Schnorr sigs vs pairing sigs

Schnorr sigs rely so heavily on the masking provided by a random nonce. There are so many easy ways to introduce bias (hash + modulo, for example).

Even 2 bits of bias can result in serious attacks:

https://ecc2017.cs.ru.nl/slides/ecc2017-tibouchi.pdf

Maybe pairing based sigs - which are slower - might be both more flexible, and better suited to secure implemetnations?

Hi Erik,

There are a strong arguments for and against pairing based sigs in Bitcoin. One very strong argument in favour over non-deterministic signatures like Schnorr over BLS is it enables a kind of signature encryption called "adaptor signatures". This construction is key to many exciting up and coming layer 2 protocols and isn't possible unless the signature scheme uses randomness.

self plug: I have a paper on this topic called "One-Time Verifiably Encrypted Signatures A.K.A Adaptor Signatures" https://github.com/LLFourn/one-time-VES/blob/master/main.pdf

LL

On Fri, Mar 6, 2020 at 6:03 AM Erik Aronesty via bitcoin-dev < bitcoin-dev@lists•linuxfoundation•org> wrote:

> Schnorr sigs rely so heavily on the masking provided by a random
> nonce.   There are so many easy ways to introduce bias (hash + modulo,
> for example).
>
> Even 2 bits of bias can result in serious attacks:
>
> https://ecc2017.cs.ru.nl/slides/ecc2017-tibouchi.pdf
>
> Maybe pairing based sigs  - which are slower - might be both more
> flexible, and better suited to secure implemetnations?
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> bitcoin-dev mailing list
> bitcoin-dev@lists•linuxfoundation•org
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>