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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