A failure in decryption process for bivariate polynomial reconstruction problem cryptosystem.

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.

Enhancing Chaos Complexity of a Plasma Model through Power Input with Desirable Random Features.

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.