Abstract
Garbled RAM (GRAM) is a powerful technique introduced by Lu and Ostrovsky that equips Garbled Circuit (GC) with a sublinear cost RAM without adding rounds of interaction. While multiple GRAM constructions are known, none are suitable for practice, due to costs that have high constants and poor scaling.
We present the first GRAM suitable for practice. For computational security parameter \(\kappa \) and for a size-n RAM that stores blocks of size \(w = \varOmega (\log ^2n)\) bits, our GRAM incurs amortized \(O(w \cdot \log ^2 n \cdot \kappa )\) communication and computation per access. We evaluate the concrete cost of our GRAM; our approach outperforms trivial linear-scan-based RAM for as few as 512 128-bit elements.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
Recursive index/position maps are typical in ORAM constructions, see e.g. [SvS+13].
- 3.
I.e. reads and writes to the lowest level underlying data structure, where access patterns are visible to \(E\).
- 4.
To be pedantic, if we account for recursively instantiated index maps, each map incurs this constant number of unpredictable reads, so there are total a logarithmic number of unpredictable reads.
- 5.
References
Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 2012, pp. 784–796. ACM Press, October 2012
Canetti, R., Chen, Y., Holmgren, J., Raykova, M.: Adaptive succinct garbled RAM or: how to delegate your database. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 61–90. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53644-5_3
Canetti, R., Holmgren, J.: Fully succinct garbled RAM. In: Sudan, M., (ed.) ITCS 2016, pp. 169–178. ACM, January 2016
Choi, S.G., Katz, J., Kumaresan, R., Zhou, H.-S.: On the security of the “Free-XOR’’ technique. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 39–53. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_3
Gentry, C., Halevi, S., Steve, L., Ostrovsky, R., Raykova, M., Wichs, D.: Garbled RAM revisited. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 405–422. Springer, Heidelberg (2014)
Guo, C., Katz, J., Wang, X., Yu, Y.: Efficient and secure multiparty computation from fixed-key block ciphers. In: 2020 IEEE Symposium on Security and Privacy, pp. 825–841. IEEE Computer Society Press, May 2020
Garg, S., Lu, S., Ostrovsky, R.: Black-box garbled RAM. In: Guruswami, V. (ed.) 56th FOCS, pp. 210–229. IEEE Computer Society Press, October 2015
Garg, S., Lu, S., Ostrovsky, R., Scafuro, A.: Garbled RAM from one-way functions. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, pp. 449–458. ACM Press, June 2015
Garg, S., Ostrovsky, R., Srinivasan, A.: Adaptive garbled RAM from laconic oblivious transfer. Cryptology ePrint Archive, Report 2018/549 (2018). https://eprint.iacr.org/2018/549
Heath, D., Kolesnikov, V.: PrORAM: Fast \({O}(\log n)\) private coin ZK ORAM (2021)
Kolesnikov, V., Schneider, T.: Improved garbled circuit: free XOR gates and applications. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 486–498. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70583-3_40
Steve, L., Ostrovsky, R.: How to garble RAM programs. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 719–734. Springer, Heidelberg (2013)
Steve, L., Ostrovsky, R.: Black-box parallel garbled RAM. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. Part II, volume 10402 of LNCS, pp. 66–92. Springer, Heidelberg (2017)
Rosulek, M., Roy, L.: Three halves make a whole? beating the half-gates lower bound for garbled circuits. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12825, pp. 94–124. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84242-0_5
Stefanov, E., et al.: Path ORAM: an extremely simple oblivious RAM protocol. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) ACM CCS 2013, pp. 299–310. ACM Press, November 2013
Waksman, A.: A permutation network. J. ACM 15(1), 159–163 (1968)
Xiao Wang, T.-H. Chan, H., Shi, E.: Circuit ORAM: On tightness of the Goldreich-Ostrovsky lower bound. In: Ray, I., Li, N., Kruegel, C. (eds.) ACM CCS 2015, pp. 850–861. ACM Press, October 2015
Zahur, S., Evans, D.: Circuit structures for improving efficiency of security and privacy tools. In: 2013 IEEE Symposium on Security and Privacy, pp. 493–507. IEEE Computer Society Press, May 2013
Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole - reducing data transfer in garbled circuits using half gates. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 220–250. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_8
Acknowledgements
This work was supported in part by NSF award #1909769, by a Facebook research award, a Cisco research award, and by Georgia Tech’s IISP cybersecurity seed funding (CSF) award. This material is also based upon work supported in part by DARPA under Contract No. HR001120C0087. Work of the third author is supported in part by DARPA under Cooperative Agreement HR0011-20-2-0025, NSF grant CNS-2001096, US-Israel BSF grant 2015782, Google Faculty Award, JP Morgan Faculty Award, IBM Faculty Research Award, Xerox Faculty Research Award, OKAWA Foundation Research Award, B. John Garrick Foundation Award, Teradata Research Award, Lockheed-Martin Research Award and Sunday Group. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of DARPA, the Department of Defense, or the U.S. Government. Distribution Statement “A” (Approved for Public Release, Distribution Unlimited). The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes not withstanding any copyright annotation therein.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 International Association for Cryptologic Research
About this paper
Cite this paper
Heath, D., Kolesnikov, V., Ostrovsky, R. (2022). EpiGRAM: Practical Garbled RAM. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13275. Springer, Cham. https://doi.org/10.1007/978-3-031-06944-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-031-06944-4_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-06943-7
Online ISBN: 978-3-031-06944-4
eBook Packages: Computer ScienceComputer Science (R0)
