Covers integers, divisibility, prime numbers, congruences, modular inverses, and the Chinese remainder theorem. These tools support later work with classical and post-quantum algorithms.

Develops probability, entropy, uniform sampling, pseudorandomness, and secure random number generation. Practical work compares safe key generation with biased or predictable randomness.

Introduces algorithms, runtime, polynomial and exponential growth, computational hardness, and security levels. Learners estimate how key sizes and attack costs change as computing power grows.

Covers hash functions, message authentication codes, block and stream ciphers, authenticated encryption, and key derivation. Exercises use established libraries to protect data and detect tampering.

Explains one-way functions, trapdoors, RSA, Diffie–Hellman, elliptic-curve cryptography, and the assumptions behind classical public-key systems. Small examples show why public and private keys can support secure communication.

Distinguishes encryption, key encapsulation mechanisms, digital signatures, certificates, and authenticated key exchange. Learners trace how keys move through a realistic secure connection.

Covers indistinguishability, chosen-plaintext and chosen-ciphertext attacks, existential forgery, random oracles, reductions, and composability. Learners practice stating what a construction promises and what an attacker may do.

Traces public-key cryptography from early proposals through quantum algorithms, the first post-quantum families, the NIST competition, and current standardization. It connects design changes and broken proposals to the systems used today.

Explains qubits, superposition, interference, quantum circuits, and the difference between theoretical and fault-tolerant quantum computers. No prior physics is assumed.

Shows how Shor’s algorithm threatens factoring and discrete logarithms, while Grover’s algorithm changes symmetric-key security more modestly. Resource estimates and “harvest now, decrypt later” scenarios turn the threat into practical risk decisions.

Separates post-quantum cryptography from quantum key distribution and quantum random-number generation. Learners compare their assumptions, infrastructure needs, failure modes, and appropriate use cases.

Covers vectors, matrices, norms, bases, determinants, and geometric reasoning in high-dimensional spaces. Exercises prepare learners to read lattice constructions and implementation code.

Introduces integer lattices, shortest and closest vector problems, basis quality, Gaussian distributions, and lattice reduction. Learners use small-dimensional examples to see why easy-to-state lattice problems can be hard to solve.

Develops Learning With Errors, Ring-LWE, Module-LWE, Short Integer Solution, and Module-SIS. It connects noisy linear equations to encryption, key encapsulation, signatures, and security reductions.

Covers polynomials, quotient rings, finite fields, number-theoretic transforms, and modular polynomial multiplication. Practical exercises implement small polynomial operations used by high-performance PQC schemes.

Explains NTRU-style constructions, structured lattices, module lattices, compression, and reconciliation. Learners compare the efficiency and security tradeoffs of major lattice design approaches.

Covers ML-KEM, formerly CRYSTALS-Kyber, from key generation and encapsulation through decapsulation and rejection behavior. Learners work with standardized parameter sets, serialized keys, test vectors, and a real library API.

Covers ML-DSA, formerly CRYSTALS-Dilithium, including Fiat–Shamir with aborts, sampling, hints, verification, and parameter sets. Exercises sign and verify artifacts while checking encoding and failure handling.

Covers FN-DSA, derived from Falcon, including NTRU lattices, trapdoor sampling, compact signatures, and floating-point implementation risks. Learners compare its performance and engineering demands with ML-DSA.

Builds hash-based signatures from one-time signatures, Merkle trees, hypertrees, and stateless constructions. Learners calculate signature sizes and trace authentication paths by hand and in code.

Covers SLH-DSA, formerly SPHINCS+, including WOTS+, FORS, hypertrees, address formats, and parameter choices. Practical work verifies standardized signatures and measures their size and runtime.

Covers LMS and XMSS, their state-management requirements, hierarchical variants, and operational failure modes. Learners design a signing process that prevents dangerous one-time-key reuse.

Introduces linear codes, generator and parity-check matrices, Hamming distance, syndromes, decoding, and the hardness of random-code decoding. Small exercises encode messages, inject errors, and recover valid codewords.

Covers the McEliece framework, Goppa codes, key generation, decoding, security history, and the large-public-key tradeoff. Learners inspect Classic McEliece parameter sets and message flows.

Covers the Hamming Quasi-Cyclic construction, its decoding problem, ciphertext structure, failure analysis, and selection as an additional NIST KEM. Learners compare HQC with ML-KEM and Classic McEliece for deployment planning.

