5Gen: A Framework for Prototyping Applications Using Multilinear Maps and Matrix Branching Programs

Secure multilinear maps (mmaps) have been shown to have remarkable applications in cryptography, such as multi-input functional encryption (MIFE) and program obfuscation. To date, there has been little evaluation of the performance of these applications. In this paper we initiate a systematic study of mmap-based constructions. We build a general framework, called 5Gen, to experiment with these applications. At the top layer we develop a compiler that takes in a high-level program and produces an optimized matrix branching program needed for the applications we consider. Next, we optimize and experiment with several MIFE and obfuscation constructions and evaluate their performance. The 5Gen framework is modular and can easily accommodate new mmap constructions as well as new MIFE and obfuscation constructions, as well as being an open-source tool that can be used by other research groups to experiment with a variety of mmap-based constructions.

[1]  Allison Bishop,et al.  Indistinguishability Obfuscation from the Multilinear Subgroup Elimination Assumption , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[2]  Craig Gentry,et al.  Graph-Induced Multilinear Maps from Lattices , 2015, TCC.

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

[4]  Brent Waters,et al.  Functional Encryption: Definitions and Challenges , 2011, TCC.

[5]  Craig Gentry,et al.  Fully Secure Attribute Based Encryption from Multilinear Maps , 2014, IACR Cryptol. ePrint Arch..

[6]  Allison Bishop,et al.  Witness Encryption from Instance Independent Assumptions , 2014, IACR Cryptol. ePrint Arch..

[7]  Craig Gentry,et al.  Zeroizing Without Low-Level Zeroes: New MMAP Attacks and their Limitations , 2015, CRYPTO.

[8]  Amit Sahai,et al.  Multi-Input Functional Encryption , 2014, IACR Cryptol. ePrint Arch..

[9]  Martin R. Albrecht,et al.  On the concrete hardness of Learning with Errors , 2015, J. Math. Cryptol..

[10]  Jung Hee Cheon,et al.  Cryptanalysis of the Multilinear Map over the Integers , 2014, EUROCRYPT.

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

[12]  Yael Tauman Kalai,et al.  Protecting Obfuscation against Algebraic Attacks , 2014, EUROCRYPT.

[13]  Brice Minaud,et al.  Cryptanalysis of the New CLT Multilinear Map over the Integers , 2016, EUROCRYPT.

[14]  Craig Gentry,et al.  Candidate Multilinear Maps from Ideal Lattices , 2013, EUROCRYPT.

[15]  Yupu Hu,et al.  Cryptanalysis of GGH Map , 2016, EUROCRYPT.

[16]  Huijia Lin,et al.  Indistinguishability Obfuscation from Constant-Degree Graded Encoding Schemes , 2016, EUROCRYPT.

[17]  Brent Waters,et al.  Low Overhead Broadcast Encryption from Multilinear Maps , 2014, IACR Cryptol. ePrint Arch..

[18]  Jean-Sébastien Coron,et al.  Practical Multilinear Maps over the Integers , 2013, CRYPTO.

[19]  Dan Boneh,et al.  Applications of Multilinear Forms to Cryptography , 2002, IACR Cryptol. ePrint Arch..

[20]  Ron Steinfeld,et al.  GGHLite: More Efficient Multilinear Maps from Ideal Lattices , 2014, IACR Cryptol. ePrint Arch..

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

[22]  Tanja Lange,et al.  Bad directions in cryptographic hash functions , 2015, IACR Cryptol. ePrint Arch..

[23]  Jean-Sébastien Coron,et al.  New Multilinear Maps Over the Integers , 2015, CRYPTO.

[24]  David J. Wu,et al.  Order-Revealing Encryption: New Constructions, Applications, and Lower Bounds , 2016, IACR Cryptol. ePrint Arch..

[25]  Martin R. Albrecht,et al.  A Subfield Lattice Attack on Overstretched NTRU Assumptions - Cryptanalysis of Some FHE and Graded Encoding Schemes , 2016, CRYPTO.

[26]  Jung Hee Cheon,et al.  An Algorithm for NTRU Problems and Cryptanalysis of the GGH Multilinear Map without an encoding of zero , 2016, IACR Cryptol. ePrint Arch..

[27]  Guy N. Rothblum,et al.  Virtual Black-Box Obfuscation for All Circuits via Generic Graded Encoding , 2014, TCC.

[28]  Martin R. Albrecht,et al.  Implementing Candidate Graded Encoding Schemes from Ideal Lattices , 2015, ASIACRYPT.

[29]  Nico Döttling,et al.  Obfuscation from Low Noise Multilinear Maps , 2018, IACR Cryptol. ePrint Arch..

[30]  Mark Zhandry,et al.  Semantically Secure Order-Revealing Encryption: Multi-input Functional Encryption Without Obfuscation , 2015, EUROCRYPT.

[31]  Eric Miles,et al.  Annihilation Attacks for Multilinear Maps: Cryptanalysis of Indistinguishability Obfuscation over GGH13 , 2016, CRYPTO.

[32]  Sanjam Garg,et al.  Obfuscation without the Vulnerabilities of Multilinear Maps , 2016, IACR Cryptol. ePrint Arch..

[33]  Eric Miles,et al.  Post-Zeroizing Obfuscation: The case of Evasive Circuits , 2015, IACR Cryptol. ePrint Arch..

[34]  Dan Boneh,et al.  Immunizing Multilinear Maps Against Zeroizing Attacks , 2014, IACR Cryptol. ePrint Arch..

[35]  Jae Hong Seo,et al.  Security Analysis of Multilinear Maps over the Integers , 2014, IACR Cryptol. ePrint Arch..

[36]  Yuval Ishai,et al.  Optimizing Obfuscation: Avoiding Barrington's Theorem , 2014, CCS.

[37]  Alex J. Malozemoff,et al.  Implementing Cryptographic Program Obfuscation , 2014, IACR Cryptol. ePrint Arch..

[38]  Tancrède Lepoint Design and Implementation of Lattice-Based Cryptography , 2014 .

[39]  Rafael Pass,et al.  Indistinguishability Obfuscation with Non-trivial Efficiency , 2016, Public Key Cryptography.

[40]  Joe Zimmerman,et al.  How to Obfuscate Programs Directly , 2015, EUROCRYPT.

[41]  J. Cheon,et al.  An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low-level encoding of zero , 2016 .

[42]  Zvika Brakerski,et al.  Obfuscating Circuits via Composite-Order Graded Encoding , 2015, TCC.

[43]  Eric Miles,et al.  Secure Obfuscation in a Weak Multilinear Map Model , 2016, TCC.

[44]  Mark Zhandry,et al.  Obfuscating Low-Rank Matrix Branching Programs , 2014, IACR Cryptol. ePrint Arch..

[45]  Rafael Pass,et al.  Indistinguishability Obfuscation from Semantically-Secure Multilinear Encodings , 2014, CRYPTO.