Foundations

Cryptographic primitives serve distinct security properties.

A signing key and a verification key have different roles.

Reduction direction determines which impossibility transfers.

Polynomial solving and polynomial verification differ.

NP-completeness combines verification and reduction hardness.

Random choices permit a stated probability of error.

NIST's project page, updated 5 August 2026 and checked 10 October, lists FIPS 203 ML-KEM, FIPS 204 ML-DSA and FIPS 205 SLH-DSA as final standards published 13 August 2024.

FIPS 203 ML-KEM uses module-LWE-based public-key structure and a key-encapsulation transformation targeting IND-CCA2 security.

FIPS 204 ML-DSA standardizes the Dilithium-derived module-lattice signature design, with ML-DSA-44/65/87 at security categories 2/3/5.

SLH-DSA is a stateless hash-based signature design, while ML-DSA uses module-lattice structure.

A migration inventory must identify long-lived confidential data, key establishment versus signatures, protocol/certificate formats and parameter/revision dependencies.

In an indistinguishability experiment, an efficient adversary selects equal-length messages and receives an encryption of one chosen by a hidden random bit.

Adaptive chosen-ciphertext security allows decryption queries before and after a challenge, excluding the challenge ciphertext itself under the experiment's rules.

Existential unforgeability under chosen-message attack requires that an efficient adversary with a tagging oracle cannot produce a valid tag for a new message with more than negligible probability.

EUF-CMA signature security gives an adversary a public verification key and signing oracle, then tests whether it can produce a valid signature on a previously unsigned message.

A reduction turns a successful scheme attacker into an attacker on a stated assumption, with explicitly related time, query count and success probability.

A proof in a black-box encryption or signature game typically exposes specified outputs and oracles, not secret-dependent timing, power, cache traces or fault responses.