Abstract
Wireless sensor networks consist of a huge number of small nodes, communicating wirelessly, to transmit any sort of measured data, like temperature, radiation, etc. At the air interface, unprotected messages can be easily intercepted and modified by an attacker. Traditionally, symmetric cryptography is deployed in sensor networks, due to the nodes being constrained in terms of energy, processing power and memory. If an attacker is now able to extract the secret symmetric key from a single node, the entire (or a huge subset of the) network is compromised. Threshold cryptography is an attractive approach to this problem: by separating the secret into several parts, an attacker has to compromise at least t + 1 nodes to be able to extract a meaningful value. In this work we investigate computational optimizations to the multiparty multiplication protocol of Gennaro, Rabin, and Rabin, thereby improving the running time of certain protocol steps by a factor of up to 6.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Algesheimer, J., Camenisch, J., Shoup, V.: Efficient Computation Modulo a Shared Secret with Application to the Generation of Shared Safe-Prime Products. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the 20th Annual Symposium on Theory of Computing (STOC 1988), pp. 1–10. ACM Press, New York (1988)
Bogetoft, P., Damgård, I., Jakobsen, T., Nielsen, K., Pagter, J., Toft, T.: A Practical Implementation of Secure Auctions Based on Multiparty Integer Computation. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, pp. 142–147. Springer, Heidelberg (2006)
Boneh, D., Franklin, M.: Efficient Generation of Shared RSA Keys. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 425–439. Springer, Heidelberg (1997)
Catalano, D.: Efficient distributed computation modulo a shared secret. In: Catalano, D., Cramer, R., Damgård, I., Di Crescenco, G., Pointcheval, D., Takagi, T. (eds.) Contemporary Cryptology. Advanced Courses in Mathematics - CRM Barcelona, pp. 1–39. Birkhäuser, Basel (2005)
Catalano, D., Gennaro, R., Halevi, S.: Computing Inverses over a Shared Secret Modulus. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 190–206. Springer, Heidelberg (2000)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: Proceedings of the 20th Annual Symposium on Theory of Computing (STOC 1988), pp. 11–19. ACM Press, New York (1988)
Cramer, R., Damgård, I.: Multiparty computation, an introduction. In: Catalano, D., Cramer, R., Damgård, I., Di Crescenco, G., Pointcheval, D., Takagi, T. (eds.) Contemporary Cryptology. Advanced Courses in Mathematics - CRM Barcelona, pp. 41–87. Birkhäuser, Basel (2005)
Cramer, R., Shoup, V.: Signature schemes based on the Strong RSA Assumption. ACM Transactions on Information and System Security (ACM TISSEC) 3(3), 161–185 (2000)
Damgård, I.: Theory and Practice of Multiparty Computation. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 360–364. Springer, Heidelberg (2006)
Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J., Toft, T.: Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)
Gennaro, R., Halevi, S., Rabin, T.: Secure Hash-and-Sign Signatures without the Random Oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 123–139. Springer, Heidelberg (1999)
Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fast-track multiparty computations with applications to threshold cryptography. In: Proceedings of the 17th ACM Symposium on Principles of Distributed Computing (PODC 1998), pp. 101–111. ACM Press, New York (1998)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of the 19th Annual Symposium on Theory of Computing (STOC 1987), pp. 218–229. ACM Press, New York (1987)
Hairer, E., Wanner, G.: Analysis by Its History, 2nd edn. Springer, Berlin (2008)
Knuth, D.: The Art of Computer Programming, vol. 2. Addison-Wesley (1998)
Koschuch, M., Hudler, M., Krüger, M., Lory, P., Wenzl, J.: Applicability of Multiparty Computation Schemes for Wireless Sensor Networks - Position Paper. In: Sevillano, J.L., Obaidat, M.O., Nicopolitidis, P. (eds.) DCNET 2010 - International Conference on Data Communication Networking - Proceedings of DCNET and OPTICS 2010, pp. 125–128. SciTePress - Science and Technology Publications (2010)
Lory, P.: Secure distributed multiplication of two polynomially shared values: Enhancing the efficiency of the protocol. In: Proceedings of the Third International Conference on Emerging Security Information, Systems and Technologies (SECURWARE 2009), pp. 486–491. IEEE Computer Society (2009)
Lory, P.: Reducing the complexity in the distributed multiplication protocol of two polynomially shared values. In: Proceedings of the 21st International Conference on Advanced Information Networking and Applications (AINA 2007), pp. 404–408. IEEE Computer Society (2007)
Der Merwe, J.V., Dawoud, D., McDonald, S.: A survey on peer-to-peer key management for mobile ad hoc networks. ACM Computing Surveys (CSUR) 39(1), 1–45 (2007)
Miller, G.L.: Riemann’s Hypothesis and tests for primality. In: Proceedings of Seventh Annual ACM Symposium on Theory of Computing, STOC 1975, pp. 234–239. ACM, New York (1975)
Rabin, M.O.: Probabilistic algorithms for testing primality. Journal of Number Theory 12, 128–138 (1980)
Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)
Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis, 3rd edn. Springer, Berlin (2002)
Wenzl, J.: Laufzeitanalyse dreier Versionen eines Mehrparteien-Multiplikationsprotokolls. In: Regensburger Diskussionsbeiträge zur Wirtschaftswissenschaft 440. Institut für Wirtschaftsinformatik, Universität Regensburg (2010)
Yao, A.C.: How to generate and exchange secrets. In: Proceedings of the 27th IEEE Symposium on Foundations of Computer Science (FOCS 1986), pp. 162–167. IEEE Computer Society (1986)
Yiliang, H., Xiaoyuan, Y., Jun, S., Delong, L.: Verifiable threshold cryptosystems based on elliptic curve. In: International Conference on Computer Networks and Mobile Computing, ICCNMC 2003, pp. 334–337. IEEE Computer Society (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koschuch, M., Hudler, M., Krüger, M., Lory, P., Wenzl, J. (2012). Shared Security: How Wireless Sensor Networks Can Benefit from Threshold Cryptography. In: Obaidat, M.S., Sevillano, J.L., Filipe, J. (eds) E-Business and Telecommunications. ICETE 2011. Communications in Computer and Information Science, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35755-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-35755-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35754-1
Online ISBN: 978-3-642-35755-8
eBook Packages: Computer ScienceComputer Science (R0)