Public-key cryptography and Chebyshev polynomials
| but.committee | doc. Ing. Luděk Nechvátal, Ph.D. (předseda) prof. RNDr. Josef Šlapal, CSc. (místopředseda) doc. RNDr. Jiří Tomáš, Dr. (člen) doc. Ing. Jiří Šremr, Ph.D. (člen) prof. RNDr. Miloslav Druckmüller, CSc. (člen) prof. Bruno Rubino (člen) prof. Giuli Massimiliano (člen) prof. Lattanzio Corrado (člen) | cs |
| but.defence | The student introduced his diploma thesis to the committee members and explained the fundamentals of his topic called Public-key cryptography and Chebyshev polynomials. The supervisor review and the opponent's review were read. The student answered the opponent's questions well. Slapal: What is the main contribution of your thesis? He answered in the same sense as supervisor wrote in the review. | cs |
| but.jazyk | angličtina (English) | |
| but.program | Applied and Interdisciplinary Mathematics | cs |
| but.result | práce byla úspěšně obhájena | cs |
| dc.contributor.advisor | Civino, Roberto | en |
| dc.contributor.author | Appiah, Francis | en |
| dc.contributor.referee | Kureš, Miroslav | en |
| dc.date.created | 2023 | cs |
| dc.description.abstract | Public-key encryption enables secure communication over an insecure network. In this thesis, we discuss two public key encryption schemes based on Chebyshev polynomials, which are a class of polynomials that exhibit chaotic properties suitable for cryptographic applications. We discuss that the RSA and ElGamal algorithms are secure, practical, and can be used for encryption. We extend the Chebyshev polynomials over a finite field and demonstrate that the new ElGamal-like and RSA-like algorithms are as secure as the original ElGamal and RSA algorithms. | en |
| dc.description.abstract | Public-key encryption enables secure communication over an insecure network. In this thesis, we discuss two public key encryption schemes based on Chebyshev polynomials, which are a class of polynomials that exhibit chaotic properties suitable for cryptographic applications. We discuss that the RSA and ElGamal algorithms are secure, practical, and can be used for encryption. We extend the Chebyshev polynomials over a finite field and demonstrate that the new ElGamal-like and RSA-like algorithms are as secure as the original ElGamal and RSA algorithms. | cs |
| dc.description.mark | B | cs |
| dc.identifier.citation | APPIAH, F. Public-key cryptography and Chebyshev polynomials [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2023. | cs |
| dc.identifier.other | 150327 | cs |
| dc.identifier.uri | http://hdl.handle.net/11012/212433 | |
| dc.language.iso | en | cs |
| dc.publisher | Vysoké učení technické v Brně. Fakulta strojního inženýrství | cs |
| dc.rights | Standardní licenční smlouva - přístup k plnému textu bez omezení | cs |
| dc.subject | Public key encryption | en |
| dc.subject | RSA | en |
| dc.subject | ElGamal algorithm | en |
| dc.subject | Chaotic maps | en |
| dc.subject | Chebyshev polynomials. | en |
| dc.subject | Public key encryption | cs |
| dc.subject | RSA | cs |
| dc.subject | ElGamal algorithm | cs |
| dc.subject | Chaotic maps | cs |
| dc.subject | Chebyshev polynomials. | cs |
| dc.title | Public-key cryptography and Chebyshev polynomials | en |
| dc.title.alternative | Public-key cryptography and Chebyshev polynomials | cs |
| dc.type | Text | cs |
| dc.type.driver | masterThesis | en |
| dc.type.evskp | diplomová práce | cs |
| dcterms.dateAccepted | 2023-06-14 | cs |
| dcterms.modified | 2023-06-16-09:16:17 | cs |
| eprints.affiliatedInstitution.faculty | Fakulta strojního inženýrství | cs |
| sync.item.dbid | 150327 | en |
| sync.item.dbtype | ZP | en |
| sync.item.insts | 2025.03.27 10:43:26 | en |
| sync.item.modts | 2025.01.15 15:40:23 | en |
| thesis.discipline | bez specializace | cs |
| thesis.grantor | Vysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematiky | cs |
| thesis.level | Inženýrský | cs |
| thesis.name | Ing. | cs |