Abstract
We consider a scenario in which a data owner outsources storage of a large graph to an untrusted server; the server performs computations on this graph in response to queries from a client (whether the data owner or others), and the goal is to ensure verifiability of the returned results. Applying generic verifiable computation (VC) would involve compiling each graph computation to a circuit or a RAM program and would incur large overhead, especially in the proof-computation time.
In this work, we address the above by designing, building, and evaluating Alitheia, a VC system tailored for graph queries such as computing shortest paths, longest paths, and maximum flows. The underlying principle of Alitheia is to minimize the use of generic VC techniques by leveraging various algorithmic approaches specific for graphs. This leads to both theoretical and practical improvements. Asymptotically, it improves the complexity of proof computation by at least a logarithmic factor. On the practical side, our system achieves significant performance improvements over current state-of-the-art VC systems (up to a 10-orders-of-magnitude improvement in proof-computation time, and a 99.9% reduction in server storage), while scaling to 200,000-node graphs.
- 2016. openSSL library. Retrieved from https://www.openssl.org/.Google Scholar
- 2017. Ate pairing. Retrievved from https://github.com/herumi/ate-pairing.Google Scholar
- Scott Ames, Carmit Hazay, Yuval Ishai, and Muthuramakrishnan Venkitasubramaniam. 2017. Ligero: Lightweight sublinear arguments without a trusted setup. In Proceedings of the ACM Conference on Computer and Communications Security (CCS’17). Google Scholar
Digital Library
- Aris Anagnostopoulos, Michael Goodrich, and Roberto Tamassia. 2001. Persistent authenticated dictionaries and their applications. In Proceedings of 4th International Conference on Information Security (ISC'01). 379--393. Google Scholar
Digital Library
- Eli Ben-Sasson, Iddo Bentov, Alessandro Chiesa, Ariel Gabizon, Daniel Genkin, Matan Hamilis, Evgenya Pergament, Michael Riabzev, Mark Silberstein, Eran Tromer, and Madars Virza. 2017. Computational integrity with a public random string from quasi-linear PCPs. In Proceedings of the Annual Conference on Advances in Cryptology (EUROCRYPT’17). 551--579.Google Scholar
Cross Ref
- Eli Ben-Sasson, Alessandro Chiesa, Daniel Genkin, Eran Tromer, and Madars Virza. 2013. SNARKs for C: Verifying program executions succinctly and in zero knowledge. In Proceedings of the Annual Conference on Advances in Cryptology (CRYPTO’13). Springer, 90--108.Google Scholar
Cross Ref
- Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, and Madars Virza. 2014. Succinct non-interactive zero knowledge for a von Neumann architecture. In Proceedings of the USENIX Security Symposium. 781--796. Google Scholar
Digital Library
- Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, and Madars Virza. 2017. Scalable zero knowledge via cycles of elliptic curves. Algorithmica 79, 4 (2017), 1102--1160. Google Scholar
Digital Library
- Nir Bitansky, Ran Canetti, Alessandro Chiesa, and Eran Tromer. 2012. From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again. In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference. 326--349. Google Scholar
Digital Library
- Nir Bitansky, Ran Canetti, Alessandro Chiesa, and Eran Tromer. 2013. Recursive composition and bootstrapping for SNARKs and proof-carrying data. In Proceedings of the 45th Annual ACM Symposium on Theory of Computing. 111--120. Google Scholar
Digital Library
- Nir Bitansky, Ran Canetti, Omer Paneth, and Alon Rosen. 2014. On the existence of extractable one-way functions. In Proceedings of the Annual ACM Symposium on Theory of Computing (STOC’14). 505--514. Google Scholar
Digital Library
- Nir Bitansky, Alessandro Chiesa, Yuval Ishai, Omer Paneth, and Rafail Ostrovsky. 2013. Succinct non-interactive arguments via linear interactive proofs. In Theory of Cryptography. Springer, 315--333. Google Scholar
Digital Library
- Elette Boyle and Rafael Pass. 2015. Limits of extractability assumptions with distributional auxiliary input. In Proceedings of the Annual Conference on Advances in Cryptology (ASIACRYPT’15). 236--261. Google Scholar
