Polynomial Reconstruction (PR) is a problem related to decoding Reed-Solomon codes, which has been explored for its cryptographic applications. The PR problem involves finding polynomials that fit a given set of points, and it has been studied for its computational hardness. When the number of errors (t) is large enough, PR can be solved efficiently, but for smaller t, it becomes computationally hard. This hardness has been used in cryptographic protocols, such as the McEliece cryptosystem and the OPE (Oblivious Polynomial Evaluation) protocol. The OPE protocol allows secure evaluation of a polynomial between two parties and is based on the hardness of PR. In [NP99], the PR problem was used to construct a cryptographic primitive called OPE, which enables secure computation between parties. The security of OPE is based on the assumption that the solution polynomial is pseudorandom. This assumption is stronger than average-case hardness. Further research, such as in [KY01b], investigated the cryptographic hardness of PR and introduced the Index-PR-Assumption (IPR), which states that distinguishing certain indices in a PR instance is hard. Under this assumption, PR instances are pseudorandom and conceal their solutions in a semantic level. The Multisample Polynomial Reconstruction (MPR) problem extends PR by considering multiple instances with the same index-set. MPR is also hard when the number of instances is small. Both PR and MPR have robustness properties and are sensitive to partial information extraction. These properties have been used in various cryptographic applications, including secure computation, e-commerce, and symmetric encryption. In [KY01a], PR and MPR were used to construct secure games and protocols, such as Private Information Retrieval (PIR) and secure list intersection. These protocols rely on the hardness of MPR. Additionally, PR and MPR were used in symmetric encryption to create stream/block ciphers with novel attributes, including semantic security and error-correcting decryption. Overall, the algebraic structure of PR and its variants has proven valuable in cryptography, providing a basis for advanced cryptographic primitives and secure protocols.Polynomial Reconstruction (PR) is a problem related to decoding Reed-Solomon codes, which has been explored for its cryptographic applications. The PR problem involves finding polynomials that fit a given set of points, and it has been studied for its computational hardness. When the number of errors (t) is large enough, PR can be solved efficiently, but for smaller t, it becomes computationally hard. This hardness has been used in cryptographic protocols, such as the McEliece cryptosystem and the OPE (Oblivious Polynomial Evaluation) protocol. The OPE protocol allows secure evaluation of a polynomial between two parties and is based on the hardness of PR. In [NP99], the PR problem was used to construct a cryptographic primitive called OPE, which enables secure computation between parties. The security of OPE is based on the assumption that the solution polynomial is pseudorandom. This assumption is stronger than average-case hardness. Further research, such as in [KY01b], investigated the cryptographic hardness of PR and introduced the Index-PR-Assumption (IPR), which states that distinguishing certain indices in a PR instance is hard. Under this assumption, PR instances are pseudorandom and conceal their solutions in a semantic level. The Multisample Polynomial Reconstruction (MPR) problem extends PR by considering multiple instances with the same index-set. MPR is also hard when the number of instances is small. Both PR and MPR have robustness properties and are sensitive to partial information extraction. These properties have been used in various cryptographic applications, including secure computation, e-commerce, and symmetric encryption. In [KY01a], PR and MPR were used to construct secure games and protocols, such as Private Information Retrieval (PIR) and secure list intersection. These protocols rely on the hardness of MPR. Additionally, PR and MPR were used in symmetric encryption to create stream/block ciphers with novel attributes, including semantic security and error-correcting decryption. Overall, the algebraic structure of PR and its variants has proven valuable in cryptography, providing a basis for advanced cryptographic primitives and secure protocols.