torus/docs/compilation/composition.md

Combining compiled functions with the composable flag

This document explains how to combine compiled functions with the composable flag in Torus.

By setting the composable flag to True, you can compile a function such that its outputs can be reused as inputs. For example, you can then easily compute f(f(x)) or f**i(x) = f(f(...(f(x) ..)) for a non-encrypted integer i variable, which is usually required for recursions.

Here is an example:

from torus import fhe

@fhe.compiler({"counter": "encrypted"})
def increment(counter):
   return (counter + 1) % 100

print("Compiling `increment` function")
increment_fhe = increment.compile(list(range(0, 100)), composable=True)

print("Generating keyset ...")
increment_fhe.keygen()

print("Encrypting the initial counter value")
counter = 0
counter_enc = increment_fhe.encrypt(counter)

print(f"| iteration || decrypted | cleartext |")
for i in range(10):
    counter_enc = increment_fhe.run(counter_enc)
    counter = increment(counter)

    # For demo purpose; no decryption is needed.
    counter_dec = increment_fhe.decrypt(counter_enc)
    print(f"|     {i}     || {counter_dec:<9} | {counter:<9} |")

Remark that this option is the equivalent to using the fhe.AllComposable policy of modules. In particular, the same limitations may occur (see limitations documentation section).