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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
-
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
- Algorithms in Elliptic Curve Cryptography.
- Creator
- Hutchinson, Aaron, Karabina, Koray, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Elliptic curves have played a large role in modern cryptography. Most notably, the Elliptic Curve Digital Signature Algorithm (ECDSA) and the Elliptic Curve Di e-Hellman (ECDH) key exchange algorithm are widely used in practice today for their e ciency and small key sizes. More recently, the Supersingular Isogeny-based Di e-Hellman (SIDH) algorithm provides a method of exchanging keys which is conjectured to be secure in the post-quantum setting. For ECDSA and ECDH, e cient and secure...
Show moreElliptic curves have played a large role in modern cryptography. Most notably, the Elliptic Curve Digital Signature Algorithm (ECDSA) and the Elliptic Curve Di e-Hellman (ECDH) key exchange algorithm are widely used in practice today for their e ciency and small key sizes. More recently, the Supersingular Isogeny-based Di e-Hellman (SIDH) algorithm provides a method of exchanging keys which is conjectured to be secure in the post-quantum setting. For ECDSA and ECDH, e cient and secure algorithms for scalar multiplication of points are necessary for modern use of these protocols. Likewise, in SIDH it is necessary to be able to compute an isogeny from a given nite subgroup of an elliptic curve in a fast and secure fashion. We therefore nd strong motivation to study and improve the algorithms used in elliptic curve cryptography, and to develop new algorithms to be deployed within these protocols. In this thesis we design and develop d-MUL, a multidimensional scalar multiplication algorithm which is uniform in its operations and generalizes the well known 1-dimensional Montgomery ladder addition chain and the 2-dimensional addition chain due to Dan J. Bernstein. We analyze the construction and derive many optimizations, implement the algorithm in software, and prove many theoretical and practical results. In the nal chapter of the thesis we analyze the operations carried out in the construction of an isogeny from a given subgroup, as performed in SIDH. We detail how to e ciently make use of parallel processing when constructing this isogeny.
Show less - Date Issued
- 2018
- PURL
- http://purl.flvc.org/fau/fd/FA00013113
- Subject Headings
- Curves, Elliptic, Cryptography, Algorithms
- Format
- Document (PDF)
- Title
- ALGORITHMS IN LATTICE-BASED CRYPTANALYSIS.
- Creator
- Miller, Shaun, Bai, Shi, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
An adversary armed with a quantum computer has algorithms[66, 33, 34] at their disposal, which are capable of breaking our current methods of encryption. Even with the birth of post-quantum cryptography[52, 62, 61], some of best cryptanalytic algorithms are still quantum [45, 8]. This thesis contains several experiments on the efficacy of lattice reduction algorithms, BKZ and LLL. In particular, the difficulty of solving Learning With Errors is assessed by reducing the problem to an instance...
Show moreAn adversary armed with a quantum computer has algorithms[66, 33, 34] at their disposal, which are capable of breaking our current methods of encryption. Even with the birth of post-quantum cryptography[52, 62, 61], some of best cryptanalytic algorithms are still quantum [45, 8]. This thesis contains several experiments on the efficacy of lattice reduction algorithms, BKZ and LLL. In particular, the difficulty of solving Learning With Errors is assessed by reducing the problem to an instance of the Unique Shortest Vector Problem. The results are used to predict the behavior these algorithms may have on actual cryptographic schemes with security based on hard lattice problems. Lattice reduction algorithms require several floating-point operations including multiplication. In this thesis, I consider the resource requirements of a quantum circuit designed to simulate floating-point multiplication with high precision.
Show less - Date Issued
- 2020
- PURL
- http://purl.flvc.org/fau/fd/FA00013543
- Subject Headings
- Cryptanalysis, Cryptography, Algorithms, Lattices, Quantum computing
- Format
- Document (PDF)
- Title
- CONTRIBUTIONS TO QUANTUM-SAFE CRYPTOGRAPHY: HYBRID ENCRYPTION AND REDUCING THE T GATE COST OF AES.
- Creator
- Pham, Hai, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Quantum cryptography offers a wonderful source for current and future research. The idea started in the early 1970s, and it continues to inspire work and development toward a popular goal, large-scale communication networks with strong security guarantees, based on quantum-mechanical properties. Quantum cryptography builds on the idea of exploiting physical properties to establish secure cryptographic operations. A particular quantum-based protocol has gathered interest in recent years for...
