A failure in decryption process for bivariate polynomial reconstruction problem cryptosystem - Yusof, Siti Nabilah; Kamel Ariffin, Muhammad Rezal; Yip, Sook-Chin; Lau, Terry Shue Chien; Mahad, Zahari; Chin, Ji-Jian; Ting, Choo-Yee (Elsevier Ltd, 2024)
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.