Signature verification is one of the hardest things to get right. One reason is, they're harder to test: when you encrypt or hash something, you have a whole bunch of bits you can check against test vectors. With signature verifications, you only have one bit: it's a match, or it's a fail.
Moreover, it's very easy to forget to check something (here, that we are using the same base point). Other constructions, like EdDSA, are simpler, and verification requires a single equality check. Harder to botch.
And even then, implementers can be tempted to get clever, which requires extra care. I've personally been bitten by not verifying mathematical jargon, and mistakenly thought "birational equivalence" was complicated speak for "bijection". Almost, but not quite. This single oversight lead to a critical, easy to find, easy to exploit vulnerability.
We found out 15 months later, 1 full year after public release, by tinkering with the tests. A cryptographer would have found it in 5 minutes, but as far as I can tell, they're all very busy.
That’s an interesting assessment. Rogaway just gave a talk at RWC about APIs for secret splitting schemes. IIRC he said that the API needed to be closer to what symmetric crypto was. But from the diagram it seemed like you were obtaining some associated data back to check that the secret was correct (not sure if this would work/is relevant with more recent DKG schemes).
A signature verification returning an actual AD would be interesting as well.
EdDSA can have something close. Long story short, an EdDSA signature has two parts, often called "R" and "s". Verification works by producing a number using the public key and "s", then checking that this number is the same as "R". There are basically 3 steps:
Steps 1 and 3 are straightforward (the hash and the constant time comparison are almost always implemented in dedicated routines, tested separately). Step 2 is the most dangerous (that's where the elliptic curve magic happens).
EdDSA Implementations would be easier to check against one another if they all exposed step 2 as part of the public API. Bonus points if step 2 can handle invalid inputs (low order point, point on the twist...) in a standard manner. I haven't seen such a thing though, probably because end users never need a separate step 2.
Still, I can already envision the benefits. I'll probably use it myself.
Signature verification is one of the hardest things to get right. One reason is, they're harder to test: when you encrypt or hash something, you have a whole bunch of bits you can check against test vectors. With signature verifications, you only have one bit: it's a match, or it's a fail.
Moreover, it's very easy to forget to check something (here, that we are using the same base point). Other constructions, like EdDSA, are simpler, and verification requires a single equality check. Harder to botch.
And even then, implementers can be tempted to get clever, which requires extra care. I've personally been bitten by not verifying mathematical jargon, and mistakenly thought "birational equivalence" was complicated speak for "bijection". Almost, but not quite. This single oversight lead to a critical, easy to find, easy to exploit vulnerability.
We found out 15 months later, 1 full year after public release, by tinkering with the tests. A cryptographer would have found it in 5 minutes, but as far as I can tell, they're all very busy.