Editing Practical Quantum Electronic Voting (section)

===Protocol 5 : LogicalOR===
''Inputs'': <math>N</math> agents, <math>N</math> boolean variables <math>x_i</math>, security parameter <math>S = (1 - 2^{-\Gamma})^\Sigma \in (0,1)</math>

''Output'': <math>y = \vee_i^N x_i </math>

''Resources'': Classical communication and random numbers

# Decide <math>N</math> random orderings, such that each voter is the last once. For each ordering repeat \Sigma times the following.
# Each voter <math>k</math> gives an input <math>x_k</math>
# If <math>x_k = 0 </math>, set <math>p_k = 0</math>, otherwise toss <math>\Gamma</math> coins and set <math>p_k</math> to <math>1</math> if the result is ‘all heads’ and to <math>0</math> otherwise
# Then each voter generates uniformly at random an <math>N</math>-bit string <math>r_k = r_k^1r_k^2...r_k^N</math>, such that <math>\bigoplus_{i=1}^N r_k^i = p_k</math> 
# Voter <math>k</math> sends <math>r_k^i</math> to voter <math>i</math> for all <math>i</math>, keeping <math>r_k^k</math>
# Each voter sums the received bits and broadcasts the parity <math>z_i = \bigoplus_{k=1}^N r_k^i </math> according to the ordering.
# Compute the parity of the original bits <math>y = \bigoplus_i z_i</math>
# From this everyone can also compute the parity of all other inputs except their own <math>w_k = \bigoplus_{i = 1}^N (z_i \otimes r_k^i)</math>
# Repeat <math>\Sigma</math> times from step 4: each time repeat with <math>p_k</math> as new inputs
# If at least once in the <math>\Sigma</math> repetitions for the various orderings <math>y = 1</math>, this is the output of the protocol, otherwise it is <math>y = 0</math>