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An Implementation of Lattice-based Proof-of-Work on Blockchain
Krivulčík, A. ; Ricci, S.
Cryptocurrencies and blockchain are skyrocketing in recent years. They rely on Proof-of-Work (PoW) mechanisms for generating a new transaction and turn this process into ”work” (i.e., puzzles) where miners are paid for. With the advent of quantum computers, also PoW starts to migrate to post-quantum cryptographic alternatives. To the best of our knowledge, we present the first implementation of a lattice-based PoW based on the Shortest Vector Problem (SVP). By implementing in Python 3 and with the use of the NumPy library, we wrote a software that uses this concept on an artificial blockchain and demonstrates its real-world use. Even if this proposal has drawbacks on GPU optimisation and storage requirements, it shows its potential in use. The experimental results show that by balancing the size and generated range of a given matrix and vector, we can easily manipulate the time required to solve SVP challenge.
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Post Quantum Cryptography on FPGA
Gyõri, A. ; Smékal, D.
This work describes the post-quantum algorithm FrodoKEM, its hardware implementation in VHDL and software simulation of implementation. The issue of postquantum cryptography and the VHDL programming language used to describe the functionality of the hardware was studied. The acquired knowledge was transformed into a functional simulation of all parts of the algorithm. All these parts have already been implemented separately, so that the functionality of every single part can be separately approached. These parts are key generation, encapsulation and decapsulation. After successful simulation. These parts will be synthetised and implemented to FPGA board NEXYS A7.
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Modern Privacy-Preserving Cryptography Protocols
Hlučková, Pavla ; Dzurenda, Petr (referee) ; Malina, Lukáš (advisor)
This thesis examines the intersection of two modern and growing branches of cryptography, namely privacy enhancing technologies and post-quantum cryptography. It describes selected privacy enhancing schemes (PETs) and families of post-quantum cryptography. In more detail, it focuses on group signatures based on mathematical problems that are difficult or intractable for both conventional and quantum computers. Furthermore, the thesis surveys the state of the art and compares the efficiency of mentioned schemes based on available data. The main part of this thesis is an implementation of a hash-based group signature and its comparison with lattice-based and code-based group signature implementations which were obtained directly from cryptographers active in this field. The post-quantum group signatures are subsequently compared to classic group signature schemes implemented by using the libgroupsig library.
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Postquantum cryptography on FPGA
Győri, Adam ; Jedlička, Petr (referee) ; Smékal, David (advisor)
This work describes the post-quantum algorithm FrodoKEM, its hardware implementation in VHDL and software simulation of implementation, subsequent implementation of the implementation on the FPGA process system. The work describes the issue of postquantum cryptography and VHDL programming language used to describe the functionality of hardware. Furthermore, the work deals with the functional implementation and simulation of all parts of the algorithm. Specifically, these are parts, key generation, encapsulation, and decapsulation. Algorithm implementation and simulations were performed in the Vivado software simulation environment, created by Xilinx. Subsequently, the synthesis and implementation was performed and the Intellectual property block was designed, the key part of which covered the functionality of the NEXYS A7 FPGA board was not available. The last part of the work deals with the workflow algorithm for implementation on FPGA board NEXYS A7.
