  Operator algebra of (not necessarily free) higher-spin conformal conserved
currents in generalized matrix spaces, that include 3d Minkowski space-time as
a particular case, is shown to be determined by an associative algebra $M$ of
functions on the twistor space. For free conserved currents, $M$ is the
universal enveloping algebra of the higher-spin algebra. Proposed construction
greatly simplifies computation and analysis of correlators of conserved
currents. Generating function for $n$-point functions of 3d (super)currents of
all spins, built from $N$ free constituent massless scalars and spinors, is
obtained in a concise form of certain determinant. Our results agree with and
extend earlier bulk computations in the HS $AdS_4/CFT_3$ framework. Generating
function for $n$-point functions of 4d conformal currents is also presented.
