Competencies: Mathematics > Cryptographic Mathematics
Cryptographic Mathematics
Body of Knowledge
| Topic | Description | Relevance | Career Tracks |
|---|---|---|---|
Cryptographic Math Concepts |
Mathematical foundations of cryptography including RSA (prime factorization), Diffie-Hellman (discrete logarithm), ECC (elliptic curves), and AES (substitution-permutation networks). Conceptual understanding for security practitioners. |
High |
Security Engineer, Security Architect, Cryptography Engineer |
Modular Arithmetic |
Modular operations, multiplicative inverse, Chinese Remainder Theorem |
High |
Security Engineer, Cryptographer |
Prime Number Theory |
Prime generation, primality testing, factorization, RSA foundations |
High |
Security Engineer, Cryptographer |
Elliptic Curve Mathematics |
Elliptic curves over finite fields, point addition, scalar multiplication |
Medium |
Cryptographer, Security Researcher |
Discrete Logarithms |
Discrete log problem, Diffie-Hellman key exchange, ElGamal |
High |
Security Engineer, Cryptographer |
Hash Function Mathematics |
Collision resistance, preimage resistance, Merkle-Damgård construction |
High |
Security Engineer, Cryptographer |
Information Theory |
Entropy, mutual information, perfect secrecy, compression bounds |
Medium |
Cryptographer, Data Scientist |
Personal Status
| Topic | Level | Evidence | Active Projects | Gaps |
|---|---|---|---|---|
Cryptographic Math Concepts |
Intermediate |
CISSP study — understand RSA (prime factorization), Diffie-Hellman (discrete logarithm), ECC (elliptic curves), AES (substitution-permutation); conceptual, not computational |
Cannot derive or prove cryptographic properties; black-box understanding only |