Public-key cryptography and Chebyshev polynomials
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Date
Authors
Appiah, Francis
Advisor
Referee
Mark
B
Journal Title
Journal ISSN
Volume Title
Publisher
Vysoké učení technické v Brně. Fakulta strojního inženýrství
ORCID
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.
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.
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.
Description
Citation
APPIAH, F. Public-key cryptography and Chebyshev polynomials [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2023.
Document type
Document version
Date of access to the full text
Language of document
en
Study field
bez specializace
Comittee
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)
Date of acceptance
2023-06-14
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.
Result of defence
práce byla úspěšně obhájena