A Simple Construction of iO for Turing Machines

We give a simple construction of indistinguishability obfuscation for Turing machines where the time to obfuscate grows only with the description size of the machine and otherwise, independent of the running time and the space used. While this result is already known [Koppula, Lewko, and Waters, STOC 2015] from \(i\mathcal {O}\) for circuits and injective pseudorandom generators, our construction and its analysis are conceptually much simpler. In particular, the main technical component in the proof of our construction is a simple combinatorial pebbling argument [Garg and Srinivasan, EUROCRYPT 2018]. Our construction makes use of indistinguishability obfuscation for circuits and \(\mathrm {somewhere\, statistically\, binding\, hash\, functions}\).

[1]  Allison Bishop,et al.  Indistinguishability Obfuscation for Turing Machines with Unbounded Memory , 2015, IACR Cryptol. ePrint Arch..

[2]  Andrew Chi-Chih Yao,et al.  How to generate and exchange secrets , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[3]  Brent Waters,et al.  New Realizations of Somewhere Statistically Binding Hashing and Positional Accumulators , 2015, ASIACRYPT.

[4]  Andrew Chi-Chih Yao,et al.  Protocols for Secure Computations (Extended Abstract) , 1982, FOCS.

[5]  Abhishek Jain,et al.  Indistinguishability Obfuscation from Compact Functional Encryption , 2015, CRYPTO.

[6]  Nico Döttling,et al.  Identity-Based Encryption from the Diffie-Hellman Assumption , 2017, CRYPTO.

[7]  Craig Gentry,et al.  Two-Round Secure MPC from Indistinguishability Obfuscation , 2014, TCC.

[8]  Aggelos Kiayias,et al.  Delegatable pseudorandom functions and applications , 2013, IACR Cryptol. ePrint Arch..

[9]  Nico Döttling,et al.  New Constructions of Identity-Based and Key-Dependent Message Secure Encryption Schemes , 2018, Public Key Cryptography.

[10]  Brent Waters,et al.  Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[11]  Shafi Goldwasser,et al.  Functional Signatures and Pseudorandom Functions , 2014, Public Key Cryptography.

[12]  Benny Applebaum,et al.  Garbled Circuits as Randomized Encodings of Functions: a Primer , 2017, Tutorials on the Foundations of Cryptography.

[13]  Prabhanjan Vijendra Ananth,et al.  Succinct Garbling Schemes from Functional Encryption through a Local Simulation Paradigm , 2018, IACR Cryptol. ePrint Arch..

[14]  Brent Waters,et al.  Witness encryption and its applications , 2013, STOC '13.

[15]  Michael J. Fischer,et al.  Relations Among Complexity Measures , 1979, JACM.

[16]  Brent Waters,et al.  How to use indistinguishability obfuscation: deniable encryption, and more , 2014, IACR Cryptol. ePrint Arch..

[17]  Mark Zhandry,et al.  Breaking the Sub-Exponential Barrier in Obfustopia , 2017, EUROCRYPT.

[18]  Brent Waters,et al.  Constrained Pseudorandom Functions and Their Applications , 2013, ASIACRYPT.

[19]  Nico Döttling,et al.  Laconic Oblivious Transfer and Its Applications , 2017, CRYPTO.

[20]  Vinod Vaikuntanathan,et al.  Anonymous IBE, Leakage Resilience and Circular Security from New Assumptions , 2018, IACR Cryptol. ePrint Arch..

[21]  Mihir Bellare,et al.  Foundations of garbled circuits , 2012, CCS.

[22]  Amit Sahai,et al.  On the (im)possibility of obfuscating programs , 2001, JACM.

[23]  Ran Canetti,et al.  Succinct Garbling and Indistinguishability Obfuscation for RAM Programs , 2015, STOC.

[24]  Nir Bitansky,et al.  Indistinguishability Obfuscation from Functional Encryption , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[25]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

[26]  Sanjam Garg,et al.  Adaptively Secure Garbling with Near Optimal Online Complexity , 2018, IACR Cryptol. ePrint Arch..

[27]  Rafail Ostrovsky,et al.  Adaptively Secure Garbled Circuits from One-Way Functions , 2016, CRYPTO.

[28]  B. Applebaum.  Cryptography in NC0 , 2014 .

[29]  Craig Gentry,et al.  Succinct Randomized Encodings and their Applications. , 2014 .

[30]  Yehuda Lindell,et al.  A Proof of Security of Yao’s Protocol for Two-Party Computation , 2009, Journal of Cryptology.

[31]  Daniel Wichs,et al.  On the Communication Complexity of Secure Function Evaluation with Long Output , 2015, IACR Cryptol. ePrint Arch..