The BSS model and cryptography
BSS model a kryptografie
diploma thesis (DEFENDED)
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http://hdl.handle.net/20.500.11956/78017Identifiers
Study Information System: 149763
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- Kvalifikační práce [10690]
Author
Advisor
Referee
Thapen, Neil
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Mathematical methods of information security
Department
Department of Algebra
Date of defense
16. 6. 2016
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
English
Grade
Excellent
Keywords (Czech)
počítání s reálnými čísly, BSS stroj, vyčíslitelná funkce, těžko invertovatelná funkceKeywords (English)
real computation, BSS machine, computable function, hard to invert functionReal numbers are usually represented by various discrete objects such as floating points or partial decimal expansions. This is mainly because the clas- sical computability theory relates to computers which work with discrete data. Nevertheless, for theoretical purposes it is interesting to look at models of com- putation that deal with real numbers as with objects of unit size. A very natural such model was suggested by Blum, Shub and Smale in 1989. In 2012 Grigoriev and Nikolenko studied various cryptographic tasks involv- ing real numbers (for example, biometric authentication) and they considered the BSS machine model. In this work we focus on hard to invert functions in this model of computation. Our main theme is to analyse whether there are real functions of one variable that are easier to compute than to invert by a BSS machine. 1