Hello,

I am trying to modify the equality protocol to make it work for primes 
congruent to 5 mod 8 (exists for Blum primes).
The problem is that I have an error with the original protocol. It works 
perfectly with p = 211 for example. But for p = 367, it doesn't.
Here is the code I'm using to test it :

from optparse import OptionParser
import viff.reactor
viff.reactor.install()
from twisted.internet import reactor
from viff.field import GF
from viff.runtime import create_runtime, gather_shares
from viff.passive import PassiveRuntime
from viff.equality_ohta import ProbabilisticEqualityMixin2
from viff.equality import ProbabilisticEqualityMixin
from viff.comparison import Toft05Runtime
from viff.config import load_config
from viff.util import rand, find_prime

class EqualityRuntime(PassiveRuntime, ProbabilisticEqualityMixin):
    """Default mix of :class:`~viff.equality.ProbabilisticEqualityMixin`
    and :class:`~viff.passive.PassiveRuntime`.
    """
    pass

class Protocol:

    def __init__(self, runtime):
        # Save the Runtime for later use
        self.runtime = runtime
        k = runtime.options.security_parameter
        print "security parameter = ", k
        Zp = GF(367)
        
        # We must secret share our input with the other parties. They
        # will do the same and we end up with three variables
        # input is equal to the player id
        
        rand = runtime.prss_share_random(Zp)
        #rand1 = runtime.prss_share_random(Zp)
        rand1 = rand
        print "rand = ", rand, "rand1 = ", rand1

        #open rand and rand1 to print their value
        open_rand = runtime.open(rand)
        open_rand1 = runtime.open(rand1)
        temp = gather_shares([open_rand, open_rand1])
        temp.addCallback(self.results_ready)
        
        # we test if rand == rand1 by using equality protocol
        test = (rand == rand1)
        test_open = runtime.open(test)
        results = gather_shares([test_open])
        results.addCallback(self.results_ready)

        runtime.schedule_callback(results, lambda _: runtime.synchronize())
        runtime.schedule_callback(results, lambda _: runtime.shutdown())

    def results_ready(self, results):
        print "ALGO_QUAD temp results =", results


    def mtemp(self, temp):
            print "local part of shares after callback ="
            print temp

      
# Parse command line arguments.
parser = OptionParser()
EqualityRuntime.add_options(parser)
options, args = parser.parse_args()

if len(args) == 0:
    parser.error("you must specify a config file")
else:
    id, players = load_config(args[0])

# Create a deferred Runtime and ask it to run our protocol when ready.
pre_runtime = create_runtime(id, players, 1, options, EqualityRuntime)
pre_runtime.addCallback(Protocol)

# Start the Twisted event loop.
reactor.run()

as you can see, I simply generate 2 random numbers, then I test if they have 
the same value, and I print the result of the test.
This will work if rand != rand1, but if I set rand1 = rand => ERROR.
This error will only happen if p = 367 (and maybe with others primes, but I 
couldn't test them all)
Here is the error :

Unhandled error in Deferred:
Traceback (most recent call last):
  File 
"/System/Library/Frameworks/Python.framework/Versions/2.5/Extras/lib/python/twisted/internet/defer.py",
 line 328, in _runCallbacks
    self.result = callback(self.result, *args, **kw)
  File "/Users/jonathanvds/opt/lib/python/viff/runtime.py", line 239, in 
_callback_fired
    self.callback(self.results)
  File 
"/System/Library/Frameworks/Python.framework/Versions/2.5/Extras/lib/python/twisted/internet/defer.py",
 line 243, in callback
    self._startRunCallbacks(result)
  File 
"/System/Library/Frameworks/Python.framework/Versions/2.5/Extras/lib/python/twisted/internet/defer.py",
 line 312, in _startRunCallbacks
    self._runCallbacks()
--- <exception caught here> ---
  File 
"/System/Library/Frameworks/Python.framework/Versions/2.5/Extras/lib/python/twisted/internet/defer.py",
 line 328, in _runCallbacks
    self.result = callback(self.result, *args, **kw)
  File "/Users/jonathanvds/opt/lib/python/viff/passive.py", line 211, in 
<lambda>
    result.addCallback(lambda (a, b): a * b)
exceptions.TypeError: unsupported operand type(s) for *: 'instance' and 
'GFElement'

I can't find where the problem comes from since I only have the error with p = 
367 (and I have the same error with my new protocol for p = 5 mod 8, but I'm 
guessing that if I can solve the problem in the existing protocol, I'll be able 
to do the same with my implementation).

Thank you for your help,

Jonathan Van den Schrieck


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