About Finite Fields
RISC Zero's computational receipts are built by converting an assertion of computational integrity into an assertion about polynomials over finite fields. This document serves as a minimal introduction to finite fields, targeted at folks who have some exposure to modular arithmetic and who are curious to learn more about the math and cryptography behind RISC Zero.
Finite Fields 101: Reciprocals, Exponents, and Generators
Loosely speaking, a field is a set of elements for which addition, subtraction, multiplication, and division work cleanly.
Here's what we mean by division working cleanly: for any field element , we should be able to find a field element