# Math Cryptography

> Analyse cryptographic constructions — symmetric, asymmetric, hashing, MACs, zero-knowledge — with security reductions, hardness assumptions, and attack analysis.

- Skill: `quantumquirkxyz/math-cryptography` (Agent Skill)
- Install (CLI): `npx skillmds@latest add quantumquirkxyz/math-cryptography`
- Raw SKILL.md: https://api.skillmd.com/api/skills/quantumquirkxyz/math-cryptography/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Security
- Author: quantumquirkxyz (https://skillmd.com/u/quantumquirkxyz)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/quantumquirkxyz/math-cryptography

---


## Contract

- **Input:** problem description and inputs defined by the skill body.
- **Output:** Markdown artifact with completed process steps.
- **Side effects:** none.
- **Dependencies:** none.
- **Stop condition:** all process steps executed; artifact saved with required sections.
- **Risk:** low.
- **Boundary:** produces reasoning artifact only; no system changes.


# Cryptographic Analysis

Analyse or design a **cryptographic construction** with explicit hardness assumptions, security reductions, and attack analysis.

## When to use

- The user wants a cryptographic protocol reviewed or designed.
- A security-critical component needs formal analysis.
- Key exchange, signatures, MACs, encryption, or ZK proofs are involved.

## Process

1. Identify the primitive type — symmetric encryption (block ciphers, stream ciphers), asymmetric (RSA, ECC, lattice-based), hash (collision-resistant, preimage), MAC / HMAC, signatures, key exchange, ZK proofs.
2. State hardness assumptions — DLP, CDH, DDH, RSA,factoring, LWE, SIS; quantify security level in bits.
3. Security goal — IND-CPA, IND-CCA, EUF-CMA, collision resistance, etc.
4. Attack analysis — birthday (hash), meet-in-the-middle, side-channel, replay, forward secrecy, oracle attacks.
5. Protocol design — if designing: use a well-known construction; do not invent primitives. Specify parties, messages, randomness sources, and secrets.
6. Deliver — artifact: primitive, hardness assumption, security goal, attack surface, and a security verdict (strong / moderate / weak / broken).