Explains multivariate quadratic systems, oil-and-vinegar designs, rank and differential attacks, and the failures of major signature candidates. The chapter shows how structural cryptanalysis can overturn attractive performance claims.

Covers MPC-in-the-head proofs, Fiat–Shamir signatures, Picnic-style designs, and their reliance on symmetric primitives. Learners trace a small proof transcript and compare conservative assumptions with signature size.

Explains elliptic-curve isogenies, supersingular curves, SIDH and SIKE, then reconstructs the attack that broke SIDH-based security. The case develops judgment about immature assumptions and rapid cryptanalytic change.

Covers classical and quantum attack models, lattice reduction cost estimates, decoding attacks, hash attacks, multi-target effects, and security margins. Learners compare claimed NIST levels without treating key length as the only measure.

Shows how timing, cache behavior, branches, memory access, power use, electromagnetic leakage, and fault injection can expose secret data. Practical work reviews constant-time patterns and tests implementations for timing variation.

Covers rejection sampling, decapsulation failures, malformed inputs, implicit rejection, oracle attacks, and strict serialization rules. Learners harden parsers and error paths that are often more vulnerable than the underlying mathematics.

Addresses entropy sources, deterministic derivation, key generation ceremonies, secure storage, rotation, backup, destruction, and compromised-key response. It also handles the unusually large keys and signatures of some PQC schemes.

Uses reference implementations, liboqs, OpenSSL providers, and language bindings to generate keys, encapsulate secrets, and create signatures. Learners build a small interoperable application without implementing production cryptography from scratch.

Covers known-answer tests, negative tests, fuzzing, differential testing, interoperability suites, and validation against standards. Learners build a test harness that catches malformed encodings, corrupted ciphertexts, and incompatible parameter choices.

Examines memory use, bandwidth, latency, vectorization, number-theoretic transforms, batching, and hardware acceleration. Learners benchmark schemes fairly and choose optimizations without weakening constant-time behavior.

Explains hybrid key exchange and hybrid signatures that combine classical and post-quantum algorithms. Learners design downgrade-resistant negotiation, combiner logic, versioning, and failure behavior.

Covers post-quantum and hybrid key exchange in TLS, including handshake size, certificate effects, fragmentation, negotiation, and operational telemetry. Practical work captures and analyzes a PQ-enabled TLS connection.

Applies PQC to SSH, IPsec, VPNs, secure messaging, and service-to-service authentication. Learners map KEMs and signatures onto protocol roles while accounting for compatibility and packet-size limits.

Covers certificate formats, certificate authorities, trust chains, revocation, algorithm identifiers, composite certificates, and long-lived roots. Learners plan how a public-key infrastructure can change algorithms without breaking identity or trust.

Applies post-quantum signatures to software releases, firmware, containers, package repositories, secure boot, and long-term archives. Learners design an update chain that remains verifiable across algorithm transitions.

Addresses constrained processors, smart cards, hardware security modules, trusted execution environments, and embedded devices. Learners evaluate whether key size, RAM, execution time, side-channel defenses, and updateability fit a target platform.

Covers cryptographic bills of materials, protocol discovery, certificate inventories, data-retention periods, dependency mapping, and quantum-risk prioritization. Learners produce an inventory that exposes hidden RSA and elliptic-curve dependencies.

Develops algorithm abstraction, versioned formats, negotiable protocols, replaceable trust anchors, and safe rollback policies. A practical design exercise turns a rigid cryptographic system into one that can survive future algorithm changes.

Covers NIST FIPS 203, 204, and 205; the continuing NIST process; IETF protocol work; ISO and ETSI activity; and government transition profiles such as CNSA 2.0. Learners identify which documents govern an algorithm, an implementation, and a deployment.

Examines threat modeling, third-party risk, export and procurement constraints, assurance evidence, incident response, and the limits of long-term confidentiality claims. Learners turn technical uncertainty into reviewable organizational decisions.

Follows a real migration from executive mandate and cryptographic inventory through risk ranking, algorithm selection, prototyping, interoperability testing, staged rollout, monitoring, rollback, and retirement. The final deliverables include an architecture, test evidence, migration plan, and operational runbook.

Covers cryptographic engineering, protocol design, implementation security, cryptanalysis, standards work, auditing, and migration consulting. It identifies entry paths, portfolio artifacts, relevant certifications, open-source contribution routes, and reliable ways to track new standards and attacks.