The following is a simplified description of EdDSA, ignoring details of encoding integers and curve points as bit strings; the full details are in the papers and RFC. An EdDSA signature scheme is a choice:
of cryptographic hash function with -bit outputs, where so that elements of and curve points in can be represented by strings of bits.
These parameters are common to all users of the EdDSA signature scheme. The security of the EdDSA signature scheme depends critically on the choices of parameters, except for the arbitrary choice of base point—for example, Pollard's rho algorithm for logarithms is expected to take approximately curve additions before it can compute a discrete logarithm, so must be large enough for this to be infeasible, and is typically taken to exceed. The choice of is limited by the choice of, since by Hasse's theorem, cannot differ from by more than. The hash function is normally modelled as a random oracle in formal analyses of EdDSA's security. In the HashEdDSA variant, an additional collision-resistant hash function is needed. Within an EdDSA signature scheme, ; Public key ; Signature ; Private key
Ed25519
Ed25519 is the EdDSA signature scheme using SHA-512 and Curve25519 where
The Bernstein team has optimized Ed25519 for the x86-64 Nehalem/Westmere processor family. Verification can be performed in batches of 64 signatures for even greater throughput. Ed25519 is intended to provide attack resistance comparable to quality 128-bit symmetric ciphers. Public keys are 256 bits in length and signatures are twice that size.
Secure coding
As security features, Ed25519 does not use branch operations and array indexing steps that depend on secret data, so as to defeat many side channel attacks. Like other discrete-log-based signature schemes, EdDSA uses a secret value called a nonce unique to each signature. In the signature schemes DSA and ECDSA, this nonce is traditionally generated randomly for each signature—and if the random number generator is ever broken and predictable when making a signature, the signature can leak the private key, as happened with the Sony PlayStation 3 firmware update signing key. In contrast, EdDSA chooses the nonce deterministically as the hash of a part of the private key and the message. Thus, once a private key is generated, EdDSA has no further need for a random number generator in order to make signatures, and there is no danger that a broken random number generator used to make a signature will reveal the private key.
Software
Notable uses of Ed25519 include OpenSSH, GnuPG and various alternatives, and the signify tool by OpenBSD. Usage of Ed25519 in SSH protocol is being standardized. In 2019 a draft version of the FIPS 186-5 standard included deterministic Ed25519 as an approved signature scheme.
SUPERCOP reference implementation
A slow but concise alternate implementation, does not include side-channel attack protection
Ed448 is the EdDSA signature scheme using SHAKE256 and Curve448 defined in RFC 8032. It has also been approved in the draft of the FIPS 186-5 standard.
