remaindertoken

A remaindertoken is a cryptographic concept primarily found in zero-knowledge proof systems, particularly in SNARKs (Succinct Non-Interactive Arguments of Knowledge). Its purpose is to encode information about the "remainder" of a computation that might not fit entirely within the primary proof structure.

In the context of arithmetic circuits used in SNARKs, computations are broken down into a series of arithmetic gates. These gates operate on field elements. However, if a computation involves values that are larger than the prime field modulus used in the SNARK, a remainder operation is necessary. The remaindertoken is a mechanism to represent these remainders.

When a computation is performed using numbers larger than the field size, the result is typically the remainder after division by the field modulus. This remainder is then used in subsequent computations within the circuit. The remaindertoken effectively captures this remainder information, allowing the zero-knowledge proof to verify the correctness of the overall computation, including these modular arithmetic operations.

Without a way to represent these remainders, proofs involving computations with large numbers would be impossible to construct accurately within the constraints of a finite field. The remaindertoken ensures that the proof correctly accounts for the modular nature of the arithmetic operations being verified. It is a technical detail crucial for the integrity and completeness of certain types of zero-knowledge proofs.