Show moreQuantum cryptography offers a wonderful source for current and future research. The idea started in the early 1970s, and it continues to inspire work and development toward a popular goal, large-scale communication networks with strong security guarantees, based on quantum-mechanical properties. Quantum cryptography builds on the idea of exploiting physical properties to establish secure cryptographic operations. A particular quantum-based protocol has gathered interest in recent years for its use of mesoscopic coherent states. The AlphaEta protocol has been designed to exploit properties of coherent states of light to transmit data securely over an optical channel. AlphaEta aims to draw security from the uncertainty of any measurement of the transmitted coherent states due to intrinsic quantum noise. We propose a framework to combine this protocol with classical preprocessing, taking into account error-correction for the optical channel and establishing a strong provable security guarantee. Integrating a state-of-the-art solution for fast authenticated encryption is straightforward, but in this case the security analysis requires heuristic reasoning.
Show less - Date Issued
- 2019
- PURL
- http://purl.flvc.org/fau/fd/FA00013339
- Subject Headings
- Cryptography, Quantum computing, Algorithms, Mesoscopic coherent states
- Format
- Document (PDF)
- Title
- Cryptography in the presence of key-dependent messages.
- Creator
- Gonzalez, Madeline., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
The aim of this work is to investigate a security model in which we allow an adversary to have access to functions of the secret key. In recent years, significant progress has been made in understanding the security of encryption schemes in the presence of key-dependent plaintexts or messages (known as KDM). Here, we motivate and explore the security of a setting, where an adversary against a message authentication code (MAC) or signature scheme can access signatures on key-dependent messages...
Show moreThe aim of this work is to investigate a security model in which we allow an adversary to have access to functions of the secret key. In recent years, significant progress has been made in understanding the security of encryption schemes in the presence of key-dependent plaintexts or messages (known as KDM). Here, we motivate and explore the security of a setting, where an adversary against a message authentication code (MAC) or signature scheme can access signatures on key-dependent messages. We propose a way to formalize the security of message authentication schemes in the presence of key-dependent MACs (KD-EUF) and of signature schemes in the presence of key-dependent signatures (KDS). An attack on a message recognition protocol involving a MAC is presented. It turns out that the situation is quite different from key-dependent encryption: To achieve KD-EUF-security or KDS-security under non-adaptive chosen message attacks, the use of a stateful signing algorithm is inevitable even in the random oracle model. After discussing the connection between key-dependent signing and forward security, we describe a compiler which lifts any EUF-CMA secure one-time signature scheme to a forward secure signature scheme offering KDS-CMA security. Then, we discuss how aggregate signatures can be used to combine the signatures in the certificate chain used in the compiler. A natural question arises about how to combine the security definitions of KDM and KDS to come up with a signcryption scheme that is secure. We also offer a connection with Leakage-Resilient Signatures, which take into account side-channel attacks. Lastly, we present some open problems for future research.
Show less - Date Issued
- 2009
- PURL
- http://purl.flvc.org/FAU/2182087
- Subject Headings
- Cryptography, Data processing, Digital signatures, Computer security, Data encryption (Computer science), Software protection
- Format
- Document (PDF)
- Title
- The discrete logarithm problem in non-abelian groups.
- Creator
- Iliâc, Ivana., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
This dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are...
Show moreThis dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are not good candidates for cryptographic applications which rely on the hardness of the GDLP. Results are presented on generalizing existing cryptographic primitives and protocols based on the hardness of the GDLP in non-abelian groups. A special instance of a cryptographic primitive dened over the groups SL(2; 2n), the Tillich-Zemor hash function, has been cryptanalyzed. In particular, an algorithm for constructing collisions of short length for any input parameter is presented. A series of mathematical results are developed to support the algorithm and to prove existence of short collisions.
Show less - Date Issued
- 2010
- PURL
- http://purl.flvc.org/FAU/3356783
- Subject Headings
- Data encryption (Computer science), Computer security, Cryptography, Combinatorial group theory, Data processing, Mapping (Mathematics)
- Format
- Document (PDF)
- Title
- Low rank transitive representations, primitive extensions, and the collision problem in PSL (2, q).
- Creator
- Thapa Magar, Krishna B., Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Every transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then...
Show moreEvery transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then investigate the construction of rank-3 transitive and primitive extensions of a simple group, such that the extension group formed is also simple. In the latter context we present a new, group theoretic construction of the famous Hoffman-Singleton graph as a rank-3 graph.
Show less - Date Issued
- 2015
- PURL
- http://purl.flvc.org/fau/fd/FA00004471, http://purl.flvc.org/fau/fd/FA00004471
- Subject Headings
- Combinatorial designs and configurations, Cryptography, Data encryption (Computer science), Finite geometries, Finite groups, Group theory, Permutation groups
- 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
-
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
- A proposal for a binary stream cipher based on chaos theory.
