phc-discussions - Makwa is broken given p and q

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Message-ID: <869155607.54688.1410407753370.open-xchange@oxuslxltgw06.lxa.perfora.net>
Date: Wed, 10 Sep 2014 22:55:53 -0500 (CDT)
From: Steve Thomas <steve@...tu.com>
To: discussions@...sword-hashing.net
Subject: Makwa is broken given p and q

Given p and q you can do:
e  = 2 ** cost
e' = 2 ** cost (mod (p-1)*(q-1))
x ** e = x ** e' (mod p*q)

You could pick the cost to be 2 ** 128. Without p and q you can't test a
password.
powConst = powm(2, pow(2, 128), (p-1)*(q-1))
hash = powm(password, powConst, p*q)
but you could just do HMAC(password, secretKey)

Sorry but even if you came up with the perfect server-specific shortcut, HMAC or
encryption with a secret key is better.

If you don't know the secret, it takes 3x longer.
vs
If you don't know the secret, you can't do anything.