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Centralized Group Key Establishment Protocol without a Mutually Trusted Third Party

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Abstract

The type of centralized group key establishment protocols is the most commonly used one due to its efficiency in computation and communication. A key generation center (KGC) in this type of protocols acts as a server to register users initially. Since the KGC selects a group key for group communication, all users must trust the KGC. Needing a mutually trusted KGC can cause problem in some applications. For example, users in a social network cannot trust the network server to select a group key for a secure group communication. In this paper, we remove the need of a mutually trusted KGC by assuming that each user only trusts himself. During registration, each user acts as a KGC to register other users and issue sub-shares to other users. From the secret sharing homomorphism, all sub-shares of each user can be combined into a master share. The master share enables a pairwise shared key between any pair of users. A verification of master shares enables all users to verify their master shares are generated consistently without revealing the master shares. In a group communication, the initiator can become the server to select a group key and distribute it to each other user over a pairwise shared channel. Our design is unique since the storage of each user is minimal, the verification of master shares is efficient and the group key distribution is centralized. There are public-key based group key establishment protocols without a trusted third party. However, these protocols can only establish a single group key. Our protocol is a non-public-key solution and can establish multiple group keys which is computationally efficient.

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References

  1. Diffie W, Hellman ME (1976) New directions in cryptography. IEEE Trans Inf Theory 22(6):644–654

    Article  MathSciNet  Google Scholar 

  2. Ingemarsson I, Tang DT, Wong CK (1982) A conference key distribution system. IEEE Trans Inf Theory 28(5):714–720

    Article  MathSciNet  Google Scholar 

  3. Steer DG, Strawczynski L, Diffie W, Wiener MJ (1988) A secure audio teleconference system. Proc. of Crypto ‘88, LNCS, vol. 403, pp 520–528

  4. Burmester M, Desmedt Y (1995) A secure and efficient conference key distribution system. Proc. of Eurocrypt ‘94, LNCS, vol. 950, pp 275–286

  5. Steiner M, Tsudik G, Waidner M (1996) Diffie-Hellman key distribution extended to group communication. Proc. Third ACM Conf. Computer and Comm. Security (CCS ‘96), pp 31–37

  6. Bresson E, Chevassut O, Pointcheval D, Quisquater J-J (2001) Provably authenticated group Diffie-Hellman key exchange. Proc. of ACM Conf. Computer and Comm. Security (CCS ‘01), pp 255–264

  7. Bohli JM (2006) A framework for robust group key agreement. Proc. of Int’l Conf. Computational Science and Applications (ICCSA ‘06), LNCS, vol. 3982, pp 355–364

    Chapter  Google Scholar 

  8. Harn L, Lin C (2014) Efficient group Diffie-Hellman key agreement protocols. Comput Electr Eng 40:1972–1980

    Article  Google Scholar 

  9. Wu Q, Qin B, Zhang L, Domingo-Ferrer J, Manjón JA (2013) Fast transmission to remote cooperative groups: a new key management paradigm. IEEE/ACM Trans Networking 21(2):621–633

    Article  Google Scholar 

  10. IEEE CS (2004) 802.1X, IEEE standard for local and metropolitan area networks, port-based network access control. The Inst. of Electrical and Electronics Engineers, Inc

  11. Laih C, Lee J, Harn L (1989) A new threshold scheme and its application in designing the conference key distribution cryptosystem. Inf Process Lett 32:95–99

    Article  MathSciNet  Google Scholar 

  12. Berkovits S (1991) How to broadcast a secret. Proc. of Eurocrypt ‘91, LCNS, vol. 547, pp 536–541

  13. Li CH, Pieprzyk J (1999) Conference key agreement from secret sharing. Proc. of Fourth Australasian Conf. Information Security and Privacy (ACISP ‘99), LNCS, vol. 1587, pp 64–76

    Chapter  Google Scholar 

  14. Saze G (2003) Generation of key predistribution schemes using secret sharing schemes. Discret Appl Math 128:239–249

    Article  MathSciNet  Google Scholar 

  15. Harn L, Lin C (2010) Authenticated group key transfer protocol based on secret sharing. IEEE Trans Comput 59(6):842–846

    Article  MathSciNet  Google Scholar 

  16. Bohli JM (2006) A framework for robust group key agreement. Proc. Int’l Conf. Computational Science and Applications (ICCSA ‘06), pp 355–364

