(2026-08) Limber; Low Overhead SNARKs for Integers from Any PCS
2026-08-07
Non-native arithmetic is a key bottleneck in SNARK design. It introduces large overheads, and application designers often have to avoid it through the use of non-standard arithmetization friendly hash-functions or other means like elliptic curve cycles. Besides performance concerns, non-native circuit arithmetization is also a major cause of implementation errors. In a collection of 27 critical bugs in real world ZK systems (0xPARC/zkbugtracker), 9 were related to non-native arithmetization. We tackle these challenges by constructing a \emph{minimal overhead} SNARK for integer computation that generically handles non-native arithmetic. We follow the recipe of Zaratan (PKC 26), which proves an integer relation such as by fingerprinting—reducing it to the same relation but over a randomly sampled prime field. Realizing this recipe requires an integer mod-PCS that commits to integer polynomials and opens their evaluations modulo a random prime, which is crucially chosen after the underlying PCS's setup and commitment phases. Our central contribution is \emph{Limber}, the first practical integer mod-PCS construction that asymptotically has multiplicative commitment overhead and can be instantiated with any standard field polynomial commitment scheme, including ones over small fields. Combining Limber with a PIOP for integer R1CS over the random prime yields our SNARK. We demonstrate its practicality by implementing our scheme and showing that we can prove RSA arithmetic more than faster than prior circuit-based approaches.