In this thesis, we address the problem of constructing efficient and secure
polynomial commitments without revealing their coefficients. The main objective
is to present a cryptographic mechanism called polynomial commitments
and to thoroughly analyze its security, efficiency, and applicability. We
focus on the KZG commitment scheme, which is based on bilinear pairings
and enables short, verifiable commitments and proofs of polynomial evaluations.
We introduce formal definitions, security assumptions, and analyze
its most important properties. The practical contribution of the thesis includes
an implementation of the KZG commitment scheme and a Verkle tree,
which represents a key component of a future upgrade to the decentralized
Ethereum system.
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