Lagrange Basis Polynomial

Definition ∞ A Lagrange Basis Polynomial is a specific mathematical construct used for polynomial interpolation, where a polynomial passes through a given set of data points. In cryptographic applications, these polynomials can be used to construct verifiable secret sharing schemes or to represent data in zero-knowledge proofs. They enable the efficient evaluation and commitment to polynomial functions without revealing underlying values. This mathematical tool is fundamental to certain advanced cryptographic protocols.
Context ∞ The use of Lagrange Basis Polynomials is prominent in advanced cryptographic research, particularly within zero-knowledge proof systems and verifiable computation. Discussions concern optimizing their computational efficiency for practical blockchain applications, such as scaling solutions. Future developments aim to reduce the overhead associated with these polynomials, making them more suitable for resource-constrained environments and high-throughput systems.