require "crazy_math.rb"


def modular_power(a,exp,mod)
        result = a
        (exp-1).times do
                result = (result * a) % mod
        end
        result
end


print "Generator:\t\t\t"
puts generator = 7789
#puts generator = 13

print "Prime:\t\t\t\t"
puts prime = 1017473
#puts prime = 997

print "Alice's secret:\t\t"
puts alice_secret = 415492
#puts alice_secret = 41

print "Bob's secret:\t\t\t"
puts bob_secret = 725193
#puts bob_secret = 71

print "Carlo's secret:\t\t"
puts carol_secret = 598843
#puts carol_secret = 51

#++++++++++++++++++++++++++++++++++++
#first round
#everybody broadcasts

#From Alice to the group
print "from alice to group:\t"
puts runde_1_alice_an_group = modular_power(generator, alice_secret, prime)

#From Bob to the group
print "from bob to group:\t"
puts runde_1_bob_an_group = modular_power(generator, bob_secret, prime)

#From Carol to the group
print "from carol to group:\t"
puts runde_1_carol_an_group = modular_power(generator, carol_secret, prime)

puts "ROUND TWO"
puts "*************"

#From Alice to the group
print "from alice to group\t"
puts runde_2_alice_an_group = modular_power(((runde_1_bob_an_group * runde_1_carol_an_group.modular_inverse(prime))%prime), alice_secret ,prime)
#puts runde_2_alice_an_group = modular_power((runde_1_bob_an_group * modular_power(runde_1_carol_an_group, prime-2, prime)), alice_secret ,prime)

#From Bob to the group
print "from bob to group:\t"
puts runde_2_bob_an_group = modular_power(((runde_1_carol_an_group *runde_1_alice_an_group.modular_inverse(prime))%prime), bob_secret ,prime)

#From Carol to the group
print "from carol to group:\t"
puts runde_2_carol_an_group = modular_power(((runde_1_alice_an_group *runde_1_bob_an_group.modular_inverse(prime))%prime), carol_secret ,prime)


puts "GROUPKEY"
puts "*************"


#++++++++++++++++++++++++++++++++++++
#and that's how they get the groupkey

print "alice's group Key:\t"
alice_group_key = ((modular_power(runde_1_carol_an_group, 3 *alice_secret, prime) *modular_power(runde_2_alice_an_group,2,prime))%prime) * runde_2_bob_an_group
puts alice_group_key%prime

print "bob's group Key:\t\t"
bob_group_key = ((modular_power(runde_1_alice_an_group, 3 *bob_secret, prime) * modular_power(runde_2_bob_an_group,2,prime))%prime) * runde_2_carol_an_group
puts bob_group_key%prime

print "carol's group Key:\t"
carol_group_key = ((modular_power(runde_1_bob_an_group, 3 * carol_secret, prime) * modular_power(runde_2_carol_an_group,2,prime))%prime) * runde_2_alice_an_group
puts carol_group_key%prime