Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS] Additional Elliptic Curves (Curve25519 etc) for TLS ECDH key agreement)

Robert Ransom <> Sun, 12 January 2014 15:13 UTC

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Date: Sun, 12 Jan 2014 07:13:16 -0800
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From: Robert Ransom <>
To: Adam Back <>
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Subject: Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS] Additional Elliptic Curves (Curve25519 etc) for TLS ECDH key agreement)
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On 1/12/14, Adam Back <> wrote:

> So actually Bernstein went in the opposite direction, not only using
> sub-group size, but double sub-group size hash, basically because he could
> without increasing the signature size, and thereby slightly even further
> reducing the dependency on hash security and hash properties.  I do not
> consider its necessary, just its because he could, slightly more security
> almost for free.  But I think an EdDSA variant that used a 512-bit curve
> could safely use a 512-bit hash, because even the double width hash is
> over-engineering.

It can for the hash of the message.

> EdDSA also uses the deterministic DSA k trick (computed from m and x the
> private key).

Deterministic generation of message keys is the primary reason that
EdDSA requires a double-length hash function.

EdDSA relies on the hash function having double-length output in two ways:

* Message key generation relies on the output being noticeably longer
than the group order in order to generate *uniform* exponents.

* EdDSA also uses the hash function to expand the secret-key bitstring
into (a) the secret exponent of the public key and (b) a secret
bitstring used to key the message key generation hash function.

I'm quite sure that I've said all of this before quite recently.

Robert Ransom