Abstract
This paper studies the question of how to define, construct, and use obfuscators for probabilistic programs. Such obfuscators compile a possibly randomized program into a deterministic one, which achieves computationally indistinguishable behavior from the original program as long as it is run on each input at most once. For obfuscation, we propose a notion that extends indistinguishability obfuscation to probabilistic circuits: It should be hard to distinguish between the obfuscations of any two circuits whose output distributions at each input are computationally indistinguishable, possibly in presence of some auxiliary input. We call the resulting notion probabilistic indistinguishability obfuscation (pIO).
We define several variants of pIO, and study relations among them. Moreover, we give a construction of one of our variants, called X-pIO, from sub-exponentially hard indistinguishability obfuscation (for deterministic circuits) and one-way functions.
We then move on to show a number of applications of pIO. In particular, we first give a general and natural methodology to achieve fully homomorphic encryption (FHE) from variants of pIO and of semantically secure encryption schemes. In particular, one instantiation leads to FHE from any X-pIO obfuscator and any re-randomizable encryption scheme that’s slightly super-polynomially secure.
We note that this constitutes the first construction of full-fledged FHE that does not rely on encryption with circular security.
Moreover, assuming sub-exponentially secure puncturable PRFs computable in NC1, sub-exponentially-secure indistinguishability obfuscation for (deterministic) NC1 circuits can be bootstrapped to obtain indistinguishability obfuscation for arbitrary (deterministic) poly-size circuits (previously such bootstrapping was known only assuming FHE with NC1 decryption algorithm).
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Keywords
- Encryption Scheme
- Homomorphic Encryption
- Pseudorandom Function
- Auxiliary Input
- Cryptology ePrint Archive
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References
Alwen, J., Barbosa, M., Farshim, P., Gennaro, R., Dov Gordon, S., Tessaro, S., Wilson, D.A.: On the relationship between functional encryption, obfuscation, and fully homomorphic encryption. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 65–84. Springer, Heidelberg (2013)
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/
Applebaum, B.: Bootstrapping obfuscators via fast pseudorandom functions. IACR Cryptology ePrint Archive, 2013:699 (2013)
Applebaum, B., Ishai, Y., Kushilevitz, E.: Cryptography in NC0. In: FOCS, pp. 166–175. IEEE Computer Society (2004)
Applebaum, B., Ishai, Y., Kushilevitz, E.: Computationally private randomizing polynomials and their applications. Computational Complexity 15(2), 115–162 (2006)
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)
Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6 (2012)
Bellare, M., Hofheinz, D., Yilek, S.: Possibility and impossibility results for encryption and commitment secure under selective opening. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 1–35. Springer, Heidelberg (2009)
Bellare, M., Stepanovs, I., Tessaro, S.: Poly-many hardcore bits for any one-way function and a framework for differing-inputs obfuscation. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 102–121. Springer, Heidelberg (2014)
Bitansky, N., Canetti, R., Cohn, H., Goldwasser, S., Kalai, Y.T., Paneth, O., Rosen, A.: The impossibility of obfuscation with auxiliary input or a universal simulator. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 71–89. Springer, Heidelberg (2014)
Bitansky, N., Garg, S., Telang, S.: Succinct randomized encodings and their applications. Cryptology ePrint Archive, Report 2014/771 (2014), http://eprint.iacr.org/
Boneh, D., Waters, B.: Constrained pseudorandom functions and their applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 280–300. Springer, Heidelberg (2013)
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)
Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 501–519. Springer, Heidelberg (2014)
Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical gapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012)
Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: ITCS, pp. 309–325 (2012)
Brakerski, Z., Rothblum, G.N.: Obfuscating conjunctions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 416–434. Springer, Heidelberg (2013)
Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: FOCS, pp. 97–106 (2011), References are to full version: http://eprint.iacr.org/2011/344
Canetti, R., Lin, H., Tessaro, S., Vaikuntanathan, V.: Obfuscation of probabilistic circuits and applications. Cryptology ePrint Archive, Report 2014/882 (2014), http://eprint.iacr.org/
Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of paillier’s probabilistic public-key system. In: Kim, K.-C. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)
Garg, S., Gentry, C., Halevi, S., Sahai, A., Raikova, M., Waters, B.: Candidate Indistinguishability Obfuscation and Functional Encryption for all circuits. In: FOCS (2013)
Garg, S., Gentry, C., Halevi, S., Wichs, D.: On the implausibility of differing-inputs obfuscation and extractable witness encryption with auxiliary input. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 518–535. Springer, Heidelberg (2014)
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178 (2009)
Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013)
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792–807 (1986)
Goldwasser, S., Kalai, Y.T.: On the impossibility of obfuscation with auxiliary input. In: FOCS, pp. 553–562. IEEE Computer Society (2005)
Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)
Hemenway, B., Libert, B., Ostrovsky, R., Vergnaud, D.: Lossy encryption: Constructions from general assumptions and efficient selective opening chosen ciphertext security. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 70–88. Springer, Heidelberg (2011)
Ishai, Y., Kushilevitz, E.: Randomizing polynomials: A new representation with applications to round-efficient secure computation. In: FOCS, pp. 294–304. IEEE Computer Society (2000)
Kiayias, A., Papadopoulos, S., Triandopoulos, N., Zacharias, T.: Delegatable pseudorandom functions and applications. In: Sadeghi, A.R., Gligor, V.D., Yung, M. (eds.) CCS, pp. 669–684. ACM (2013)
Kol, G., Naor, M.: Games for exchanging information. In: STOC, pp. 423–432 (2008)
Lin, H., Pass, R.: Succinct garbling schemes and applications. Cryptology ePrint Archive, Report 2014/766 (2014), http://eprint.iacr.org/
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. SIAM J. Comput. 40(6), 1803–1844 (2011)
Prabhakaran, M., Rosulek, M.: Rerandomizable RCCA encryption. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 517–534. Springer, Heidelberg (2007)
Sahai, A., Waters, B.: How to use indistinguishability obfuscation: deniable encryption, and more. In: STOC, pp. 475–484 (2014)
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Canetti, R., Lin, H., Tessaro, S., Vaikuntanathan, V. (2015). Obfuscation of Probabilistic Circuits and Applications. In: Dodis, Y., Nielsen, J.B. (eds) Theory of Cryptography. TCC 2015. Lecture Notes in Computer Science, vol 9015. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46497-7_19
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DOI: https://doi.org/10.1007/978-3-662-46497-7_19
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