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

Area of Science:

• Cryptography
• Computer Science
• Information Security

Background:

• Current post-quantum cryptography often separates encryption and digital signatures, increasing complexity.
• Existing signcryption schemes typically use complex mathematical structures like lattices or polynomials.
• The need for efficient and implementable quantum-resistant cryptographic solutions is growing.

Purpose of the Study:

• To present a novel post-quantum public-key encryption and signature (PQES) scheme.
• To develop a scheme based solely on scalar integer operations for simplicity and efficiency.
• To enhance the implementability of quantum-resistant cryptography on constrained devices.

Main Methods:

• Developed a PQES scheme using scalar integers modulo n for keys, ciphertext, and operations.
• Adapted modified learning-with-errors (LWE) assumptions to a scalar setting.
• Evaluated security and performance, including signcryption and unsigncryption times.

Main Results:

• The proposed PQES scheme operates entirely on scalar integers, reducing computational and memory overhead.
• Achieved signcryption time of 0.0007s and unsigncryption time of 0.0011s.
• Demonstrated strong security properties resistant to quantum attacks.

Conclusions:

• The novel scalar-integer-based PQES scheme offers a practical balance between efficiency and quantum resistance.
• The simplified structure enhances implementability on resource-constrained devices.
• This approach provides a viable alternative to complex lattice-based or ring-based post-quantum cryptographic schemes.