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Goppa codes and their applications
Kotil, Jaroslav ; Drápal, Aleš (advisor) ; Šťovíček, Jan (referee)
Title: Goppa codes and their applications Author: Bc. Jaroslav Kotil Department: Department of algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc. Abstract: In this diploma paper we introduce Goppa codes, describe their para- metres and inclusion in Alternant codes, which are residual Generalized Reed- Solomon codes, and Algebraic-geometry codes. Aftewards we demonstrate deco- ding of Goppa codes and introduce Wild Goppa codes. We also describe post- quantum cryptography member: McEliece cryptosystem for which no effective attacks with quantum computers are known. We outline a usage of this crypto- system with Goppa codes and describe the security of the cryptosystem together with possible attacks of which the most effective ones are based on information- set decoding. Keywords: Goppa codes, Generalized Reed-Solomon codes, Algebraic-geometry codes, Post-quantum cryptography, McEliece cryptosystem 1
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MQ problem
Středa, Adolf ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
The aim of this thesis is to describe a general MQ Problem with a focus on its variant called HFE, outline several attacks on a basic scheme based on HFE and describe a new attack on HFEz, a cryptosystem based on special polynomials over finite fields with a modification, which discards a portion of the output from the initial transformation. This ensures a dependency on more variables while keeping the same size of the field. The attack starts with a translation of HFE into HFE with branches, followed by a branch separating algorithm described in [Fel06]. The separation algorithm uses the public key to derive an operation, which induces (with addition) a non-associative algebra. Utilising some properties of non-associative algebras, a matrix, which can separate variables into distinct sets according to branches, is calculated. This leads to stripping off the HFEz modification and thus allowing us to attack directly the HFE polynomial. Powered by TCPDF (www.tcpdf.org)
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Post-Quantum Ciphers
Novosadová, Tatiana ; Ricci, Sara (referee) ; Hajný, Jan (advisor)
Národný inštitút pre štandardy a technológie (NIST) zahájil proces na získanie, vyhodnotenie a štandardizáciu jedného alebo viacerých kryptografických algoritmov využívajúcich verejný kľúč prostredníctvom verejnej súťaže. Cieľom tejto dimplomovej práce je naštudovať dostupné postkvantové algoritmy pre ustanovenie kľúča, ktoré boli zverejnené v treťom kole tejto súťaže. Po dôkladnej analýze a porovnaní bol jeden zo študovaných algoritmov implementovaný s využitím knižníc dostupných pre daný algoritmus, následne bol program optimalizovaný a zdokumentovaný.
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Cryptoanalysis of a Post-quantum Cryptography Algorithm
Štumpf, Daniel ; Hojsík, Michal (advisor) ; Příhoda, Pavel (referee)
National Institute of Standards and Technology (NIST) is currently running a stan- dardization process for a post-quantum cryptography primitives. Depending on the al- gorithms building blocks these primitives can be divided into five categories. In the first part of this thesis we described all five categories and compared their characteristics. The most important aspect of the schemes for NIST is security against both classical and quantum adversaries. We chose one of the five categories (namely, we picked lattice- based cryptosystems) for further cryptanalysis. As we think that the security analysis of some of the second round candidates in the NIST standardization project is not suffi- ciently well described in their specification documents and some known attacks are not considered at all, we provide a unified security analysis of these schemes. We described two currently known attacks (primal and dual attacks) against lattice-based schemes, estimated cost of these attacks against the lattice-based candidates in the second round of the NIST standardization project and compared these values with the security claimed by these candidates. In most cases our estimations matches those published in the speci- fication documents and therefore we conclude that the security estimates claimed by the candidates are...
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Securing Narrowband Wireless Communication In Licensed Band
Kolaja, David
With everlasting growth of development of devices in the Internet of Things, there is also a difficulty to keep up with the requirements of security-related topics on such devices. This is no exception for expanding the scale of Low Powered Wide Area Network (LPWAN) devices which communicate over Narrowband IoT. Such devices have constrained computing power. Thus developers of these devices are limited to use as much as possible for the implementation of functions, not having enough space for securing its communication. This article focuses on how to possibly secure these communications.
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Post-quantum cryptography on constrained devices
Matula, Lukáš ; Dzurenda, Petr (referee) ; Malina, Lukáš (advisor)
In recent years, there has been a lot of technological development, which among other things, brings the designs and implementation of quantum computing. Using Shor’s algorithm for quantum computing, it is highly likely that the mathematical problems, which underlie the cryptographic systems, will be computed in polynomial time. Therefore, it is necessary to pay attention to the development of post-quantum cryptography, which is able to secure systems against quantum attacks. This work includes the summary and the comparison of different types of post-quantum cryptography, followed by measuring and analysing its levels of difficulty in order to implement them into limited devices, such as smart cards. The measured values on the PC are used to determine the most suitable implementation on the circuit card and then the verification method itself is implemented on it.
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