Paper 2019/1076

Fractal: Post-Quantum and Transparent Recursive Proofs from Holography

Alessandro Chiesa, Dev Ojha, and Nicholas Spooner


We present a new methodology to efficiently realize recursive composition of succinct non-interactive arguments of knowledge (SNARKs). Prior to this work, the only known methodology relied on pairing-based SNARKs instantiated on cycles of pairing-friendly elliptic curves, an expensive algebraic object. Our methodology does not rely on any special algebraic objects and, moreover, achieves new desirable properties: it is *post-quantum* and it is *transparent* (the setup is public coin). We exploit the fact that recursive composition is simpler for SNARKs with *preprocessing*, and the core of our work is obtaining a preprocessing zkSNARK for rank-1 constraint satisfiability (R1CS) that is post-quantum and transparent. We obtain this latter by establishing a connection between holography and preprocessing in the random oracle model, and then constructing a holographic proof for R1CS. We experimentally validate our methodology, demonstrating feasibility in practice.

Available format(s)
Publication info
A major revision of an IACR publication in Eurocrypt 2020
succinct argumentsholographic proofsrecursive proof compositionpost-quantum cryptography
Contact author(s)
alexch @ berkeley edu
2020-07-15: last of 3 revisions
2019-09-23: received
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      author = {Alessandro Chiesa and Dev Ojha and Nicholas Spooner},
      title = {Fractal: Post-Quantum and Transparent Recursive Proofs from Holography},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1076},
      year = {2019},
      note = {\url{}},
      url = {}
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