Huda Naeem Hleeb Al-Jabbari

arXiv2025

Pólya-Ostrowski Group and Unit Index in Real Biquadratic Fields

The Pólya-Ostrowski group of a Galois number field $K$, is the subgroup $Po(K)$ of the ideal class group $Cl(K)$ of $K$ generated by the classes of all the strongly ambiguous ideals of $K$. The number field $K$ is called a Pólya field, whenever $Po(K)$ is trivial. In this paper, using some results of Bennett Setzer \cite{Bennett} and Zantema \cite{Zantema}, we give an explicit relation between the order of Pólya groups and the Hasse unit indices in real biquadratic fields. As an application, we refine Zantema's upper bound on the number of ramified primes in Pólya real biquadratic fields.

math.NT↗

arXiv2025

A Digital signature scheme based on Module-LWE and Module-SIS

In this paper, we present an improved version of the digital signature scheme proposed by Sharafi and Daghigh based on Module-LWE and Module-SIS problems. Our proposed signature scheme has a notably higher security level and smaller decoding failure probability, than the ones in the Sharaf-Daghigh scheme, at the expense of enlarging the module of the underlying basic ring.

cs.CR↗