How to Cheat with Math – The Russian Cards Problem(winux-arch.github.io)
winux-arch.github.io
How to Cheat with Math – The Russian Cards Problem
https://winux-arch.github.io/Russian-Cards-Problem/
7 comments
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)
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)Is the modulo required? Is just "The sum of my cards is x" sufficient?
Yes. For instance, if a player says the sum of their cards is 3, Eve immediately knows they have cards 0, 1 and 2.
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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
Problem solved!
Problem solved!
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