A Characteristic Set Method for Solving Boolean Equations

Background CS Method Implementation Experiment Conclusion
Nonlinear Filter Generators
LFSR of length L:
Initial State: S0 = (s0, s1, . . . , sL−1) ∈ F L 2
An infinite sequence satisfying
si = c1si−1 + c2si−2 + · · · cLsi−L, i = L, L + 1, · · · .
Nonlinear Filter.
f (x1, . . . , xm): a Boolean polynomial with m variables.
A new sequence: zi = f (si−m, . . . , si−1), i = m, m + 1, · · · .
The Test Problem. Given f , ci, and zm, zm+1, . . . , zr·m, recover
the initial state S0 from the following algebraic equations:
zi = f (si−m, . . . , si−1), i = m, m + 1, · · · , r · m.