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  1. Yusof SN, Kamel Ariffin MR, Yip SC, Lau TSC, Mahad Z, Chin JJ, et al.
    Heliyon, 2024 Feb 29;10(4):e25470.
    PMID: 38370193 DOI: 10.1016/j.heliyon.2024.e25470
    In 1999, the Polynomial Reconstruction Problem (PRP) was put forward as a new hard mathematics problem. A univariate PRP scheme by Augot and Finiasz was introduced at Eurocrypt in 2003, and this cryptosystem was fully cryptanalyzed in 2004. In 2013, a bivariate PRP cryptosystem was developed, which is a modified version of Augot and Finiasz's original work. This study describes a decryption failure that can occur in both cryptosystems. We demonstrate that when the error has a weight greater than the number of monomials in a secret polynomial, p, decryption failure can occur. The result of this study also determines the upper bound that should be applied to avoid decryption failure.
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