Agent skill · research science · aiskillstore
air-cryptographer
This skill should be used when the user asks about "AIR", "algebraic intermediate representation", "ZK constraints", "trace design", "constraint soundness", "polynomial commitments", "FRI", "STARK", "lookup arguments", "permutation arguments", "memory consistency", "transition constraints", "boundary constraints", "vanishing polynomial", "quotient polynomial", "Fiat-Shamir", or needs expert-level cryptographic review of constraint systems.
Why this skill is useful
Provides expert-level guidance on designing and auditing AIRs in zero-knowledge proof systems, including specific constraints and polynomial mechanics that are not widely known.
What it needs
About 5k tokens when loaded. Last updated 2026-08-07. 405 stars on the source repository.
What this skill does
AIR Cryptographer Expertise Expert-level knowledge for designing, implementing, and auditing Algebraic Intermediate Representations (AIRs) in zero-knowledge proof systems. Core Mindset Soundness-first thinking: Every constraint review starts with "how could a cheater slip through?" Think adversarially. Construct counterexample traces by hand. Exploit polynomial identity loopholes. Algebraic precision: Constraints define solution spaces over finite fields. A missing constraint isn't just a bug—it's extra degrees of freedom for a malicious prover. Finite Field Foundations Essential intuitions: Characteristics and inverses: Every non-zero element has a multiplicative inverse. No zero divisors. Roots of unity: Multiplicative subgroups of order 2^k enable FFT-friendly evaluation domains. Extension fields: When you need more algebraic structure (e.g., M31 → QM31 for Stwo). Frobenius endomorphism: The map x → x^p is field-linear; crucial for extension field arithmetic. Polynomial Mechanics Interpolation: Given n points, unique polynomial of degree < n passes through them. Lagrange basis makes this explicit. Vanishing polynomials: ZH(x) = ∏(x - h) for h ∈ H vanishes exactly on domain H. This is the foundation of constraint enforcement. Degree behavior: Multiplication: deg(f·g) = deg(f) + deg(g) Composition: deg(f∘g) = deg(f) · deg(g) Low-degree testing verifies a function is "close to" a low-degree polynomial Evaluation domains: Multiplicative cosets for separation. Blowup factor determines security margin between trace degree and domain size. Trace Design Principles Column Classification Type Definition Example ------------------- ---------------------------- ---------------------------- Source of truth Canonical witness data PC, registers, memory values Derived Computed from source columns Flags, decompositions Auxiliary Added to reduce degree Intermediate products Critical rule: Every column must be constrained. An unconstrained column is a free variable for the prover. …
How to use it
Reference it in AdaL, Claude Code, Cursor or any coding agent — nothing to install:
@skills aiskillstore/air-cryptographer