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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
CRC-codes
 Lorenc, Filip ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
This thesis deals with description of CRC codes, which is a type of polynomial error correction codes, and description of CAN and CAN FD protocols used in automobiles for data transmission between sensors. One of the security elements is usage of the CRC codes with the Hamming distance 6. Unfortunately, both protocols contain a design vulnerability which causes that some received messages with one wrong bit do not have to be detected by the protocol. The aim of the thesis was to describe this vulnerability and found out, if it was possible to eliminate it by using different CRC code. It managed to characterize all messages, which are not during this vulnerability detected by CRC code and based on that it was possible to prove, that the probability of error does not depend on a CRC code choice of a fixed length. 1
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Algorithms for factorization of integers of particular form
 Lorenc, Filip ; Příhoda, Pavel (advisor) ; Růžička, Pavel (referee)
This bachelor thesis deals with three factorization algorithms - Pollard p-1 method, Williams p+1 method and elliptic curve method ECM. This work aims to describe these algorithms theoretically and then compare them on real inputs. For each algorithm we describe its basic and extended version and then we derive their time complexity. In the first chapter we define B-powersmooth and B-smooth number and we state their approximation. The second, third and fourth chapter is about description of algorithms and in the last chapter we compare their effectiveness and performance. A part of the work contains basic theory about elliptic curves, which is necessary in ECM. There is also included a program containing all these algorithms.
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