Paper 2026/1656

BinarySpartan: Spartan over binary fields

Abstract

Spartan is a SNARK for R1CS that can be instantiated with any multilinear polynomial commitment scheme. We instantiate Spartan over a binary field, using Ligerito as the commitment scheme along with the ring-switching technique of Diamond and Posen; we refer to the instantiation as BinarySpartan. It is transparent, so it requires no trusted setup, and it provides polylogarithmic-sized proofs. Its security rests on a hash function, so it is plausibly post-quantum secure. We apply well-known optimizations to Spartan and sum-check. We implement and evaluate BinarySpartan end to end. On a MacBook Pro M4 Max (using only its 12 performance cores, and without GPU/Metal acceleration), BinarySpartan proves BLAKE3 at 872,000 hashes/second, SHA-256 at 401,000 hashes/second, and Keccak-f at 287,000 permutations/second, including witness generation. All three clear the 200,000 hashes/second rate proposed as sufficient for a post-quantum Ethereum transition, as well as the roughly 37,000–180,000 hashes/second a possible post-quantum Bitcoin transition would require. At comparable security, BinarySpartan is 16.3–37.8× faster than Plonky3, 6.3–15.7× faster than Binius64, and 4.0× faster than Hashcaster, which only supports Keccak. On all three hash functions, BinarySpartan’s peak throughput matches or exceeds that of Flock, the prior state-of-the-art system. On BLAKE3 and Keccak, BinarySpartan also reaches those rates on far less memory: Flock needs 1.9× and 5.3× more to reach its own best rates. We also evaluate BinarySpartan on the Ethereum Foundation’s client-side proving benchmark, where it proves a single SHA-256 of a 2 KiB message in 6.2 ms, the fastest in the suite and 4.2× faster than Flock.