No sum (NS) sequence based post-quantum cryptography

Quantum computing is becoming a significant technology for addressing complex problems, including those in cryptography. Traditional cryptography now faces serious threats due to the rapid computational capabilities of quantum computers, highlighting the need for new quantum-resistant public-key algorithms. This paper discusses the various sequences and compares them with the no-sum sequence (NS). Also, this article presents the use (NS) sequence to improve the current widely used public and private key cryptosystem that enhances security against brute-force attacks from quantum computers and enhances them to a quantum-safe level. Lastly, we demonstrate the use of NS sequence, improving the implementation of the quantum key distribution (QKD) system and enhancing the verifiability of parties involved in key exchange. The system's effectiveness relies on the starting element of the NS sequence and the offset used to derive prime numbers. This cryptosystem demonstrates the potential of NS sequences in creating quantum-resistant cryptographic solutions.