The Goldilocks field as a standalone Rust crate. Provides field arithmetic (add, sub, mul, inv, eq, lt) and NTT over roots of unity in $\mathbb{F}_p$ where $p = 2^{64} - 2^{32} + 1$.
nebu is the foundational primitive for the entire cyber computational stack. hemera consumes it for hashing, nox consumes it for VM execution, trident consumes it for compilation, and GFP accelerates it in hardware.
scope
Six field operations matching nox Layer 1 arithmetic patterns:
| op | definition |
|---|---|
| add | $(a + b) \bmod p$ |
| sub | $(a - b) \bmod p$ |
| mul | $(a \times b) \bmod p$ |
| inv | $a^{p-2} \bmod p$ (Fermat) |
| eq | equality test |
| lt | ordering test |
Plus NTT — the Number Theoretic Transform over $2^{32}$ roots of unity that $p - 1 = 2^{32}(2^{32} - 1)$ provides. Used by stark proofs, TFHE polynomial rings, and hemera permutations.
Extension fields F_p², F_p³, F_p⁴ for algebraic operations that require higher degree. 7-byte absorption rate for constant-time stream processing.
dependency graph
nebu (field)
↓
hemera (hash)
↓
nox (VM)