Mathematics
In this collection 77
- Additive Group Diffie-Hellman Break (Trivial Discrete Log in Additive Groups)
- AES-GCM Forbidden Attack (Nonce Reuse Tag Forgery)
- Algebraic Attack via Boolean Polynomial Ring (Gröbner Basis Key Recovery)
- Annihilator Attack on Filtered LFSRs (Quadratic Linearization)
- Baby-Step Giant-Step Algorithm
- Batch GCD Attack (Shared RSA Prime Across Keys)
- Bayes' theorem and inference
- Berlekamp-Massey Algorithm
- Boneh-Durfee Attack (Lattice Attack on Small RSA Private Exponent)
- Boolean Functions and Algebraic Normal Form (ANF)
- Byte-Integer Encoding (bytes_to_long - long_to_bytes)
- Cayley-Hamilton Reduction of Matrix Exponentiation to Polynomial Coefficients
- Chinese Remainder Theorem
- Complex Multiplication (CM) Prime Factorization Backdoor
- Composite-Modulus Key Exchange Break (CRT Projection Attack)
- Conic-Non-Elliptic Curve DLP Reduction (Fake ECC)
- Coppersmith's Method for Stereotyped-Partially-Known Messages
- Correlation Attack on Filtered LFSRs (Belief Propagation)
- Descriptive statistics and graphs
- Diffie-Hellman (Textbook Construction)
- Discrete Log Reduction via Chosen Composite Modulus n=q² (Paillier's Trick)
- Discrete Log Signature Forgery via Smooth-Order Modulus Lifting (n=p², Pohlig-Hellman + Hensel Lift)
- Discrete Logarithm Problem (DLP)
- Discrete random variables and distributions
- Dual EC-Style PRNG Backdoor (Chosen Related Points)
- Duplicate Signature Key Selection (DSKS) Attack
- ECDH (Elliptic Curve Diffie-Hellman) — Textbook Construction
- ElGamal (Subgroup and Quadratic-Residue Leakage)
- Elliptic Curves (Group Law Basics)
- Event (Probability)
- Experiment (Probability)
- Exponent Recovery via Repeated Eigenvalue (Logarithmic Derivative Trick)
- Extended Euclidean Algorithm
- Factoring Products of Mersenne-Form Numbers (2^a-1)(2^b-1)
- Fermat's Factorization Method (Close Primes)
- Fermat's Little Theorem
- Finite Fields (Galois Fields: GF(p) and GF(2^n))
- Fooling Fixed-Basis Miller-Rabin (Arnault Strong Pseudoprimes)
- Franklin-Reiter Related Message Attack
- Geffe Generator (Nonlinear LFSR Combination via Multiplexer)
- Groups (Group Theory Basics)
- Hastad's Broadcast Attack
- Hidden Subset Sum - Knapsack Recovery via Lattice Reduction (LLL)
- Integer Factorization via ECM - Sage's factor()
- Legendre Symbol
- LFSR State via Companion Matrix (Time-Reversal)
- Linear Congruential Generator (State and Parameter Recovery)
- Linear S-Box Cryptanalysis (Affine Cipher Break)
- LLL Algorithm (Lattice Basis Reduction)
- Low-Exponent Cube-Root Attack (Unpadded RSA)
- Matrix Discrete Log via Characteristic Polynomial Factorization (Extension Fields + CRT)
- Matrix Groups & Textbook-RSA-Style Attacks over Matrices
- Miller-Rabin Primality Test
- Modular Binomial Equation Attack
- Partial-Match RSA Verification Exploit (Suffix Forgery via Small Modulus)
- Pohlig-Hellman Algorithm
- Point Compression (Elliptic Curve X-Coordinate + Parity Bit)
- Probability, counting, and trees
- Quadratic Residue
- Quantitative vs Qualitative Data
- Recovering an Unknown Modulus via GCD (Successive Powers)
- Recursive RSA-Style Factorization via Known φ(N) (Multi-Prime Moduli)
- ROCA Vulnerability (Infineon RSA Key Generation Weakness)
- Roots of Unity mod N (Non-Trivial Roots Reveal Factors)
- RSA (Textbook Construction)
- RSA Blinding Attack (Signature Malleability)
- RSA Factorization from Known (N, e, d)
- RSA Fixed-Point Leakage (Unconcealed Messages) → Factorization
- RSA with Non-Coprime Exponent (e Shares a Factor with φ(N))
- RSA with p = q (Repeated Prime Factor)
- Sequential Confidence Amplification for Noisy Binary Oracles (SPRT-style)
- Small-Subgroup - Smooth-Prime Static-Key Extraction Attack (Diffie-Hellman)
- Smooth Numbers & Constructing Smooth Primes
- Statistical foundations and measurement
- Tonelli-Shanks Algorithm
- Wiener's Attack (Continued Fractions, Small Private Exponent)
- XOR Uniformity Lemma