Abstract
Modular exponentiations have been considered the most expensive operation in discrete-logarithm based cryptographic protocols. In this paper, we propose a new secure outsourcing algorithm for exponentiation modular a prime in the one-malicious model. Compared with the state-of-the-art algorithm [33], the proposed algorithm is superior in both efficiency and checkability. We then utilize this algorithm as a subroutine to achieve outsource-secure Cramer-Shoup encryptions and Schnorr signatures. Besides, we propose the first outsource-secure and efficient algorithm for simultaneous modular exponentiations. Moreover, we prove that both the algorithms can achieve the desired security notions.
Chapter PDF
Similar content being viewed by others
References
Atallah, M.J., Frikken, K.B.: Securely outsourcing linear algebra computations. In: Proceedings of the 5th ACM Symposium on Information, Computer and Communications Security (CCS), pp. 48–59 (2010)
Abadi, M., Feigenbaum, J., Kilian, J.: On hiding information from an oracle. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing (STOC), pp. 195–203 (1987)
Atallah, M.J., Pantazopoulos, K.N., Rice, J.R., Spafford, E.H.: Secure outsourcing of scientific computations. Advances in Computers 54, 216–272 (2001)
Atallah, M.J., Li, J.: Secure outsourcing of sequence comparisons, International Journal of Information Security, 277–287 (2005)
Ateniese, G., de Medeiros, B.: Identity-Based Chameleon Hash and Applications. In: Juels, A. (ed.) FC 2004. LNCS, vol. 3110, pp. 164–180. Springer, Heidelberg (2004)
Ateniese, G., de Medeiros, B.: On the Key Exposure Problem in Chameleon Hashes. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 165–179. Springer, Heidelberg (2005)
Blanton, M.: Improved Conditional E-Payments. In: Bellovin, S.M., Gennaro, R., Keromytis, A.D., Yung, M. (eds.) ACNS 2008. LNCS, vol. 5037, pp. 188–206. Springer, Heidelberg (2008)
Benjamin, D., Atallah, M.J.: Private and cheating-free outsourcing of algebraic computations. In: Proceeding of the 6th Annual Conference on Privacy, Security and Trust (PST), pp. 240–245 (2008)
Brassard, G., Chaum, D., Crepeau, C.: Minimum disclosure proofs of knowledge. Journal of Computer and System Sciences 37(2), 156–189 (1988)
Beaver, D., Feigenbaum, J., Kilian, J., Rogaway, P.: Locally random reductions: Improvements and applications. Journal of Cryptology 10(1), 17–36 (1997)
Ben-Or, M., Goldwasser, S., Kilian, J., Wigderson, A.: Multi-prover interactive proofs: How to remove intractability assumptions. In: Proceedings of the ACM Symposium on Theory of Computing (STOC), pp. 113–131 (1988)
Benabbas, S., Gennaro, R., Vahlis, Y.: Verifiable Delegation of Computation over Large Datasets. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 111–131. Springer, Heidelberg (2011)
Blum, M., Luby, M., Rubinfeld, R.: Program result checking against adaptive programs and in cryptographic settings. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 107–118 (1991)
Blum, M., Luby, M., Rubinfeld, R.: Self-testing/correcting with applications to numerical problems. Journal of Computer and System Science, 549–595 (1993)
Boyko, V., Peinado, M., Venkatesan, R.: Speeding up Discrete Log and Factoring Based Schemes via Precomputations. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 221–235. Springer, Heidelberg (1998)
Di Crescenzo, G., Ostrovsky, R.: On Concurrent Zero-Knowledge with Pre-processing (Extended Abstract). In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 485–502. Springer, Heidelberg (1999)
Chaum, D., Pedersen, T.P.: Wallet Databases with Observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)
Cramer, R., Shoup, V.: Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack. SIAM Journal of Computing 33, 167–226 (2003)
Carbunar, B., Tripunitara, M.: Conditional Payments for Computing Markets. In: Franklin, M.K., Hui, L.C.K., Wong, D.S. (eds.) CANS 2008. LNCS, vol. 5339, pp. 317–331. Springer, Heidelberg (2008)
Carbunar, B., Tripunitara, M.: Fair payments for outsourced computations. In: Proceedings of the 7th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks (SECON), pp. 529–537. IEEE (2010)
Chen, X., Zhang, F., Kim, K.: Chameleon Hashing Without Key Exposure. In: Zhang, K., Zheng, Y. (eds.) ISC 2004. LNCS, vol. 3225, pp. 87–98. Springer, Heidelberg (2004)
Chen, X., Zhang, F., Susilo, W., Mu, Y.: Efficient Generic On-Line/Off-Line Signatures Without Key Exposure. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 18–30. Springer, Heidelberg (2007)
