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 for Cryptography
Comprehensive mastery of the number theoretic and algebraic foundations that underpin modern cryptography. Core topics include modular arithmetic and modular exponentiation, prime number theory and primality testing, integer factorization problems, the discrete logarithm problem in multiplicative groups, quadratic residues and Legendre and Jacobi symbols, Euler theorem, group theory, ring theory, finite fields, and elliptic curve groups. Candidates should be able to apply these concepts to analyze and explain public key systems such as Rivest Shamir Adleman, Diffie Hellman key exchange, ElGamal, and elliptic curve cryptography, and to show why security reduces to the hardness of integer factorization or discrete logarithm in the appropriate group. The scope covers algorithmic tools and their practical complexity including the extended Euclidean algorithm, fast modular exponentiation, Chinese remainder theorem, Miller Rabin and deterministic primality tests, trial division, Pollard rho and Pollard p minus one factorization methods, elliptic curve method for factorization, quadratic sieve, general number field sieve, baby step giant step, Pollard rho for discrete logarithm, and index calculus approaches. Candidates should be comfortable solving representative problems by hand or with small code examples such as computing modular inverses, performing modular exponentiation, applying the Chinese remainder theorem, solving small discrete logarithm instances, and reasoning about how algorithmic advances translate into concrete key size and security recommendations.
Zero Knowledge Proofs and Advanced Cryptography
Core concepts and practical considerations for zero knowledge proofs and other advanced cryptographic constructions. Topics include interactive and non interactive zero knowledge proofs, succinct zero knowledge proof systems and scalable transparent proof systems, formal properties such as completeness and soundness, trusted setup considerations, performance and verification costs, applications such as privacy preserving identity and selective disclosure, integration and parameter selection, and implementation pitfalls and mitigations.
Applying Cryptography to Real World Problems
Demonstrate systematic problem-solving for cryptographic scenarios. Given a problem (e.g., designing encryption for real-time messaging), show how you would identify requirements, analyze threat model, select algorithms, design protocol flow, and identify implementation pitfalls. At senior level, discuss tradeoffs between security strength, performance, platform constraints, and compliance requirements. Show awareness of when cryptography alone is insufficient and what else is needed.
Key Establishment and Agreement
Deep understanding of key exchange mechanisms including Diffie-Hellman, ECDH, and modern constructions using KDFs (HKDF). Understanding of parameter negotiation, protection against downgrade attacks, forward secrecy properties. Knowledge of key confirmation mechanisms and post-handshake key updates. Awareness of post-quantum key exchange candidates and transition strategies.
Authenticated Encryption with Associated Data (AEAD)
Comprehensive understanding of AEAD modes (AES-GCM, ChaCha20-Poly1305, AES-SIV) and why authenticated encryption is essential rather than separate encryption and MAC. Common implementation pitfalls and how they compromise security. When different AEAD schemes are appropriate.
Cryptographic Algorithm Implementation
Skills and knowledge for correctly implementing cryptographic algorithms and primitives in code. Candidates should be able to translate algorithm specifications and mathematical definitions into correct implementations, handling binary data layouts, bit operations such as shifts and exclusive or, and large integer arithmetic required for modular operations. Expect to implement core operations and components including Advanced Encryption Standard encryption rounds, Rivest Shamir Adleman modular exponentiation, Secure Hash Algorithm 256 message scheduling, substitution boxes in block ciphers, mixing functions, substitution and permutation operations, and simplified cipher operations for demonstration. Understand appropriate data structure choices and their performance and security implications, including constant time considerations, endianness, padding rules, and proper randomness. Implement and verify against official test vectors and build verification procedures and test harnesses. Emphasize correctness and clear explanation over premature optimization and recognize when to prefer well vetted cryptographic libraries to custom implementations.
Mathematical Modeling and Formal Verification of Algorithms
Ability to build mathematical models of cryptographic algorithms, understand formal verification techniques and their applicability. Knowledge of what can be proven formally vs. what requires empirical validation. Experience using or understanding formal methods tools for cryptographic analysis.
Algorithmic Problem Solving Fundamentals
Core foundation for solving entry level algorithmic problems. Focuses on arrays, strings, basic mathematics and number theory problems, simple bit manipulation, basic linked list and tree operations, stacks and queues, basic sorting and searching algorithms, simple recursion, and use of hash based data structures for counting and lookup. Emphasizes understanding asymptotic time and space complexity, selecting appropriate data structures for a task, and clear step by step problem solving including writing a brute force solution and analyzing correctness.
Cryptographic Techniques and Trends
Broad knowledge of contemporary and emerging cryptographic primitives, protocols, and research directions. Includes understanding of authenticated encryption with associated data and why it is preferred over legacy constructions, password based key derivation functions such as PBKDF2, Argon2, and scrypt and the role of salting and key stretching, elliptic curve cryptography design and trade offs, and an awareness of post quantum cryptography candidates including lattice based, multivariate, and hash based approaches. Also encompasses familiarity with the modern threat landscape such as quantum computing risks, how cryptographic research progresses into standards and real world practice, how to follow relevant conferences and journals, and the ability to synthesize research findings into practical recommendations for design, migration, and policy decisions.