[curves] Unifying public key formats

Paul Lambert paul at marvell.com
Wed Jan 21 21:08:50 PST 2015

On 1/21/15, 6:44 PM, "Trevor Perrin" <trevp at trevp.net> wrote:

>On Wed, Jan 21, 2015 at 4:09 PM, Paul Lambert <paul at marvell.com> wrote:
>> On 1/21/15, 6:02 PM, "Trevor Perrin" <trevp at trevp.net> wrote:
>>>So the Montgomery ladder function could be modified to recover the
>>>Edwards x sign bit at very low cost.
>>>Would you prefer this for a unified format, instead of using a
>>>single-coordinate format with the sign bit implied as zero (Jivsov)
>>  Š no extra bits, no leaks, shorter, etc., sounds like a good idea.
>> So how is the bit implied?
>Generate a keypair and calculate the sign bit, e.g. as explained
>above.  If the sign bit is one instead of zero, negate the private
>scalar.  Now the sign bit is always zero.

>>>encoded into signatures (your idea)?
>> Also a cute trick .. But makes you modify the signature algorithm based
>> the received point format (not everyone would be Œuniversal¹)
>That's easy, though:  if your public-key format doesn't include the
>sign bit, just copy it from the signature, then run existing
>signature-verify code.  For example, in Ed25519:
>Anyways, I like the Jivsov and Ransom approaches to single-coordinate
>public keys for signatures, but I'm not sure they'll work for all
>protocols (?)

Likewise - single coordinate has benefits.

 … are we talking here about public key format or generic point format …
It’s hard to predict and analyze multiple unknown protocols.  However, I’m
not sure it’s necessary.



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