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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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Free algebraic structures and their application for segmentation of a digital image
Čambalová, Kateřina ; Solovjovs, Sergejs (referee) ; Pavlík, Jan (advisor)
The thesis covers methods for image segmentation. Fuzzy segmentation is based on the thresholding method. This is generalized to accept multiple criteria. The whole process is mathematically based on the free algebra theory. Free distributive lattice is created from poset of elements based on image properties and the lattice members are represented by terms used by the threshoding. Possible segmentation results compose the equivalence classes distribution. The thesis also contains description of resulting algorithms and methods for their optimization. Also the method of area subtracting is introduced.
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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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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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Small roots of multivariate polynomials with integral coefficients
Todorovová, Dora ; Příhoda, Pavel (advisor) ; Žemlička, Jan (referee)
This thesis focuses on the Coppersmith method for finding roots of mo- dular polynomials. The method is based on the base reduction of a lattice. Firstly, we define a lattice and show a simplified form of the LLL algorithm. Then we describe the Coppersmith method and related theorems. Further- more, we introduce a solved example from the article written by D. Boneh and G. Durfee. The general form of the method from the article written by E. Jochemsz and A. May snd we add some proofs. In the last chapter we solve examples using the method in general form. 1
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Attacks on RSA based on lattice reduction
Vaněček, Jaromír ; Příhoda, Pavel (advisor) ; Jedlička, Přemysl (referee)
This thesis aims to describe in detail the Coppersmith's algorithm for fin- ding small solutions to polynomial congruences which is based on lattice basis reduction. This algorithm is a cornerstone of several attacks on the most wi- despread asymmetric cryptosystem RSA, therefore, next aim of the thesis is a description of selected attacks. As an important and current example, we can mention so-called ROCA attack which factorizes RSA modulus whenever the pri- mes are specifically crafted. At the end of the thesis, we implement both the Coppersmith's algorithm and the ROCA and several measurements and experi- ments are done. From the resulting data, one can deduce how the running time of the algorithm is affected by different parameters or what are the ideal values for these parameters in various situations. 1
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Quantum logic and projective spaces
Peksová, Lada ; Krýsl, Svatopluk (advisor) ; Cejnar, Pavel (referee)
A set of statements about the properties of a quantum system is looked at as at a partially ordered set of subspaces of finite or infinite dimensional Hilbert space. The operation of ordering is performed on a set of propositions comparing the truth values of these propositions and on the set of subspaces as the opera- tion of inclusion. Based on the required properties these structures are translated into operations on the lattice. The correspondence with Heisenberg uncertainty principle is shown there. Furthermore, it is shown that the lattices correspond- ing to the subspaces of infinite dimensional Hilbert space are not modular. This property is replaced with weaker property of orthomodularity, when operation of the negation is added. Following the work of G. Birkhoff and J. von Neumann, the structure of quantum logic is looked for in projective spaces, which are in- troduced either arithmetically or axiomatically. The examples of quantum logic, their physical implementation and eventual implementation in projective spaces are analysed. 1
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Free algebraic structures and their application for segmentation of a digital image
Čambalová, Kateřina ; Solovjovs, Sergejs (referee) ; Pavlík, Jan (advisor)
The thesis covers methods for image segmentation. Fuzzy segmentation is based on the thresholding method. This is generalized to accept multiple criteria. The whole process is mathematically based on the free algebra theory. Free distributive lattice is created from poset of elements based on image properties and the lattice members are represented by terms used by the threshoding. Possible segmentation results compose the equivalence classes distribution. The thesis also contains description of resulting algorithms and methods for their optimization. Also the method of area subtracting is introduced.
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