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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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LWE and provably secure key exchange schemes
Václavek, Jan ; Příhoda, Pavel (advisor) ; Žemlička, Jan (referee)
The threat of large-scale quantum computers motivates cryptographers to base cryptosystems on problems believed to be resistant against quantum computers. In this thesis, we focus on the LWE problem which is believed to be resistant against quantum computers. First, we describe lattices which are closely related to the LWE problem. We introduce basic notions, describe lattice problems and solve exercises related to the covering radius of lattice. After that, we introduce the LWE problem and its variants. We prove reductions from two lattice problems to certain variant of the LWE problem. We define the notion of statistical distance and prove some lemmata about it which we need within reductions. Moreover, we show concrete application of the LWE problem. We describe a scheme for key exchange and briefly prove its security under the assumption that the LWE problem is hard. 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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