Digital Library
- Benjamin Braun, Ariel J. Feldman, Zuocheng Ren, Srinath Setty, Andrew J Blumberg, and Michael Walfish. 2013. Verifying computations with state. In Proceedings of the 24th ACM Symposium on Operating Systems Principles. 341--357. Google Scholar
Digital Library
- Dario Catalano and Dario Fiore. 2013. Vector commitments and their applications. In Public Key Cryptography. 55--72.Google Scholar
- Alessandro Chiesa, Eran Tromer, and Madars Virza. 2015. Cluster computing in zero knowledge. In Proceedings of the Annual Conference on Advances in Cryptology (EUROPCRYPT’15). 371--403.Google Scholar
Cross Ref
- Kai-Min Chung, Yael Tauman Kalai, and Salil P. Vadhan. 2010. Improved delegation of computation using fully homomorphic encryption. In Proceedings of the Annual Conference on Advances in Cryptology (CRYPTO’10). 483--501. Google Scholar
Digital Library
- Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009. Introduction to Algorithms (3rd ed.). MIT Press. Google Scholar
Digital Library
- Craig Costello, Cédric Fournet, Jon Howell, Markulf Kohlweiss, Benjamin Kreuter, Michael Naehrig, Bryan Parno, and Samee Zahur. 2015. Geppetto: Versatile verifiable computation. In Proceedings of the IEEE Symposium on Security and Privacy (S&P’’’15). 253--270. Google Scholar
Digital Library
- George Danezis, Cédric Fournet, Jens Groth, and Markulf Kohlweiss. 2014. Square span programs with applications to succinct NIZK arguments. In Proceedings of the Annual Conference on Advances in Cryptology (ASIACRYPT’14). 532--550.Google Scholar
Cross Ref
- DIMACS. 2006. 9th DIMACS Implementation Challenge—Shortest Paths. Retrieved from http://www.dis.uniroma1.it/challenge9/.Google Scholar
- Jittat Fakcharoenphol and Satish Rao. 2006. Planar graphs, negative weight edges, shortest paths, and near linear time. J. Comput. Syst. Sci. 72, 5 (2006), 868--889. Google Scholar
Digital Library
- Dario Fiore, Cédric Fournet, Esha Ghosh, Markulf Kohlweiss, Olga Ohrimenko, and Bryan Parno. 2016. Hash first, argue later: Adaptive verifiable computations on outsourced data. In Proceedings of the 2016 ACM Conference on Computer and Communications Security. 1304--1316. Google Scholar
Digital Library
- Eli Fox-Epstein, Shay Mozes, Phitchaya Mangpo Phothilimthana, and Christian Sommer. 2016. Short and simple cycle separators in planar graphs. J. Exp. Algor. 21, 2 (2016), 2--2. Google Scholar
Digital Library
- Rosario Gennaro, Craig Gentry, and Bryan Parno. 2010. Non-interactive verifiable computing: Outsourcing computation to untrusted workers. In Proceedings of the Annual Conference on Advances in Cryptology (CRYPTO’10), 465--482. Google Scholar
Digital Library
- Rosario Gennaro, Craig Gentry, Bryan Parno, and Mariana Raykova. 2013. Quadratic span programs and succinct NIZKs without PCPs. In Proceedings of the Annual Conference on Advances in Cryptology (EUROCRYPT’13). 626--645.Google Scholar
Cross Ref
- Michael T. Goodrich, Roberto Tamassia, and Nikos Triandopoulos. 2011. Efficient authenticated data structures for graph connectivity and geometric search problems. Algorithmica 60, 3 (2011), 505--552.Google Scholar
Digital Library
- Jens Groth. 2016. On the size of pairing-based non-interactive arguments. In Proceedings of the Annual Conference on Advances in Cryptology (EUROCRPYPT’16). 305--326.Google Scholar
Cross Ref
- Ahmed E. Kosba, Dimitrios Papadopoulos, Charalampos Papamanthou, Mahmoud F. Sayed, Elaine Shi, and Nikos Triandopoulos. 2014. TRUESET: Faster verifiable set computations. In Proceedings of the USENIX Security Symposium 2014. 765--780. Google Scholar
Digital Library
- LEDA. 2017. LEDA library. Retrieved from http://www.algorithmic-solutions.com/leda/index.htm.Google Scholar
- Helger Lipmaa. 2013. Succinct non-interactive zero knowledge arguments from span programs and linear error-correcting codes. In Proceedings of the Annual Conference on Advances in Cryptology (ASIACRYPT’13). 41--60. Google Scholar
Digital Library
- Richard J. Lipton and Robert Endre Tarjan. 1979. A separator theorem for planar graphs. SIAM J. Appl. Math. 36, 2 (1979), 177--189.Google Scholar
