Poseidon: A New Hash Function for Zero-Knowledge Proof Systems

Lorenzo Grassi, Dmitry Khovratovich, Christian Rechberger, Arnab Roy, Markus Schofnegger*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paper


The area of practical computational integrity proof systems, like SNARKs, STARKs, Bulletproofs, is seeing a very dynamic development with several constructions having appeared recently with improved properties and relaxed setup requirements. Many use cases of such systems involve, often as their most expensive apart, proving the knowledge of a preimage under a certain cryptographic hash function, which is expressed as a circuit over a large prime field. A notable example is a zero-knowledge proof of coin ownership in the Zcash cryptocurrency, where the inadequacy of the SHA-256 hash function for such a circuit caused a huge computational penalty.

In this paper, we present a modular framework and concrete instances of cryptographic hash functions which work natively with GF(p) objects. Our hash function Poseidon uses up to 8x fewer constraints per message bit than Pedersen Hash.

Our construction is not only expressed compactly as a circuit, but can also be tailored for various proof systems using specially crafted polynomials, thus bringing another boost in performance. We demonstrate this by implementing a 1-out-of-a-billion membership proof with Merkle trees in less than a second by using Bulletproofs.
Original languageEnglish
Title of host publicationProceedings of the 30th USENIX Security Symposium
PublisherUSENIX Association
Publication statusAccepted/In press - 2020
Event30th USENIX Security Symposium - Virtuell, Canada
Duration: 11 Aug 202113 Aug 2021


Conference30th USENIX Security Symposium
Abbreviated titleUSENIX Security '21


  • snark
  • stark
  • bulletproofs
  • hash
  • zkp


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