    Chapter  Google Scholar 

  17. Katz J, Yung M (2007) Scalable protocols for authenticated group key exchange. J Cryptol 20:85–113

    Article  MathSciNet  Google Scholar 

  18. Chor B, Goldwasser S, Micali S, Awerbuch B (1985) Verifiable secret sharing and achieving simultaneity in the presence of faults. In Proceedings of the 26th IEEE Symposium on the Foundations of Computer Science. IEEE Press, pp 383–395

  19. Feldman P (1987) A practical scheme for non-interactive verifiable secret sharing. In Proceedings of the 28th IEEE Symposium on Foundations of Computer Science, 27–29 October, Los Angeles, IEEE Computer Society, pp 427–437

  20. Pedersen TP (1992) Non-interactive and information-theoretic secure verifiable secret sharing. In Advances in Cryptology - CRYPTO ‘91, LNCS, vol. 576, Springer-Verlag, pp129–140

  21. Benaloh JC (1987) Secret sharing homomorphisms: keeping shares of a secret secret. In Advances in Cryptology - CRYPTO ‘86, Lecture Notes in Computer Science, vol. 263, Springer-Verlag, pp 251–260

  22. Stadler M (1996) Publicly verifiable secret sharing. In Advances in Cryptology - EUROCRYPT ‘96, LNCS, vol. 1070, Springer-Verlag, pp 190–199

  23. Fujisaki E, Okamoto T (1998) A practical and provably secure scheme for publicly verifiable secret sharing and its applications. In Advances in Cryptology - EUROCRYPT ‘98, LNCS, vol. 1403, Springer-Verlag, pp 32–46

  24. Fiat A, Shamir A (1987) How to prove yourself: Practical solutions to identification and signature problems. In Advances in Cryptology - CRYPTO 1986, LNCS, vol. 263, Springer-Verlag, pp186–194

  25. Peng A, Wang L (2010) One publicly verifiable secret sharing scheme based on linear cod. In Proceeding of 2nd Conference on Environmental Science and Information Application Technology, pp 260–262

  26. Ruiz A, Villar JL (2005) Publicly verifiable secret sharing from Paillier’s cryptosystem. In Proceedings of WEWoRC ‘05, LNI P-74, pp 98–108

  27. Paillier P (1999) Public-key cryptosystems based on composite degree residuosity classes. In Advances in Cryptology - EUROCRYPT ‘99, LNCS, vol. 1592, Springer-Verlag, pp 223–238

  28. Tian Y, Peng C, Ma J (2012) Publicly verifiable secret sharing schemes using bilinear pairings. Int J Netw Secur 14(3):142–148

    Google Scholar 

  29. Wu T, Tsenga Y (2011) A pairing-based publicly verifiable secret sharing scheme. J Syst Sci Complex 24(1):186–194

    Article  MathSciNet  Google Scholar 

  30. Gennaro R, Ishai Y, Kushilevitz E, Rabin T (2001) The round complexity of verifiable secret sharing and secure multicast. STOC, pp 580–589

  31. Katz J, Koo C, Kumaresan R (2008) Improved the round complexity of VSS in point-to-point networks. Proceedings of ICALP ‘08, Part II, in: LNCS, vol. 5126, Springer, pp 499–510

  32. Kumaresan R, Patra A, Rangan CP (2010) The round complexity of verifiable secret sharing: the statistical case. Advances in Cryptology - ASIACRYPT 2010, LNCS, vol. 6477, Springer, pp 431–447

  33. Nikov V, Nikova S (2005) On proactive secret sharing schemes. LNCS, vol. 3357, Springer, pp 308–325

  34. Standard N F. Announcing the advanced encryption standard (AES)[J]. Federal Information Processing Standards Publication, 2001, 197: 1-51.

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Authors and Affiliations

  1. Department of Computer Science Electrical Engineering, University of Missouri-Kansas City, Kansas City, 64110, MO, USA

    Lein Harn

  2. Computer School, Central China Normal University, 430079, Wuhan, China

    Ching-Fang Hsu

  3. School of Optical and Electronic Information, Huazhong University of Science and Technology, 430074, Wuhan, China

    Bohan Li

Authors
  1. Lein Harn
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  2. Ching-Fang Hsu
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  3. Bohan Li
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Corresponding author

Correspondence to Ching-Fang Hsu.

Additional information

Lein Harn and ChingFang Hsu contributed equally to this work.

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Harn, L., Hsu, CF. & Li, B. Centralized Group Key Establishment Protocol without a Mutually Trusted Third Party. Mobile Netw Appl 23, 1132–1140 (2018). https://doi.org/10.1007/s11036-016-0776-7

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