  Garbling schemes are vital primitives for privacy-preserving protocols and
secure two-party computation. This paper presents a projective garbling scheme
that assigns $2^n$ values to wires in a circuit comprising XOR and unary
projection gates. A generalization of FreeXOR allows the XOR of wires with
$2^n$ values to be very efficient. We then analyze the performance of our
scheme by evaluating substitution-permutation ciphers. Using our proposal, we
measure high-speed evaluation of the ciphers with a moderately increased cost
in garbling and bandwidth. Theoretical analysis suggests that for evaluating
the nine examined ciphers, one can expect a 4- to 70-fold improvement in
evaluation performance with, at most, a 4-fold increase in garbling cost and,
at most, an 8-fold increase in communication cost compared to the Half-Gates
(Zahur, Rosulek and Evans; Eurocrypt'15) and ThreeHalves (Rosulek and Roy;
Crypto'21) garbling schemes. In an offline/online setting, such as secure
function evaluation as a service, the circuit garbling and communication to the
evaluator can proceed in the offline phase. Thus, our scheme offers a fast
online phase. Furthermore, we present efficient Boolean circuits for the
S-boxes of TWINE and Midori64 ciphers. To our knowledge, our formulas give the
smallest number of AND gates for the S-boxes of these two ciphers.
