Analysis, design and efficient implementation of next-generation cryptosystems

Recent progress on information security in post-quantum era brings five problem sets to build new generation cryptosystems. These cryptosystems can be categorized as hash-based, code-based, multivariate, lattice-based and lastly isogeny-based cryptography. These new problems come with new difficulties, such as big key sizes and domains to do calculations on it. Lattice-based cryptography is one of the next-generation cryptosystems, and because of their high performance and security claims they receive a lot of attention from academia as well as the industry. In this thesis, we focus on lattice-based cryptography and investigate their efficiency and security in three chapters. In the first chapter, Analysis, we start with definition of the lattice problems, then we discuss about algorithms that have been proposed to solve those problems. In addition to this, in this chapter, we give a reduction from the ring version of lattice problems to an easier problem, which is known as an open problem. In the Design chapter, security claims for proposed schemes are discussed and we propose a new representation to improve the efficiency, and lastly in the Implementation chapter we give information about implementing building blocks, matrix-vector multiplication and polynomial multiplication, for these cryptosystems.