# A Post-Quantum Public-Key Signcryption Scheme over Scalar Integers Based on a Modified LWE Structure

## TL;DR

This paper introduces a new post-quantum cryptographic scheme that combines encryption and digital signatures using simple integer operations for better efficiency and security.

## Contribution

A novel post-quantum signcryption scheme using scalar integers instead of complex structures, improving efficiency and implementability.

## Key findings

- The scheme achieves signcryption in 0.0007 seconds and unsigncryption in 0.0011 seconds.
- It uses scalar integers modulo n, reducing computational and memory overhead.
- The design is based on modified LWE assumptions, suitable for constrained devices and quantum resistance.

## Abstract

To ensure confidentiality and integrity in the era of quantum computing, most post-quantum cryptographic schemes are designed to achieve either encryption or digital signature functionalities separately. Although a few signcryption schemes exist that combine these operations into a single, more efficient process, they typically rely on complex vector, matrix, or polynomial-based structures. In this work, a novel post-quantum public-key encryption and signature (PQES) scheme based entirely on scalar integer operations is presented. The proposed scheme employs a simplified structure where the ciphertext, keys, and core cryptographic operations are defined over scalar integers modulo n, significantly reducing computational and memory overhead. By avoiding high-dimensional lattices or ring-based constructions, the PQES approach enhances implementability on constrained devices while maintaining strong security properties. The design is inspired by modified learning-with-errors (LWE) assumptions, adapted to scalar settings, making it suitable for post-quantum applications. Security and performance evaluations, achieving a signcryption time of 0.0007 s and an unsigncryption time of 0.0011 s, demonstrate that the scheme achieves a practical balance between efficiency and resistance to quantum attacks.