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- # This module defines multiplication on SharedScalars, using the SPDZ
- # algorithm for multiplication [1].
- #
- # [1] https://bristolcrypto.blogspot.com/2016/10/what-is-spdz-part-2-circuit-evaluation.html
- # Small hack:
- #
- # We can't import the SharedScalar class in this module as that would
- # create a circular dependency.
- #
- # However, we'd obviously still like to be able to construct new
- # SharedScalars here when doing arithmetic. To be able to do so,
- # we can use `type(sh)` to get access to the SharedScalar class &
- # constructor.
- from .finite_ring import mod, rand_element
- from .secret_sharing import n_to_shares
- from random import choice
- def mult_2sh(sh1, sh2):
- '''Implements multiplication on two SharedScalars.'''
- # Make sure that these two SharedScalars are compatible
- sh1._assert_can_operate(sh2)
-
- # Generate a random multiplication triple (public)
- a, b = rand_element(sh1.Q), rand_element(sh1.Q)
- c = mod(a * b, sh1.Q)
- # Share the triple across all machines
- # (It'd be nicer to use the higher-level PrivateScalar.share() here,
- # but we don't have access to PrivateScalar in this module.)
- machines = list(sh1.owners)
- shared_a = type(sh1)(n_to_shares(a, machines, sh1.Q), sh1.Q)
- shared_b = type(sh1)(n_to_shares(b, machines, sh1.Q), sh1.Q)
- shared_c = type(sh1)(n_to_shares(c, machines, sh1.Q), sh1.Q)
- # Compute sh1 - a, sh2 - b (shared)
- shared_sh1_m_a = sh1 - shared_a
- shared_sh2_m_b = sh2 - shared_b
- # Reconstruct sh1 - a, sh2 - b (public)
- rand_machine = choice(machines)
- sh1_m_a = shared_sh1_m_a.reconstruct(rand_machine).value
- sh2_m_b = shared_sh2_m_b.reconstruct(rand_machine).value
- # Magic! Compute each machine's share of the product
- shared_prod = shared_c + (sh1_m_a * shared_b) + (sh2_m_b * shared_a) + (sh1_m_a * sh2_m_b)
- return shared_prod
- def mult_sh_pub(sh, pub):
- '''Implements multiplication on a SharedScalar and a public integer.'''
- # To do the multiplication, we multiply the integer with all shares
- prod_shares = [share * pub for share in sh.shares]
- return type(sh)(prod_shares, Q=sh.Q)
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