This guide teaches how costly table lookups are, and how to optimize them to improve the execution time of Concrete circuits.
The most costly operation in Concrete is the table lookup operation, so one of the primary goals of optimizing performance is to reduce the amount of table lookups.
Furthermore, the bit width of the input of the table lookup plays a major role in performance.
import time
import numpy as np
import matplotlib.pyplot as plt
from concrete import fhe
def f(x):
return x // 2
bit_widths = list(range(2, 9))
complexities = []
timings = []
for bit_width in bit_widths:
inputset = fhe.inputset(lambda _: np.random.randint(0, 2 ** bit_width))
compiler = fhe.Compiler(f, {"x": "encrypted"})
circuit = compiler.compile(inputset)
circuit.keygen()
for sample in inputset[:3]: # warmup
circuit.encrypt_run_decrypt(*sample)
current_timings = []
for sample in inputset[3:13]:
start = time.time()
result = circuit.encrypt_run_decrypt(*sample)
end = time.time()
assert np.array_equal(result, f(*sample))
current_timings.append(end - start)
complexities.append(int(circuit.complexity))
timings.append(float(np.mean(current_timings)))
print(f"{bit_width} bits -> {complexities[-1]:>13_} complexity -> {timings[-1]:.06f}s")
figure, complexity_axis = plt.subplots()
color = "tab:red"
complexity_axis.set_xlabel("bit width")
complexity_axis.set_ylabel("complexity", color=color)
complexity_axis.plot(bit_widths, complexities, color=color)
complexity_axis.tick_params(axis="y", labelcolor=color)
timing_axis = complexity_axis.twinx()
color = 'tab:blue'
timing_axis.set_ylabel('execution time', color=color)
timing_axis.plot(bit_widths, timings, color=color)
timing_axis.tick_params(axis='y', labelcolor=color)
figure.tight_layout()
plt.show()
