Abstract
Recent proposals for plausible candidate constructions of multilinear maps and obfuscation have radically transformed what we imagined to be possible in cryptography. For over a decade cryptographers had been very skeptical about the existence of such objects. In this article, we provide a very brief introduction to these results and some of their interesting consequences.
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Ananth, P., Boneh, D., Garg, S., Sahai, A., Zhandry, M.: Differing-inputs obfuscation and applications. Cryptology ePrint Archive, Report 2013/689 (2013), http://eprint.iacr.org/2013/689
Boyle, E., Chung, K.-M., Pass, R.: On Extractability Obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 52–73. Springer, Heidelberg (2014)
Beimel, A.: Secret-sharing schemes: A survey. In: Chee, Y.M., Guo, Z., Ling, S., Shao, F., Tang, Y., Wang, H., Xing, C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 11–46. Springer, Heidelberg (2011)
Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (Im)possibility of Obfuscating Programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001)
Barak, B., Garg, S., Kalai, Y.T., Paneth, O., Sahai, A.: Protecting Obfuscation against Algebraic Attacks. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 221–238. Springer, Heidelberg (2014)
Brakerski, Z., Rothblum, G.N.: Virtual Black-Box Obfuscation for All Circuits via Generic Graded Encoding. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 1–25. Springer, Heidelberg (2014)
Boneh, D., Silverberg, A.: Applications of multilinear forms to cryptography. Cryptology ePrint Archive, Report 2002/080 (2002), http://eprint.iacr.org/2002/080
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)
Boneh, D., Zhandry, M.: Multiparty key exchange, efficient traitor tracing, and more from indistinguishability obfuscation. Cryptology ePrint Archive, Report 2013/642 (2013), http://eprint.iacr.org/2013/642
Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical Multilinear Maps over the Integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476–493. Springer, Heidelberg (2013)
Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory 22(6), 644–654 (1976)
Gentry, C.: Fully homomorphic encryption using ideal lattices. In Michael Mitzenmacher. In: 41st ACM STOC, pp. 169–178. ACM Press (May/June 2009)
Goldwasser, S., Dov Gordon, S., Goyal, V., Jain, A., Katz, J., Liu, F.-H., Sahai, A., Shi, E., Zhou, H.-S.: Multi-input Functional Encryption. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 578–602. Springer, Heidelberg (2014)
Garg, S., Gentry, C., Halevi, S.: Candidate Multilinear Maps from Ideal Lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013)
Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th FOCS, pp. 40–49. IEEE Computer Society Press (October 2013)
Garg, S., Gentry, C., Halevi, S., Raykova, M.: Two-Round Secure MPC from Indistinguishability Obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 74–94. Springer, Heidelberg (2014)
Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In Dan Boneh, Tim Roughgarden, and Joan Feigenbaum. In: 45th ACM STOC. ACM Press, pp. 467–476 (June 2013)
Goyal, V., Jain, A., Koppula, V., Sahai, A.: Functional encryption for randomized functionalities. Cryptology ePrint Archive, Report 2013/729 (2013), http://eprint.iacr.org/2013/729
Goldwasser, S., Rothblum, G.N.: On Best-Possible Obfuscation. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 194–213. Springer, Heidelberg (2007)
Hada, S.: Zero-knowledge and code obfuscation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 443–457. Springer, Heidelberg (2000)
Joux, A.: A one round protocol for tripartite Diffie-Hellman. Journal of Cryptology 17(4), 263–276 (2004)
O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Report 2010/556 (2010), http://eprint.iacr.org/2010/556
Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signature and public-key cryptosystems. Communications of the Association for Computing Machinery 21(2), 120–126 (1978)
Rudich, S.: Unpublished (1989)
Sahai, A., Waters, B.: How to use indistinguishability obfuscation: deniable encryption, and more. In: Shmoys, D.B. (ed.) 46th ACM STOC, pp. 475–484. ACM Press (May/June 2014)
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Garg, S. (2014). Program Obfuscation via Multilinear Maps. In: Abdalla, M., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2014. Lecture Notes in Computer Science, vol 8642. Springer, Cham. https://doi.org/10.1007/978-3-319-10879-7_6
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DOI: https://doi.org/10.1007/978-3-319-10879-7_6
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