An Explicit Construction of Orthogonal Basis in $p$-adic Fields

TL;DR

This paper presents a method to construct orthogonal bases in $p$-adic fields with large residue degree, aiming to improve the security of $p$-adic cryptographic schemes by addressing vulnerabilities related to ramified extension fields.

Contribution

The paper introduces a novel explicit construction of orthogonal bases in $p$-adic fields with large residue degree, enhancing cryptographic scheme security.

Findings

Constructed orthogonal bases in $p$-adic fields with large residue degree

Potential to modify $p$-adic cryptosystems for better security

Addresses vulnerabilities due to ramification in extension fields

Abstract

In 2021, the $p$-adic signature scheme and public-key encryption cryptosystem were introduced. These schemes have good efficiency but are shown to be not secure. The attack succeeds because the extension fields used in these schemes are totally ramified. In order to avoid this attack, the extension field should have a large residue degree. In this paper, we propose a method of constructing a kind of specific orthogonal basis in $p$-adic fields with a large residue degree, which would be helpful to modify the $p$-adic signature scheme and public-key encryption cryptosystem.