- Creator
- Kanser, Heather Lianna, Florida Atlantic University, Mullin, Ronald C., Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Today new secure cryptosystems are in great demand. Computers are becoming more powerful and old cryptosystems, such as the Data Encryption Standard (DES), are becoming outdated. This thesis describes a new binary additive strewn cipher (HK cryptosystem) that is based on the logistic map. The logistic map is not random, but works under simple rules to become complex, thus making it ideal for implementation in cryptography. Instead of basing the algorithm on one logistic map, the HK...
Show moreToday new secure cryptosystems are in great demand. Computers are becoming more powerful and old cryptosystems, such as the Data Encryption Standard (DES), are becoming outdated. This thesis describes a new binary additive strewn cipher (HK cryptosystem) that is based on the logistic map. The logistic map is not random, but works under simple rules to become complex, thus making it ideal for implementation in cryptography. Instead of basing the algorithm on one logistic map, the HK cryptosystem. averages several uncoupled logistic maps. Averaging the maps increases the dimension of such a system, thus providing greater security. This thesis will explore the strengths and weaknesses of the HK cryptosystem and will end by introducing a modified version, called the HK8 cryptosystem that does not have the apparent weakness of the HK system.
Show less - Date Issued
- 2000
- PURL
- http://purl.flvc.org/fcla/dt/12685
- Subject Headings
- Chaotic behavior in systems, Computers--Access control, Cryptography
- Format
- Document (PDF)
- Title
- Quantum Circuits for Cryptanalysis.
- Creator
- Amento, Brittanney Jaclyn, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Finite elds of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these elds can have a signi cant impact on the resource requirements for quantum arithmetic. In particular, we show how the Gaussian normal basis representations and \ghost-bit basis" representations can be used to implement inverters with a quantum circuit of depth O(mlog(m)). To the best of our knowledge, this is the rst construction with...
Show moreFinite elds of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these elds can have a signi cant impact on the resource requirements for quantum arithmetic. In particular, we show how the Gaussian normal basis representations and \ghost-bit basis" representations can be used to implement inverters with a quantum circuit of depth O(mlog(m)). To the best of our knowledge, this is the rst construction with subquadratic depth reported in the literature. Our quantum circuit for the computation of multiplicative inverses is based on the Itoh-Tsujii algorithm which exploits the property that, in a normal basis representation, squaring corresponds to a permutation of the coe cients. We give resource estimates for the resulting quantum circuit for inversion over binary elds F2m based on an elementary gate set that is useful for fault-tolerant implementation. Elliptic curves over nite elds F2m play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with a ne or projective coordinates. In this thesis we show that changing the curve representation allows a substantial reduction in the number of T-gates needed to implement the curve arithmetic. As a tool, we present a quantum circuit for computing multiplicative inverses in F2m in depth O(mlogm) using a polynomial basis representation, which may be of independent interest. Finally, we change our focus from the design of circuits which aim at attacking computational assumptions on asymmetric cryptographic algorithms to the design of a circuit attacking a symmetric cryptographic algorithm. We consider a block cipher, SERPENT, and our design of a quantum circuit implementing this cipher to be used for a key attack using Grover's algorithm as in [18]. This quantum circuit is essential for understanding the complexity of Grover's algorithm.
Show less - Date Issued
- 2016
- PURL
- http://purl.flvc.org/fau/fd/FA00004662, http://purl.flvc.org/fau/fd/FA00004662
- Subject Headings
- Artificial intelligence, Computer networks, Cryptography, Data encryption (Computer science), Finite fields (Algebra), Quantum theory
- Format
- Document (PDF)
- Title
- Quantum Circuits for Symmetric Cryptanalysis.
- Creator
- Langenberg, Brandon Wade, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Quantum computers and quantum computing is a reality of the near feature. Companies such as Google and IBM have already declared they have built a quantum computer and tend to increase their size and capacity moving forward. Quantum computers have the ability to be exponentially more powerful than classical computers today. With this power modeling behavior of atoms or chemical reactions in unusual conditions, improving weather forecasts and traffic conditions become possible. Also, their...
Show moreQuantum computers and quantum computing is a reality of the near feature. Companies such as Google and IBM have already declared they have built a quantum computer and tend to increase their size and capacity moving forward. Quantum computers have the ability to be exponentially more powerful than classical computers today. With this power modeling behavior of atoms or chemical reactions in unusual conditions, improving weather forecasts and traffic conditions become possible. Also, their ability to exponentially speed up some computations makes the security of todays data and items a major concern and interest. In the area of cryptography, some encryption schemes (such as RSA) are already deemed broken by the onset of quantum computing. Some encryption algorithms have already been created to be quantum secure and still more are being created each day. While these algorithms in use today are considered quantum-safe not much is known of what a quantum attack would look like on these algorithms. Specifically, this paper discusses how many quantum bits, quantum gates and even the depth of these gates that would be needed for such an attack. The research below was completed to shed light on these areas and offer some concrete numbers of such an attack.