Fischlin, M., Fischlin, R.: Efficient Non-malleable Commitment Schemes. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 413–431. Springer, Heidelberg (2000)
Even, S., Goldreich, O., Micali, S.: On-line/Off-line digital signatures. Journal of Cryptology 9(1), 35–67 (1996)
Gennaro, R.: Multi-trapdoor Commitments and Their Applications to Proofs of Knowledge Secure Under Concurrent Man-in-the-Middle Attacks. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 220–236. Springer, Heidelberg (2004)
Green, M., Hohenberger, S., Waters, B.: Outsourcing the Decryption of ABE Ciphertexts. In: Proceedings of the 20th USENIX Conference on Security (2011), http://static.usenix.org/events/sec11/tech/full-papers/Green.pdf
Gennaro, R., Gentry, C., Parno, B.: Non-interactive Verifiable Computing: Outsourcing Computation to Untrusted Workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010)
Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. In: Proceedings of the ACM Symposium on the Theory of Computing (STOC), pp. 113–122 (2008)
Girault, M., Lefranc, D.: Server-Aided Verification: Theory and Practice. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 605–623. Springer, Heidelberg (2005)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems. SIAM Journal on Computing 18(1), 186–208 (1989)
Golle, P., Mironov, I.: Uncheatable Distributed Computations. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 425–440. Springer, Heidelberg (2001)
Garay, J., MacKenzie, P., Yang, K.: Strengthening Zero-knowledge Protocols Using Signatures. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 177–194. Springer, Heidelberg (2003)
Hohenberger, S., Lysyanskaya, A.: How to Securely Outsource Cryptographic Computations. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 264–282. Springer, Heidelberg (2005), http://www.cs.jhu.edu/
Kilian, J.: A note on efficient zero-knowledge proofs and arguments. In: Proceedings of the ACM Symposium on Theory of Computing (STOC), pp. 723–732 (1992)
Kilian, J.: Improved Efficient Arguments. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 311–324. Springer, Heidelberg (1995)
Krawczyk, H., Rabin, T.: Chameleon hashing and signatures. In: Proceeding of the 7th Annual Network and Distributed System Security Symposium (NDSS), pp. 143–154 (2000)
Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press (1996)
Micali, S.: CS proofs. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science (FOCS), pp. 436–453 (1994)
Matsumoto, T., Kato, K., Imai, H.: Speeding up Secret Computations with Insecure Auxiliary Devices. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 497–506. Springer, Heidelberg (1990)
Nguyen, P.Q., Shparlinski, I.E., Stern, J.: Distribution of modular sums and the security of server aided exponentiation. In: Proceedings of the Workshop on Comp. Number Theory and Crypt., pp. 1–16 (1999)
Parno, B., Raykova, M., Vaikuntanathan, V.: How to Delegate and Verify in Public: Verifiable Computation from Attribute-Based Encryption. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 422–439. Springer, Heidelberg (2012)
Schnorr, C.P.: Efficient signature generation for smart cards. Journal of Cryptology 4(3), 239–252 (1991)
Shi, L., Carbunar, B., Sion, R.: Conditional E-Cash. In: Dietrich, S., Dhamija, R. (eds.) FC 2007 and USEC 2007. LNCS, vol. 4886, pp. 15–28. Springer, Heidelberg (2007)
Shamir, A., Tauman, Y.: Improved Online/Offline Signature Schemes. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 355–367. Springer, Heidelberg (2001)
Wang, C., Ren, K., Wang, J.: Secure and practical outsourcing of linear programming in cloud computing. In: Proceedings of the 30th IEEE International Conference on Computer Communications (INFOCOM), pp. 820–828 (2011)
Wu, W., Mu, Y., Susilo, W., Huang, X.: Server-Aided Verification Signatures: Definitions and New Constructions. In: Baek, J., Bao, F., Chen, K., Lai, X. (eds.) ProvSec 2008. LNCS, vol. 5324, pp. 141–155. Springer, Heidelberg (2008)
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
Chen, X., Li, J., Ma, J., Tang, Q., Lou, W. (2012). New Algorithms for Secure Outsourcing of Modular Exponentiations. In: Foresti, S., Yung, M., Martinelli, F. (eds) Computer Security – ESORICS 2012. ESORICS 2012. Lecture Notes in Computer Science, vol 7459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33167-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-33167-1_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33166-4
Online ISBN: 978-3-642-33167-1
eBook Packages: Computer ScienceComputer Science (R0)