Technical Fundamentals & Core Skills Topics
Core technical concepts including algorithms, data structures, statistics, cryptography, and hardware-software integration. Covers foundational knowledge required for technical roles and advanced technical depth.
Number Theory and Mathematical Foundations of Cryptography
The classical mathematics underpinning cryptographic hardness assumptions: modular arithmetic, prime generation and primality testing, the structure of the discrete logarithm and integer factorization problems, group and finite field theory, elliptic curve arithmetic, and pairings and bilinear groups. Covers deriving why a scheme's underlying hard problem is believed hard, the classical algorithms (index calculus, the Number Field Sieve, Pollard's rho, baby step giant step, BKZ) used to estimate its concrete difficulty as an input to parameter sizing, and how that difficulty maps to classical parameter sizes (RSA moduli, DH/DSA group sizes, EC curve sizes, pairing group balance). Every question should ground the math in an actual cryptographic scheme (RSA, Diffie-Hellman, (EC)DSA/Schnorr, ECC, or a primality testing pipeline), not bare textbook number theory. Distinct from the constructive lattice-, code-, and multivariate-based post-quantum schemes and their concrete-security estimation, which post-quantum-and-lattice-cryptography owns; this topic retains a small set of foundational lattice-object definitions (a lattice and its basis, the Gaussian heuristic, BKZ's root-Hermite relation, NTRU decryption-failure bounds, discrete-Gaussian sampler proofs, new-assumption vetting methodology) and the isogeny hardness assumption that the closed topic's own curation does not ship, kept here rather than deleted, plus a three-question footnote on why Shor collapses these classical assumptions together. Also distinct from formal security-reduction proofs and cryptanalytic attack methodology, owned by cryptanalysis-and-security-proofs. The theory layer distinguishing a cryptographer from a library user.
Post-Quantum and Lattice-Based Cryptography
Cryptography designed to resist quantum attacks: lattice-based schemes, the underlying hard problems (LWE, SIS), and the mathematics of post-quantum standards. Covers why current public-key schemes are vulnerable to quantum algorithms and how migration candidates work. A specialized, forward-looking cryptography area.
Symmetric Encryption and Block Ciphers
How symmetric-key primitives are constructed and why they work: block-cipher internals (Feistel networks vs substitution-permutation networks, the AES round structure and S-box design, key schedules and why a weak one degrades security), stream ciphers (ChaCha20 and CTR-mode keystream generation), and the internal mechanics of modes of operation (ECB, CBC, CTR, XTS, GCM), including why some are parallelizable, why ECB leaks structure, and why some require a unique nonce. Covers authenticated encryption construction internals (how GHASH and Poly1305 work, why nonce reuse breaks their security algebraically, formal security notions like IND-CPA and INT-CTXT), padding schemes and the mechanics of padding-oracle attacks, and cryptanalysis of block ciphers (differential and linear cryptanalysis, reduced-round attacks). This is the design and internals layer: how these primitives are built and proven secure, distinct from choosing which algorithm or mode to deploy, managing key lifecycle and rotation, or architecting data protection for a system, which belong to the applied cryptography layer.
Cryptography Fundamentals
Core concepts and vocabulary of cryptography: confidentiality, integrity, authentication, and non-repudiation; the difference between symmetric and asymmetric primitives; and how standard algorithms, libraries, and protocols fit together. Covers threat models, common standards, and applying primitives and cryptographic libraries correctly to real-world security problems. The entry point for the cryptography track.
Asymmetric Encryption and Key Exchange
The construction and mathematics-adjacent mechanics of public-key (asymmetric) cryptography: how RSA, Diffie-Hellman, and elliptic-curve schemes actually work, including the group law and point-arithmetic formulas, scalar-multiplication algorithms (double-and-add, Montgomery ladder, windowed methods, GLV, multi-scalar batching), curve models and coordinate systems, and the hardness assumptions (integer factorization, discrete log, ECDLP) each scheme rests on. Covers key-establishment and authenticated key-exchange protocol design: forward-secrecy mechanics, key confirmation, downgrade protection, key-derivation and context binding, group and multi-party key agreement, and hybrid classical/post-quantum key-exchange composition. Also covers implementation-level attacks against these primitives and their mitigations: timing and side-channel leakage in modular exponentiation and scalar multiplication, invalid-curve and small-subgroup attacks, fault attacks, and padding-oracle attacks. Distinct from selecting, deploying, and operating these primitives in production: PKI certificate lifecycle, CA hierarchy, revocation, and key storage and rotation belong to applied cryptography and key management.
Hashing and Hash Tables
How hash tables and hash-based structures work internally, and how to reason about their performance and correctness. Covers hash function properties (determinism, uniform distribution, speed, avalanche effect), cryptographic versus non-cryptographic hash choices, collision resolution (separate chaining, open addressing: linear probing, quadratic probing, double hashing, Robin Hood hashing, cuckoo hashing), load factor and amortized-cost resizing, and what makes an object hashable (the __hash__/__eq__ contract, immutability, custom composite keys). Covers hash-map-backed cache design (LRU and LFU eviction, TTL) and thread-safe concurrent hash maps (lock striping, CAS-based updates, safe concurrent resizing). Also covers hash-based structures beyond arrays and strings: consistent hashing for distributed routing and sharding, hash joins, hash-flooding and algorithmic-complexity security attacks and their mitigations, and probabilistic membership/cardinality structures such as Bloom filters, Cuckoo filters, Count-Min Sketch, and HyperLogLog. Excludes using a hash map purely as an optimization trick inside an array or string problem (two-sum, group anagrams, longest substring without repeating characters); that pattern belongs to Arrays, Strings, and Hashing. This topic is about the hash table itself: how it is built, how it fails under skewed or adversarial input, and how it scales.
Zero-Knowledge Proofs and Advanced Primitives
Advanced cryptographic constructions: zero-knowledge proofs, commitment schemes, secure multiparty computation, and homomorphic techniques. Covers the properties (completeness, soundness, zero-knowledge) and the settings where these primitives enable privacy-preserving verification. Frontier material for research-oriented cryptography roles.
Cryptographic Hashing and Digital Signatures
Cryptographic hash functions (collision resistance, preimage resistance), message authentication codes, and digital-signature schemes. Covers HMAC, signature verification, and how hashing underpins integrity, commitments, and authentication. Distinct from non-cryptographic hashing used in data structures.
Bit Manipulation
Working directly with binary representations: bitwise operators, masking, shifting, bit counting, and integer-encoding tricks. Covers using bit-level operations for compact state, fast arithmetic, and low-level optimization. Especially relevant where memory and cycles are constrained.