namely, for more secure primitives that would prevail in the post-quantum era. The aim of this dissertation is to exploit some hard problems arising from group theory for use in cryptography. Over the years, there have been many such proposals. We first look at two recently proposed schemes based on some form of a generalization of the discrete logari thm problem (DLP), identify their weaknesses, and cryptanalyze them. By applying the exper tise gained from the above cryptanalyses, we define our own generalization of the DLP to arbitrary finite groups. We show that such a definition leads to the design of signature schemes and pseudo-random number generators with provable security under a security assumption based on a group theoretic problem. In particular, our security assumption is based on the hardness of factorizing elements of the projective special linear group over a finite field in some representations. We construct a one-way function based on this group theoretic assumption and provide a security proof.
Show less - Date Issued
- 2006
- PURL
- http://purl.flvc.org/fau/fd/FA00000878
- Subject Headings
- Group theory, Mathematical statistics, Cryptography, Combinatorial designs and configurations, Data encryption (Computer science), Coding theory
- Format
- Document (PDF)
- Title
- Signature schemes in single and multi-user settings.
- Creator
- Villanyi, Viktoria., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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In the first chapters we will give a short introduction to signature schemes in single and multi-user settings. We give the definition of a signature scheme and explain a group of possible attacks on them. In Chapter 6 we give a construction which derives a subliminal-free RSA public key. In the construction we use a computationally binding and unconditionally hiding commitment scheme. To establish a subliminal-free RSA modulus n, we have to construct the secret primes p and q. To prove p and...
Show moreIn the first chapters we will give a short introduction to signature schemes in single and multi-user settings. We give the definition of a signature scheme and explain a group of possible attacks on them. In Chapter 6 we give a construction which derives a subliminal-free RSA public key. In the construction we use a computationally binding and unconditionally hiding commitment scheme. To establish a subliminal-free RSA modulus n, we have to construct the secret primes p and q. To prove p and q are primes we use Lehmann's primality test on the commitments. The chapter is based on the paper, "RSA signature schemes with subliminal-free public key" (Tatra Mountains Mathematical Publications 41 (2008)). In chapter 7 a one-time signature scheme using run-length encoding is presented, which in the random oracle model offers security against chosen-message attacks. For parameters of interest, the proposed scheme enables about 33% faster verification with a comparable signature size than a construction of Merkle and Winternitz. The public key size remains unchanged (1 hash value). The main cost for the faster verification is an increase in the time required for signing messages and for key generation. The chapter is based on the paper "A one-time signature using run-length encoding" (Information Processing Letters Vol. 108, Issue 4, (2008)).
Show less - Date Issued
- 2009
- PURL
- http://purl.flvc.org/FAU/215289
- Subject Headings
- Information technology, Security measures, Cryptography, Coding theory, Data encryption (Computer science), DIgital watermarking
- Format
- Document (PDF)