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Key dependent message security
Hostáková, Kristina ; Hojsík, Michal (advisor) ; Kazda, Alexandr (referee)
In this work, we deal with cryptosystems which are provably secure even if we encrypt a key-dependent message. These cryptosystems are called KDM-secure. First, we define KDM-security and discuss its relationship with other kinds of security, especially IND-CPA-security. Thereafter, we construct the public- key and the symmetric-key encryption scheme of Applebaum et al. (CRYPTO 2009) and we prove KDM-security of these cryprosystems with respect to the set of affine functions. The security of our cryptosystems is based on the LWE problem and the LPN problem as its special case. We study these problems and their variants. Moreover, we give a brief introduction to lattices and hard lattice problems because there exist reductions from hard lattice problems to LWE. 1
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The BSS model and cryptography
Hostáková, Kristina ; Krajíček, Jan (advisor) ; Thapen, Neil (referee)
Real 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
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Key dependent message security
Hostáková, Kristina ; Hojsík, Michal (advisor) ; Kazda, Alexandr (referee)
In this work, we deal with cryptosystems which are provably secure even if we encrypt a key-dependent message. These cryptosystems are called KDM-secure. First, we define KDM-security and discuss its relationship with other kinds of security, especially IND-CPA-security. Thereafter, we construct the public- key and the symmetric-key encryption scheme of Applebaum et al. (CRYPTO 2009) and we prove KDM-security of these cryprosystems with respect to the set of affine functions. The security of our cryptosystems is based on the LWE problem and the LPN problem as its special case. We study these problems and their variants. Moreover, we give a brief introduction to lattices and hard lattice problems because there exist reductions from hard lattice problems to LWE. 1
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