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- # This module defines addition on SharedScalars, using the SPDZ algorithm
- # for addition [1].
- #
- # Technically, this method is extremely simple as it follows directly
- # from additive secret sharing, and likely predates SPDZ.
- #
- # [1] "Computations" on pg 6 of https://eprint.iacr.org/2011/535.pdf
- # 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.
- def add_2sh(sh1, sh2):
- '''Implements addition on two SharedScalars.'''
- # To do the addition, we add each machine's shares together
- sh1._assert_can_operate(sh2)
- sum_shares = [sh1.share_of[owner] + sh2.share_of[owner]
- for owner in sh1.owners]
- return type(sh1)(sum_shares, Q=sh1.Q)
- def add_sh_pub(sh, pub):
- '''Implements addition on a SharedScalar and a public integer.'''
- # To do the addition, we add the integer to one (random) share only
- new_shares = [sh.shares[0] + pub] + sh.shares[1:]
- return type(sh)(new_shares, sh.Q)
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