Cryptographic Boolean Functions in Lean

3. Boolean functions and cryptography🔗

Chapter 4 develops nonlinearity and its Walsh formula, Rodier's sharp random-nonlinearity interval, general odd-dimensional bounds and exact values in dimensions one, three, five, and seven, balanced, PC(1), and degree-n-1 constructions above the quadratic bound, higher-order lower bounds, the rank-seven weight-sixteen classification, and the sharp fixed-order higher-order upper bound, Reed--Muller coset distances, resiliency, propagation criteria, linear structures, algebraic immunity, autocorrelation indicators, maximum correlation, and scalar complexity criteria.

  1. 3.1. Distribution of algebraic degree
  2. 3.2. Nonlinearity
  3. 3.3. Higher-order nonlinearity
  4. 3.4. Balancedness and resiliency
  5. 3.5. Propagation criteria
  6. 3.6. Linear structures
  7. 3.7. Algebraic immunity
  8. 3.8. Autocorrelation indicators
  9. 3.9. Maximum correlation
  10. 3.10. Other criteria