Digital Library
- Ross M. McConnell, Kurt Mehlhorn, Stefan Näher, and Pascal Schweitzer. 2011. Certifying algorithms. Comput. Sci. Rev. 5, 2 (2011), 119--161. Google Scholar
Digital Library
- Silvio Micali. 2000. Computationally sound proofs. SIAM J. Comput. 30, 4 (2000), 1253--1298. Google Scholar
Digital Library
- Charalampos Papamanthou, Elaine Shi, Roberto Tamassia, and Ke Yi. 2013. Streaming authenticated data structures. In Proceedings of the Annual Conference on Advances in Cryptology (EUROCRYPT’13). 353--370.Google Scholar
Cross Ref
- Charalampos Papamanthou and Roberto Tamassia. 2007. Time and space efficient algorithms for two-party authenticated data structures. In Proceedings of 9th International Conference Information and Communications Security (ICICS'07). 1--15. Google Scholar
Digital Library
- Charalampos Papamanthou, Roberto Tamassia, and Nikos Triandopoulos. 2011. Optimal verification of operations on dynamic sets. In Proceedings of the Annual Conference on Advances in Cryptology (CRYPTO’11). 91--110. Google Scholar
Digital Library
- Bryan Parno, Jon Howell, Craig Gentry, and Mariana Raykova. 2013. Pinocchio: Nearly practical verifiable computation. In Proceedings of the IEEE Symposium on Security and Privacy (S8P’13). 238--252. Google Scholar
Digital Library
- Srinath Setty, Benjamin Braun, Victor Vu, Andrew J. Blumberg, Bryan Parno, and Michael Walfish. 2013. Resolving the conflict between generality and plausibility in verified computation. In Proceedings of the 8th ACM European Conference on Computer Systems. 71--84. Google Scholar
Digital Library
- Srinath T. V. Setty, Richard McPherson, Andrew J. Blumberg, and Michael Walfish. 2012. Making argument systems for outsourced computation practical (sometimes). In Proceedings of the Network and Distributed System Security Symposium, Vol. 1. 17.Google Scholar
- Roberto Tamassia. 2003. Authenticated data structures. In Proceedings of European Symposium on Algorithms, Vol. 2832. 2--5.Google Scholar
Cross Ref
- Roberto Tamassia and Nikos Triandopoulos. 2010. Certification and authentication of data structures. In Proceedings of the 4th Alberto Mendelzon International Workshop on Foundations of Data Management.Google Scholar
- Victor Vu, Srinath T. V. Setty, Andrew J. Blumberg, and Michael Walfish. 2013. A hybrid architecture for interactive verifiable computation. In Proceedings of the IEEE Symposium on Security and Privacy (S&P’’’13). 223--237. Google Scholar
Digital Library
- Riad S. Wahby, Srinath T. V. Setty, Zuocheng Ren, Andrew J. Blumberg, and Michael Walfish. 2015. Efficient RAM and control flow in verifiable outsourced computation. In Proceedings of the Network and Distributed System Security Symposium.Google Scholar
Cross Ref
- Man Lung Yiu, Yimin Lin, and Kyriakos Mouratidis. 2010. Efficient verification of shortest path search via authenticated hints. In Proceedings of the IEEE International Conference on Data Engineering (ICDE’10). 237--248.Google Scholar
Cross Ref
- Yupeng Zhang, Daniel Genkin, Jonathan Katz, Dimitrios Papadopoulos, and Charalampos Papamanthou. 2017. vSQL: Verifying arbitrary SQL queries over dynamic outsourced databases. In Proceedings of the IEEE Symposium on Security and Privacy (S8P’17). 863--880.Google Scholar
Cross Ref
- Y. Zhang, D. Genkin, J. Katz, D. Papadopoulos, and C. Papamanthou. 2018. vRAM: Faster verifiable RAM with program-independent preprocessing. In Proceedings of the IEEE Symposium on Security and Privacy (S8P’18). 203--220.Google Scholar
- Yupeng Zhang, Jonathan Katz, and Charalampos Papamanthou. 2017. An expressive (zero-knowledge) set accumulator. In Proceedings of the IEEE European Symposium on Security and Privacy (EuroS8P’17). 158--173.Google Scholar
Cross Ref
- Yupeng Zhang, Charalampos Papamanthou, and Jonathan Katz. 2014. Alitheia: Towards practical verifiable graph processing. In Proceedings of the 2014 ACM Conference on Computer and Communications Security. 856--867. Google Scholar
Digital Library
Index Terms
Verifiable Graph Processing
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