User:Gmaxwell/derandomized nonce notes
Shouldn't Bitcoin use ed25519 because it has derandomized nonces?
Nonce generation in all conventional DL signature systems is purely an implementation function. The ed25519 specific had the foresight to specify a specific reasonable nonce generation scheme but unfortunately it's not possible to enforce that any particular scheme is used. As a result people have still managed to create implementations of ed25519 with insecure nonce generation, and worse.
RFC6979 specifies a nonce scheme that any DL signature system (such as ECDSA with secp256k1) can use. It's been in common use in Bitcoin since 2015 and is now nearly ubiquitous.
Both standard RFC6979 and the ed25519 scheme have demonstrated some minor weaknesses in the fact of differential power analysis (power/emi side-channels) and as a result the state of the art these days is "synthetic nonces" which combine most of the advantages of de-randomization with by hashing secret values with the message and a counter or random input to make it so a DPA attacker can't get multiple recordings of the same trace.
Both RFC6979 and ed25519 also lack a clear an unambiguous domain separation in their hashing. If you use the same nonce scheme in different protocols (potentially even w/ different curves) you may inadvertently reuse a nonce and compromise your security. This issue can be avoided through the use of tagged hashes and/or synthetic nonces.
Bitcoin's BIP340 learns from ed25519 and incorporates a recommended secure nonce scheme in the BIP to reduce the risk that implementer will get it wrong. The recommended scheme also learns from the limitations of the ed25519 spec by using tagged hashes and supporting (optionally) synthetic nonces.
It isn't technically possible to mandate any particular scheme for any of these cryptosystems, and it's just as well: People have also constructed specialized nonce schemes for BIP340 which achieve other useful properties such as provability eliminating signing devices using the nonce as a cover sidechannel, and also generating nonces in a way which is provably deterministic (using a large additional zero knowledge proof) which is potentially useful in some multiparty protocols.
- some parties have have falsely assumed that the deterministic nonces were mandatory with ed25519 and made the signatures unique resulting in serious vulnerabilities in some cryptocurrencies.