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Date: Thu, 3 Apr 2014 20:50:46 +0200
From: Thomas Pornin <>
Subject: Re: [PHC] babbling about trends

On Thu, Apr 03, 2014 at 02:00:14PM -0400, Bill Cox wrote:
> Is it fair to say that the most interesting aspect of your entry is
> the delegation capability?

That's the whole justification, yes. On the paper, using RSA-like
computations _should_ make the function more vulnerable to GPU. I quite
expected GPU to be very good at doing RSA. When I looked for figures,
the best I found was a 2011 study which came to a different conclusion,
namely that for RSA, CPU and GPU offered very similar throughput per
dollar. This was a happy surprise.

I still expect that someone will show up with a detailed analysis
showing that a cheap ASIC can be built, which crunches Makwa hashes at
high speed. The idea of Makwa is that delegation allows to enlist enough
extra power to more than compensate for such effects.

> IIRC, there's no arbitrary hash function called during delegation.  Is
> it possible to add a memory-hard hash function call to the delegated
> password hashing?

I cannot prove it to be impossible, but I don't know how to do such a
thing. The RSA-based masking (in fact, more Rabin-based than RSA-based)
is the only method I found to do delegation. Initially, I wanted
something with elliptic curves (for purely aesthetic reasons), but I did
not find anything.

> However, I get confused as to why this is better than just having a
> server master password used to decrypt password/user specific secret
> secondary keys?

I, too, have trouble finding a realistic scenario where the shortcut is
a really essential feature. The best I can think of is the following:
the shortcut cannot be evaded.

A shortcut can always be added with asymmetric encryption: there is an
asymmetric key pair (Kpub,Kpriv), and when a password pw must be
registered, the registering system stores both PHS(pw) and E_Kpub(h(pw))
(the second value is the encryption with Kpub of h(pw) for a hash
function h(), e.g. SHA-256). When a system (the same or another) must
verify a password, then it either decrypts it (D_Kpriv(E_Kpub(pw)) = pw)
if it has access to Kpriv, or it recomputes PHS(pw) otherwise. This
scheme works with any password-hashing function h(), and the asymmetric
encryption thing can be space-efficient if using, e.g., ECDH+AES (do
some ECDH for key exchange, use AES to encrypt h(pw) truncated to 16
bytes as a single block; encrypted value size will be 48 bytes: 32 bytes
for a P-256 curve point, and 16 bytes for the AES output).

With such a generic system, a rogue registration system could compute
PHS(pw) faithfully, but produce random junk instead of E_Kpub(h(pw)).
This would not be detected until a server knowing Kpriv comes around.
This situation cannot arise if PHS(pw) has an inherent shortcut ability:
namely, if a password can be verified at all with Makwa, then the
shortcut MUST necessarily work.

This is a pretty specific situation and I fail to imagine a plausible
scenario where it would apply. But absence of proof is not proof of
absence -- maybe someone has an idea where the shortcut is a killer
feature ?

In the case of Makwa, when the optional pre- and post-hashing are not
applied, the shortcut actually turns into an escrow mechanism, which IS
useful in some cases, e.g. to support authentication protocol such as
APOP where the actual password must be known a priori by the server.
There again, escrow can be added to any PHS with an extra asymmetric
encryption. The ability of an algorithm to combine slow hashing and
escrow is more a safety against implementation errors than an actual
security feature.

	--Thomas Pornin

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