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.

Cryptanalysis of the SHMW signature scheme.

In recent research, Durandal, a signature scheme based on rank metrics following Schnorr's approach, was introduced to conceal secret key information by selectively manipulating the vector subspace of signatures. Later, an enhancement, namely the SHMW signature scheme, with smaller keys and signatures while maintaining EUF-CMA security, was proposed. Both Durandal and SHMW require adversaries to solve hard problems (i.