A Bluffers Guide to EdDSA and ECDSA

Well, if you’re into cybersecurity, hopefully, you see beyond the fact that ECDSA stands for Elliptic Curve Digital Signature Algorithm, and EdDSA stands for Edwards-curve Digital Signature Algorithm. Both are used to create digital signatures, and where Bob uses his private key to sign for a message, and then Alice proves the signature with the message, the signature and Bob’s public key. Once Bob has signed the message, there should be no way of going back and changing the key to a different key or changing the message — as these would not verify the signature.

Figure 1 shows an outline of the signatures used in elliptic curve methods. With this, Bob uses his private key (sk) to sign a hash to the message, and produces a signature: (r,s). This signature is then sent to Alice with the message. Alice then also takes a hash of the message and the signature (r,s), and applies Bob’s public key (pk). If the signature checks-out, Alice knows that Bob signed the message.

Figure 1

So what’s the difference? And when would you use ECDSA rather and EdDSA, and vice-versa. For something that is compatible with Bitcoin and Ethereum, ECDSA provides the best solution. Unfortunately it relies on a random nonce…