Does "the sum of my cards modulo 7 is [x]" work? It should let Bob know what the missing card is but I can't tell if it conveys sufficiently little information to Eve for it to count.
The article's definition of not revealing information is a bit unclear, but if we understand it as Eve not knowing who holds any single card, your solution seems to work. At least assuming the following code is correct :)
import itertools
import functools
for eve_card in range(7):
cards_left = set(range(7))
cards_left.remove(eve_card)
mod_to_cards = [[], [], [], [], [], [], []]
for c in itertools.combinations(cards_left, 3):
mod = sum(c) % 7
mod_to_cards[mod].append(set(c))
for combs in mod_to_cards:
i = functools.reduce(lambda x, y: x.intersection(y), combs)
if len(i) != 0:
print("intersection", eve_card, combs, i)
u = functools.reduce(lambda x, y: x.union(y), combs)
if len(u) != 6:
print("union", eve_card, combs, u)
The advised reader could devise a solution using public / private key where:
- Alice communicates her public key
- Bob communicates his
- Alice encoders her cards with Bob’s public key
- Bob does the same
7 comments
[ 2.9 ms ] story [ 21.1 ms ] threadimport itertools import functools
for eve_card in range(7): cards_left = set(range(7)) cards_left.remove(eve_card)
Problem solved!