What problem does it solve?
This Skill helps you mount lattice-based cryptanalytic attacks to recover hidden cryptographic values (such as RSA small roots/exponents, DSA/ECDSA biased nonce secrets, and knapsack/NTRU solutions) when algebraic methods alone are insufficient or mislead a model.
Core Features & Use Cases
- LLL/BKZ reduction guidance: Choose the right lattice reduction strategy and parameters (e.g., start with LLL, escalate to BKZ with tuned block sizes) to obtain useful short vectors.
- Coppersmith small-roots playbooks: Apply univariate and partial/exposure variants using correct bounds (X) and heuristic parameters (beta/epsilon) to recover RSA-related unknowns.
- Hidden Number Problem (HNP) for nonce recovery: Build the CVP-style lattice from biased nonce signatures and solve it with reduction to recover DSA/ECDSA private keys.
- Knapsack and NTRU lattice attacks: Use low-density lattice embedding for subset sum and construct NTRU lattices for short-key recovery via reduction.
- Common pitfalls & decision tree: Diagnose failure modes like wrong scaling, incorrect beta, insufficient dimension, or too-large root bounds.
Quick Start
Ask your AI agent: "Given RSA parameters n and e plus a ciphertext c and the known MSB bits of the plaintext, use the lattice/Coppersmith method from lattice-crypto-attacks to recover the missing message bits, explaining the parameter choices and verification steps."
