The Polynomial Reconstruction Problem (PRP) was introduced in 1999 as a new hard problem in post-quantum cryptography. Augot and Finiasz were the first to design a cryptographic system based on a univariate PRP, which was published at Eurocrypt 2003 and was broken in 2004. In 2013, a bivariate PRP was proposed. The design is a modified version of Augot and Finiasz’s design. Our strategic method, comprising the modified Berlekamp–Welch algorithm and Coron strategies, allowed us to obtain certain secret parameters of the bivariate PRP. This finding resulted in us concluding that the bivariate PRP is not secure against Indistinguishable Chosen-Plaintext Attack (IND-CPA).

Carreau fluidis a type generalised fluid where viscosity depends upon the shear rate of the fluid and thenuses it to obtain a formulation for the boundary layer equations of the Carreau fluidThe objective of the present study is to analyze the development of the slip effect on the MHD stagnation-point flow of Carreau fluid past a shrinking sheet. The mathematical modeling of Carreau fluid has been developed for boundary layer problem and the governing partial differential equations are transformed into ordinary differential equation using self-similarity transformation. The effect of velocity slip is taken into account and controlled by non-dimensional parameter. The dual solutions are obtained when the sheet is shrunk. The study shows that the skin friction decreases with an increase in velocity slip.

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.