By which to Rule Them All

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Closing the lattice subseries by separating proof-level security from implementation-level fragility across ML-KEM, ML-DSA, Falcon, and real attack surfaces.

Reread: Bad Agent:

Inserting and Activating Backdoor Attacks in LLM Agents

References: https://github.com/DPamK/BadAgent

keyword ⛵ : Backdoor Attacks; LLM Agents; Data Poisoning; ASR; FSR; Mind2Web

Reading: Peikert’s survey as the wide-angle frame[^peikert-survey], Albrecht-Player-Scott for concrete-LWE attack modeling[^aps], Chen-Nguyen for BKZ quality heuristics[^cn11], the Homomorphic Encryption Standard for published parameter-table practice[^he-standard], and the LWE Estimator for the operational interface between these papers and actual numbers[^estimator].

Parts 0-3 fixed the geometric vocabulary: bases, reduced bases, SVP/CVP, cosets, and short modular witnesses. A deployed lattice scheme then adds concrete parameters such as dimension, modulus, secret distribution, error distribution, and sample count. None of those symbols, by itself, proves that one parameter set costs an attacker $2^{128}$ steps. That last sentence is not a theorem output. It is an attacker model layered on top of the theorem.

So this chapter stays on the attacker side of the interface. The real objects are primal attacks, dual attacks, BKZ block size, root-Hermite factor, and the estimator-style chain that turns $(n,q,\chi,k,m)$ into a work factor only after a long list of modeling decisions has been fixed.

This chapter therefore separates asymptotic hardness claims from concrete parameter-setting practice. It defines primal and dual attack viewpoints clearly, then uses concrete security estimation and attack-cost modeling to map parameter choices to attack-cost estimates.

In that exact sense, the goal is to connect BKZ quality assumptions to concrete lattice-scheme security reasoning rather than to repeat a security badge from the reduction side.

From lattice trapdoors to identity-derived keys, hierarchical delegation, attribute policies, and function-restricted decryption.