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Date: Wed, 10 Sep 2014 22:57:35 -0700
From: Andy Lutomirski <>
To: discussions <>
Subject: Re: [PHC] Makwa is broken given p and q

On Wed, Sep 10, 2014 at 8:55 PM, Steve Thomas <> wrote:
> 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)

This is described (in the CRT formulation) in the Makwa paper.

> 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.

Huh?  I don't think that anyone is proposing using Makwa with cost 2^128.


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