Paper 2019/1021

Recursive Proof Composition without a Trusted Setup

Sean Bowe, Jack Grigg, and Daira Hopwood


Non-interactive arguments of knowledge are powerful cryptographic tools that can be used to demonstrate the faithful execution of arbitrary computations with publicly verifiable proofs. Increasingly efficient protocols have been described in recent years, with verification time and/or communication complexity that is sublinear in the size of the computation being described. These efficiencies can be exploited to realize recursive proof composition: the concept of proofs that attest to the correctness of other instances of themselves, thereby allowing large computational effort to be incrementally verified. All previously known realizations of recursive proof composition have required a trusted setup and cycles of expensive pairing-friendly elliptic curves. We obtain and implement Halo, the first practical example of recursive proof composition without a trusted setup, using the discrete log assumption over normal cycles of elliptic curves. In the process we develop several novel techniques that may be of independent interest.

Available format(s)
Cryptographic protocols
Publication info
Preprint. MINOR revision.
recursive proofsincrementally verifiable computationzero knowledge
Contact author(s)
sean @ electriccoin co
2020-02-18: last of 2 revisions
2019-09-11: received
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Creative Commons Attribution


      author = {Sean Bowe and Jack Grigg and Daira Hopwood},
      title = {Recursive Proof Composition without a Trusted Setup},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1021},
      year = {2019},
      note = {\url{}},
      url = {}
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