Secure Key Exchange Using Boolean algebra: A New Method Based on NP-Hard Problem
Keywords:Key exchange, Boolean algebra, NP-hard problem, Cryptography, Security, Public-key cryptography; secure communication, Man-in-the-middle attack, Private Key, Shared key
Secure key exchange is essential for maintaining the confidentiality and integrity of transmitted data in contemporary communication systems. To restrict unwanted access to the transferred keys, traditional key exchange techniques relied on computational complexity. Traditional approaches could be attacked, though, if modern computing resources become more powerful. This article suggests a novel method for secure key exchange based on NP-hardness and Boolean algebra. The method creates a public value from the private keys of two participants and other information, and each person then uses their own private key and the other public value to obtain the shared key. The fact that the private keys are not disclosed and that both users compute the secret key using their respective sets of private keys and values received from the other side makes the system resistant to man-in-the-middle attacks. The major goal of the suggested solution is to safely retrieve the same value as a shared key for both participants, even if others already know the public values. Boolean algebra and an NP-hard issue offer higher security assurances than conventional techniques that only consider computational complexity. The study uses a key size of 128 bits, which produces good results and offers higher security guarantees than conventional techniques. The study has also created a brand-new key exchange strategy that enhances current methods. Overall, this method marks a substantial advancement in the use of Boolean algebra and NP-hard issues to achieve secure key exchange.
Bellare, M., Rogaway, P., & Stepanovs, I. (2015). The universal composability (UC) security framework. Foundations and Trends® in Theoretical Computer Science, 10(1-2), 1-239.
Boneh, D., & Shoup, V. (2019). A graduate course in applied cryptography (updated version). https://toc.cryptobook.us
Boneh, D., & Shoup, V. (2015). A graduate course in applied cryptography. https://toc.cryptobook.us
Boneh, D., & Shoup, V. (2017). A graduate course in applied cryptography. https://toc.cryptobook.us
Buchmann, J. (2001). Introduction to cryptography (2nd Ed.). Springer.
Canetti, R. (2016). Universally composable security: A new paradigm for cryptographic protocols. Foundations and Trends® in Theoretical Computer Science, 10(1-2), 1-239.
Diffie, W., & Hellman, M. (1976). New directions in cryptography. IEEE Transactions on Information Theory,
Rivest, R. L., Shamir, A., & Adleman, L. M. (1978). A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21(2), 120-126.
Ferguson, N., Schneier, B., & Kohno, T. (2010). Cryptography engineering: design principles and practical applications. John Wiley & Sons.
Ferguson, N., Schneier, B., & Kohno, T. (2015). Cryptography engineering: Design principles and practical applications. Wiley.
Goldreich, O. (2017). Foundations of cryptography: Volume 2, basic applications. Cambridge University Press.
K. Ahmed, S. Pal & R. Mohan (2023) A review of the tropical approach in cryptography, Cryptologia, 47:1, 63-87, DOI:10.1080/01611194.2021.1994486.
Katz, J., & Lindell, Y. (2019). Introduction to modern cryptography (3rd Ed.). CRC Press.
Katz, J., & Lindell, Y. (2014). Introduction to modern cryptography (2nd Ed.). Chapman and Hall/CRC.
Li, R., & Zhang, K. (2019). Secure Key Exchange Protocol Based on Boolean algebra and NP-Hard Problem. In 2019 IEEE 9th Annual Computing and Communication Workshop and Conference (CCWC) (pp. 0575-0580).
Li, R., & Zhang, K. (2020). An Efficient Secure Key Exchange Scheme Based on Boolean Algebra and NP-Hard Problem. In International Conference on Computing, Networking and Communications (ICNC) (pp. 269-273).
Lindell, Y., & Katz, J. (2019). Modern cryptography, probabilistic proofs and pseudo randomness (2nd Ed.). Cambridge University Press.
Mao, W. (2003). Modern cryptography: Theory and practice. Prentice Hall.
Menezes, A. J., van Oorschot, P. C., & Vanstone, S. A. (1996). Handbook of applied cryptography. CRC press.
Paar, C., Pelzl, J., & Preneel, B. (2016). Understanding cryptography: A textbook for students and practitioners. Springer.
Paar, C., & Pelzl, J. (2010). Understanding cryptography: A textbook for students and practitioners. Springer.
Ristenpart, T., Shrimpton, T., & Shrimpton, E. (2016). Foundations of cryptography: Volume 1, basic tools. Cambridge University Press.
Rogaway, P. (2015). The science of cryptography. Cryptology ePrint Archive, Report 2015/067. http://eprint.iacr.org/2015/067.
Schneier, B. (1996). Applied cryptography: Protocols, algorithms, and source code in C (2nd Ed.). Wiley.
Singh, T., & Babu, M. S. P. (2018). Secure Key Exchange Using Boolean algebra and NP-Hard Problem. In 2018 International Conference on Computer Communication and Informatics (ICCCI) (pp. 1-5).
Singh, T., & Babu, M. S. P. (2021). Enhanced Secure Key Exchange Using Boolean algebra and NP-Hard Problem. In 2021 International Conference on Communication and Signal Processing (ICCSP) (pp. 1055-1059).
Stallings, W. (2017). Cryptography and network security: Principles and practice (7th Ed.). Pearson Education.
Stallings, W. (2013). Cryptography and network security: Principles and practice (6th Ed.). Pearson Education.
Vetrivelan, S., & Padmavathi, G. (2019). Secure Key Exchange by Using Boolean algebra and NP-Hard Problem. International Journal of Advanced Research in Computer Science, 10(1), 13-18.
Wu, T., & Chen, X. (2017). A novel public-key cryptosystem based on Boolean function. Journal of Communications, 12(3), 166-171.
Yoshi H., Rahul I., and Hanlin R. (2023), NP-Hardness of Approximating Meta-Complexity: A Cryptographic Approach, 55th Annual ACM Symposium on Theory of Computing, DOI: 10.1145/3564246.3585154.
Zeng, X., & Yu, C. (2020). Secure Key Exchange Protocol Based on Boolean algebra and NP-Hard Problem. In 2020 International Conference on Cybersecurity and Protection (ICCS&P) (pp. 1-5).
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