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The topic of this thesis is a cryptosystem, precisely a public key encryption scheme, that is based on the knapsack problem. At first we formulate terms like \mathcal{NP} -complete problem, one-way function, hard-core predicate, public key encryption scheme and semantic security which we connect in this thesis. After that we present the knapsack problem. Then we prove that the knapsack problem with appropriate parameters has a property that leads to semantic security of the encryption scheme which we present afterwards. This public key encryption scheme is based on the scheme proposed by Vadim Lyubashevsky, Adriana Palacio and Gil Segev. Powered by TCPDF (www.tcpdf.org)