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From FE Combiners to Secure MPC and Back

  • Prabhanjan AnanthEmail author
  • Saikrishna Badrinarayanan
  • Aayush Jain
  • Nathan Manohar
  • Amit Sahai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11891)

Abstract

Cryptographic combiners allow one to combine many candidates for a cryptographic primitive, possibly based on different computational assumptions, into another candidate with the guarantee that the resulting candidate is secure as long as at least one of the original candidates is secure. While the original motivation of cryptographic combiners was to reduce trust on existing candidates, in this work, we study a rather surprising implication of combiners to constructing secure multiparty computation protocols. Specifically, we initiate the study of functional encryption combiners and show its connection to secure multiparty computation.

Functional encryption (FE) has incredible applications towards computing on encrypted data. However, constructing the most general form of this primitive has remained elusive. Although some candidate constructions exist, they rely on nonstandard assumptions, and thus, their security has been questioned. An FE combiner attempts to make use of these candidates while minimizing the trust placed on any individual FE candidate. Informally, an FE combiner takes in a set of FE candidates and outputs a secure FE scheme if at least one of the candidates is secure.

Another fundamental area in cryptography is secure multi-party computation (MPC), which has been extensively studied for several decades. In this work, we initiate a formal study of the relationship between functional encryption (FE) combiners and secure multi-party computation (MPC). In particular, we show implications in both directions between these primitives. As a consequence of these implications, we obtain the following main results.
  • A two-round semi-honest MPC protocol in the plain model secure against up to \(n-1\) corruptions with communication complexity proportional only to the depth of the circuit being computed assuming learning with errors (LWE). Prior two round protocols based on standard assumptions that achieved this communication complexity required trust assumptions, namely, a common reference string.

  • A functional encryption combiner based on pseudorandom generators (PRGs) in \(\mathsf {NC}^1\). This is a weak assumption as such PRGs are implied by many concrete intractability problems commonly used in cryptography, such as ones related to factoring, discrete logarithm, and lattice problems [11]. Previous constructions of FE combiners, implicit in [7], were known only from LWE. Using this result, we build a universal construction of functional encryption: an explicit construction of functional encryption based only on the assumptions that functional encryption exists and PRGs in \(\mathsf {NC}^1\).

Keywords

Functional encryption Cryptographic combiners Multi-party computation 

Notes

Acknowledgements

We thank the anonymous TCC reviewers for their helpful comments.

Saikrishna Badrinarayanan, Aayush Jain, Nathan Manohar and Amit Sahai were supported in part from a DARPA/ARL SAFEWARE award, NSF Frontier Award 1413955, and NSF grant 1619348, BSF grant 2012378, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. Saikrishna Badrinarayanan is also supported by an IBM PhD fellowship. Aayush Jain is also supported by a Google PhD fellowship award in Privacy and Security. This material is based upon work supported by the Defense Advanced Research Projects Agency through the ARL under Contract W911NF-15-C- 0205. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, the U.S. Government, IBM, or Google.

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  • Prabhanjan Ananth
    • 1
    Email author
  • Saikrishna Badrinarayanan
    • 2
  • Aayush Jain
    • 2
  • Nathan Manohar
    • 2
  • Amit Sahai
    • 2
  1. 1.UCSBSanta BarbaraUSA
  2. 2.UCLALos AngelesUSA

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