Re: [Cfrg] I-D Action: draft-irtf-cfrg-hash-to-curve-07.txt

"Riad S. Wahby" <rsw@jfet.org> Tue, 28 April 2020 16:31 UTC

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Date: Tue, 28 Apr 2020 09:31:15 -0700
From: "Riad S. Wahby" <rsw@jfet.org>
To: =?utf-8?B?QmrDtnJu?= Haase <bjoern.m.haase@web.de>
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Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-hash-to-curve-07.txt
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Hi Björn,

Björn Haase <bjoern.m.haase@web.de> wrote:
> Iwould understand a zero-padding that would first insert some
> information that should be maintained confidential and a Z_pad string
> that fills up the remaining rest of the input block of the hash function
> with zeros. However, I did not get the point, why filling the first
> block with zeros should provide any advantage.

Good question! The answer is that this zero block allows one to prove
this construction indifferentiable from a random oracle when the M-D
compression function is modeled as a random oracle (which is effectively
the strongest statement we could hope for in this context).

In particular, prepending a block of zeros instantiates an NMAC
construction, as described in Section 3.5 of the following paper
(the full version linked below gives a security proof).

    Coron, Dodis, Malinaud, and Puniya. "Merkle-Damgaard revisited:
    How to construct a hash function." Proc. CRYPTO 2005.
    https://cs.nyu.edu/~dodis/ps/merkle.pdf

This is discussed in the "Security Considerations" section of the
document. I will go back and double check that Section 5 makes
a clear forward ref to that discussion.

Thanks for the feedback and take care,

-=rsw