Daniel Lubarov

Paper 2023/824 Reed-Solomon Codes over the Circle Group , Polygon Labs Abstract In this note we discuss Reed-Solomon codes with domain of definition within the unit circle of the complex extension $\mathbb C(F)$ of a Mersenne prime field $F$. Within this unit circle the interpolants of “real”, i.e. $F$-valued, functions are again almost real, meaning that their values can be rectified to a real representation at almost no extra cost.

Paper 2022/1470 Casting out Primes: Bignum Arithmetic for Zero-Knowledge Proofs , Polygon Zero , Polygon Hermez Abstract We describe a nondeterministic method for bignum arithmetic. It is inspired by the "casting out nines" technique, where some identity is checked modulo 9, providing a probabilistic result. More generally, we might check that some identity holds under a set of moduli, i.e. $f(\vec{x}) = 0 \mod m_i$ for each $m_i \in M$.

Paper 2022/1050 RapidUp: Multi-Domain Permutation Protocol for Lookup Tables , Universitat Politècnica de Catalunya , Polygon Hermez , Mir Protocol , Universitat Politècnica de Catalunya SNARKs for some standard cryptographic primitives tend to be plenty designed with SNARK-unfriendly operations such as XOR. Previous protocols such as [GW20] worked around this problem by the introduction of lookup arguments. However, these protocols were only appliable over the same circuit.