Pseidogadījumu virkņu izveide ar lineāro nobīdes reģistru un to dešifrēšana
Date
2021
Authors
Lielbārdis, Artūrs
Journal Title
Journal ISSN
Volume Title
Publisher
Latvijas Universitāte
Abstract
Darbā tiek apskatītas lineāro nobīdes reģistru veidotās virknes un to nejaušība. Šo virkņu nejaušība tiek pārbaudīta ar trīs Golomba postulātiem un statistiskajiem biežuma testiem: testu ar monobitu metodi un testu bloku ietvaros. Tiek izskaidrots, kā teksts tiek pārveidots binārajā kodā un aizšifrēts ar iegūtajām lineāri rekurentajām virknēm, kas pēc tam tiek dešifrēts ar vienādojumu sistēmu vai Berlekampa-Masseja algoritmu. Praktiskajā daļā tiek apskatīts pseidogadījumu virkņu veidošana dažādos garumos, to uzlaušanas un raksturīgo polinomu atrašanas laikietilpīgums.
This thesis looks at number sequences generated by linear-feedback shift registers and their randomness. This randomness is verified using Golomb's postulates and frequency tests: frequency (monobit) test and frequency test within a block. It is explained how text is converted to binary code and encrypted with linear recurrent sequences, and how the cipher text can be deciphered by solving a system of linear equations or by using Berlekamp-Massey algorithm. There is also a practical investigation in the generation of pseudorandom number sequences of different lengths, and the time it takes to decipher them and find their corresponding polynomials.
This thesis looks at number sequences generated by linear-feedback shift registers and their randomness. This randomness is verified using Golomb's postulates and frequency tests: frequency (monobit) test and frequency test within a block. It is explained how text is converted to binary code and encrypted with linear recurrent sequences, and how the cipher text can be deciphered by solving a system of linear equations or by using Berlekamp-Massey algorithm. There is also a practical investigation in the generation of pseudorandom number sequences of different lengths, and the time it takes to decipher them and find their corresponding polynomials.
Description
Keywords
Matemātika , Lineārais nobīdes reģistrs , A5/1 , Golomba postulāti , pseidogadījumu virkņu statistiskie testi , Berlekampa-Masseja algoritms