Abstract
Functional encryption provides more sophisticated and flexible expression between the encryption key ek and decryption key dk by deriving from attribute vectors \(\overrightarrow{x}\) and policy vector \(\overrightarrow{v}\), respectively. There is a function \(f({\overrightarrow{x}},\overrightarrow{v})\) that determines what type of a user with a secret key dk can decrypt the ciphertext encrypted under ek. This allows an encryptor to specify a functional formula as a decryptable policy describing what users can learn from the ciphertext without knowing the decryptor’s identities or public keys.
In this paper, we explore two geometric-area-based key generation and functional encryption schemes (GeoEnc), where secret keys are associated with a point on a planar coordinate system and encrypt policies are associated with a line (GeoEncLine scheme) or a convex polygon (GeoEncHull scheme). If the attribute point lies on the line or inside the convex hull, the decryption key holder can decrypt the ciphertext associated with the geometric policy such as the line or the convex polygon. The proposed schemes have policy hiding as well as payload hiding characteristics. To the best of our knowledge, they are the first functional encryptions using geometric-area-based keys and policies. We give an evaluation of key distribution in a practical coordinate system and also give a security analysis with a hybrid model. The proposed schemes have many applications as sources for keys generation and policies encryption such as computer graphics security, network topology protection, secure routing and mobile networking, secure multiparty computation, secure GPS/GIS, military area protection, etc.
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
Asghar, H.J., Li, S., Pieprzyk, J., Wang, H.: Cryptanalysis of the convex hull click human identification protocol. In: Burmester, M., Tsudik, G., Magliveras, S., Ilić, I. (eds.) ISC 2010. LNCS, vol. 6531, pp. 24–30. Springer, Heidelberg (2011)
Boneh, D., Hamburg, M.: Generalized identity based and broadcast encryption schemes. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 455–470. Springer, Heidelberg (2008)
Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)
Boneh, D., Sahai, A., Waters, B.: Functional encryption: Definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253–273. Springer, Heidelberg (2011)
Boyen, X., Waters, B.: Anonymous hierarchical identity-based encryption (Without random oracles). In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 290–307. Springer, Heidelberg (2006)
Brakerski, Z., Goldwasser, S.: Circular and leakage resilient public-key encryption under subgroup indistinguishability. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 1–20. Springer, Heidelberg (2010)
Chandran, N., Goyal, V., Moriarty, R., Ostrovsky, R.: Position based cryptography. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 391–407. Springer, Heidelberg (2009)
Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory IT-22, 644–654 (1976)
Gentry, C.: Practical identity-based encryption without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006)
Gentry, C., Halevi, S.: Hierarchical identity based encryption with polynomially many levels. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 437–456. Springer, Heidelberg (2009)
Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. ACM CCS 2006, 89–98 (2006)
Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008)
Kleinjung, T., Aoki, K., Franke, J., Lenstra, A.K., Thomé, E., Bos, J.W., Gaudry, P., Kruppa, A., Montgomery, P.L., Osvik, D.A., te Riele, H., Timofeev, A., Zimmermann, P.: Factorization of a 768-bit RSA modulus. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 333–350. Springer, Heidelberg (2010)
Lenstra Jr., H.W.: Factoring integers with elliptic curves. Annals of Mathematics, 649–673 (1987)
Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: Attribute-based encryption and (Hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010)
Lewko, A., Waters, B.: New techniques for dual system encryption and fully secure HIBE with short ciphertexts. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 455–479. Springer, Heidelberg (2010)
Park, J.H.: Inner-product encryption under standard assumption. Des. Codes Cryptogr. 58(3), 235–257 (2011)
O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Report 2010/556
Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005)
Sahai, A., Waters, B.: Fuzzy identities and attributed-based encryption. In: Tuyls, P., Å koric, B., Kerenaar, T. (eds.) Security with noisy data, Springer, Heidelberg (2007)
Seo, J.H., Kobayashi, T., Ohkubo, M., Suzuki, K.: Anonymous hierarchical identity-based encryption with constant size ciphertext. IEICE Trans. on Fundamentals E94-A(1), 45–56 (2011)
Shen, E., Shi, E., Waters, B.: Predicate privacy in encryption systems. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 457–473. Springer, Heidelberg (2009)
Shi, E., Waters, B.: Delegating capabilities in predicate encryption systems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 560–578. Springer, Heidelberg (2008)
Sobrado, L., Birget, J.C.: Graphical passwords. The Rutgers Scholar, 4 (2002), http://rutgersscholar.rutgers.edu/volume04/sobrbirg
Waters, B.: Dual system encryption: Realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009)
Waters, B., Felten, E.W.: Secure, privacy proof of locations. TR-667-03
Wiedenbeck, S., Waters, J., Sobrado, L., Birget, J.C.: Design and evaluation of a shoulder-surfing resistant graphical password scheme. In: AVI 2006, pp. 177–184. ACM, New York (2006)
Zhao, H., Li, X.: S3PAS: A scalable shoulder-surfing resistant textual-graphical password authentication scheme. In: AINAW 2007, pp. 467–472. IEEE Computer Society, Los Alamitos (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, M., Takagi, T. (2011). GeoEnc: Geometric Area Based Keys and Policies in Functional Encryption Systems. In: Parampalli, U., Hawkes, P. (eds) Information Security and Privacy. ACISP 2011. Lecture Notes in Computer Science, vol 6812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22497-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-22497-3_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22496-6
Online ISBN: 978-3-642-22497-3
eBook Packages: Computer ScienceComputer Science (R0)