Reinforced Concrete

Grassi, Lorenzo; Khovratovich, Dmitry; Lüftenegger, Reinhard; Rechberger, Christian; Schofnegger, Markus; Walch, Roman

doi:10.1145/3548606.3560686

Cited by 15 publications

(20 citation statements)

References 10 publications

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“…Thus, in an implementation to reduce the number of multiplicative constraints we are well advised to implement the equivalent circuit instead of the naive circuit. We also would like to note that the same trick was applied in Griffin [32] to reduce the number of constraints.…”

Section: Reducing the Number Of Constraintsmentioning

confidence: 99%

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Arion: Arithmetization-Oriented Permutation and Hashing from Generalized Triangular Dynamical Systems

Johann¹,

Trevisani²

2023

Preprint

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In this paper we propose the (keyed) permutation Arion and the hash function ArionHash over Fp for odd and particularly large primes. The design of Arion is based on the newly introduced Generalized Triangular Dynamical System (GTDS), which provides a new algebraic framework for constructing (keyed) permutation using polynomials over a finite field. At round level Arion is the first design which is instantiated using the new GTDS. We provide extensive security analysis of our construction including algebraic cryptanalysis (e.g. interpolation and Gröbner basis attacks) that are particularly decisive in assessing the security of permutations and hash functions over Fp. From a application perspective, ArionHash is aimed for efficient implementation in zkSNARK protocols and Zero-Knowledge proof systems. For this purpose, we exploit that CCZ-equivalence of graphs can lead to a more efficient implementation of Arithmetization-Oriented primitives. We compare the efficiency of ArionHash in R1CS and Plonk settings with other hash functions such as Poseidon, Anemoi and Griffin. For demonstrating the practical efficiency of ArionHash we implemented it with the zkSNARK libraries libsnark and Dusk Network Plonk. Our result shows that ArionHash is significantly faster than Poseidon -a hash function designed for zero-knowledge proof systems. We also found that an aggressive version of ArionHash is considerably faster than Anemoi and Griffin in a practical zkSNARK setting.

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Section: Reducing the Number Of Constraintsmentioning

confidence: 99%

“…Gen I: LowMC [3], MiMC [2] Gen II: Hades [35], Neptune & Poseidon [34], GMiMC [1], Rescue-Prime [4] Gen III: Reinforced Concrete [33], Griffin [32], Anemoi [15], Arion (this paper)…”

Section: Introductionmentioning

confidence: 99%

Arion: Arithmetization-Oriented Permutation and Hashing from Generalized Triangular Dynamical Systems

Johann¹,

Trevisani²

2023

Preprint

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show abstract

“…For the commitment scheme, we used Pedersen commitment [29]. We used Poseidon as the Merkle tree hash function because it can efficiently compute hashes of 2 elements at once [14]. We implemented MiMC as the primary hash function as well as PRF due to its low multiplicative complexity [3].…”

Section: Chapter 7 Implementationmentioning

confidence: 99%

“…Specifically, we use Ed25519 curve of order 2 255 − 19 for zero-knowledge proofs based on Bulletproofs. We use standard Poseidon Hash parameters for the Merkle tree including width t = 6, full rounds R F = 8 and partial rounds R p = 130 [14]. We use MiMC hash function with rate 512 and capacity 513.…”

Section: Chapter 8 Experimentsmentioning

confidence: 99%

“…system for checking set membership is more complicated compared to that of the other gadgets. Specifically, it requires proving and verifying (in zero-knowledge) d = 64 Poseidon hash pre-images, each of which incurs 3 × t × R F + 3 × R p = 534 number of multiplication constraints[14].that is needed for the backend zero-knowledge proof (i.e., Bulletproofs), which takes around 1.5 seconds in total. Without CRS, the proving and verification time for Store operation is 0.35 seconds and 85 milliseconds, respectively, which are about 60 times lesser than Assign, Share and Access.…”

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confidence: 99%

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