Score:2

ECDSA simpler formula?

sk flag

In ECDSA, if Alice wants to send a message to Bob, she computes $s=k^{-1}(z+rd_A)$.

I was thinking that the formula could simply be $s=k^{-1}zrd_A$ and the algorithm would work just as well, and the verification would be simpler, because the recipient would just have to calculate $X=s^{-1}zrQ_A$ instead of a sum $X=s^{-1}zG+s^{-1}rQ_A$.

Is there something I'm missing?

Gilles 'SO- stop being evil' avatar
cn flag
ECDSA is more complicated than it needs to be because it works around a patent, but it can't be simplified that much. It's a variant of [Schnorr signatures](https://en.wikipedia.org/wiki/Schnorr_signature) (the patented original idea). There are many variants, but they all have a pair of numbers as output with one of the numbers ($s$ in ECDSA) being an additive combination of two values involving different inputs.
DannyNiu avatar
vu flag
DLog-based DSS need formula over fields (equipped with addition and multiplication) to achieve security. Otherwise, you'd be looking at pairing based algorithms such as BLS.
Score:9
my flag

Is there something I'm missing?

It would make it be easy to generate forgeries; let $X = Q_A$ and $r$ its $x$-coordinate. Let $s = zr$, and then $(r, s)$ is a forgery of the message with hash $z$

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