Show less - Date Issued
- 2018
- PURL
- http://purl.flvc.org/fau/fd/FA00013010
- Subject Headings
- Quantum computing, Cryptography, Cryptanalysis, Data encryption (Computer science), Computer algorithms
- Format
- Document (PDF)
- Title
- Quantum-Resistant Key Agreement and Key Encapsulation.
- Creator
- Robinson, Angela, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
We explore quantum-resistant key establishment and hybrid encryption. We nd that while the discrete logarithm problem is e ciently solved by a quantum computer using Shor's algorithm, some instances are insecure even using classical computers. The discrete logarithm problem based on a symmetric group Sn is e - ciently solved in polynomial time. We design a PUF-based 4-round group key establishment protocol, adjusting the model to include a physical channel capable of PUF transmission, and...
Show moreWe explore quantum-resistant key establishment and hybrid encryption. We nd that while the discrete logarithm problem is e ciently solved by a quantum computer using Shor's algorithm, some instances are insecure even using classical computers. The discrete logarithm problem based on a symmetric group Sn is e - ciently solved in polynomial time. We design a PUF-based 4-round group key establishment protocol, adjusting the model to include a physical channel capable of PUF transmission, and modify adversarial capabilities with respect to the PUFs. The result is a novel group key establishment protocol which avoids computational hardness assumptions and achieves key secrecy. We contribute a hybrid encryption scheme by combining a key encapsulation mechanism (KEM) with a symmetric key encryption scheme by using two hash functions. We require only one-way security in the quantum random oracle model (QROM) of the KEM and one-time security of the symmetric encryption scheme in the QROM. We show that this hybrid scheme is IND-CCA secure in the QROM. We rely on a powerful theorem by Unruh that provides an upper bound on indistinguishability between the output of a random oracle and a random string, when the oracle can be accessed in quantum superposition. Our result contributes to the available IND-CCA secure encryption schemes in a setting where quantum computers are under adversarial control. Finally, we develop a framework and describe biometric visual cryptographic schemes generically under our framework. We formalize several security notions and de nitions including sheet indistinguishability, perfect indistinguishability, index recovery, perfect index privacy, and perfect resistance against false authentication. We also propose new and generic strategies for attacking e-BVC schemes such as new distinguishing attack, new index recovery, and new authentication attack. Our quantitative analysis veri es the practical impact of our framework and o ers concrete upper bounds on the security of e-BVC.
Show less - Date Issued
- 2018
- PURL
- http://purl.flvc.org/fau/fd/FA00013023
- Subject Headings
- Quantum computing, Data encryption (Computer science), Cryptography
- Format
- Document (PDF)
- Title
- SELECTED TOPICS IN QUANTUM AND POST-QUANTUM CRYPTOGRAPHY.
- Creator
- Johnson, Floyd, Bai, Shi, Steinwandt, Rainer, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
In 1994 when Peter Shor released his namesake algorithm for factoring and solving the discrete logarithm problem he changed cryptography forever. Many of the state-of-the-art cryptosystems for internet and other computerized communications will become obsolete with the advent of quantum computers. Two distinct approaches have grown to avoid the downfall of secure communication: quantum cryptography which is based in physics and information theory, and post-quantum cryptography which uses...
Show moreIn 1994 when Peter Shor released his namesake algorithm for factoring and solving the discrete logarithm problem he changed cryptography forever. Many of the state-of-the-art cryptosystems for internet and other computerized communications will become obsolete with the advent of quantum computers. Two distinct approaches have grown to avoid the downfall of secure communication: quantum cryptography which is based in physics and information theory, and post-quantum cryptography which uses mathematical foundations believed not to be weak against even quantum assisted adversaries. This thesis is the culmination of several studies involving cryptanalysis of schemes in both the quantum and post-quantum paradigms as well as mathematically founded constructions in the post-quantum regime. The first two chapters of this thesis on background information are intended for the reader to more fully grasp the later chapters. The third chapter shows an attack and ultimate futility of a variety of related quantum authentication schemes. The fourth chapter shows a parametric improvement over other state-of-the-art schemes in lattice based cryptography by utilizing a different cryptographic primitive. The fifth chapter proposes an attack on specific parameters of a specific lattice-based cryptographic primitive. Finally, chapter six presents a construction for a fully homomorphic encryption scheme adapted to allow for privacy enhanced machine learning.
Show less - Date Issued
- 2022
- PURL
- http://purl.flvc.org/fau/fd/FA00014088
- Subject Headings
- Quantum cryptography, Cryptography, Homomorphisms (Mathematics), Lattices (Mathematics)
- 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
-
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)