In public-key cryptography, Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on twisted Edwards curves.
[1] It is designed to be faster than existing digital signature schemes without sacrificing security.
It was developed by a team including Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, and Bo-Yin Yang.
[2] The reference implementation is public-domain software.
[3] 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.
[4][2][1] An EdDSA signature scheme is a choice:[4]: 1–2 [2]: 5–6 [1]: 5–7 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,[5] so
must be large enough for this to be infeasible, and is typically taken to exceed 2200.
is normally modelled as a random oracle in formal analyses of EdDSA's security.
Ed25519 is the EdDSA signature scheme using SHA-512 (SHA-2) and an elliptic curve related to Curve25519[2] where
is known as edwards25519,[7][1] and is birationally equivalent to the Montgomery curve known as Curve25519.
The original 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.
[10] Ed25519 is designed to avoid implementations that use branch conditions or array indices that depend on secret data,[2]: 2 [1]: 40 in order to mitigate side-channel attacks.
As with 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.
[11][12][13][14] 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.
[2]: 8 Note that there are two standardization efforts for EdDSA, one from IETF, an informational RFC 8032 and one from NIST as part of FIPS 186-5.
[15] The differences between the standards have been analyzed,[16][17] and test vectors are available.
[18] Notable uses of Ed25519 include OpenSSH,[19] GnuPG[20] and various alternatives, and the signify tool by OpenBSD.
[21] Usage of Ed25519 (and Ed448) in the SSH protocol has been standardized.
[22] In 2023 the final version of the FIPS 186-5 standard included deterministic Ed25519 as an approved signature scheme.
[15] Ed448 is the EdDSA signature scheme defined in RFC 8032 using the hash function SHAKE256 and the elliptic curve edwards448, an (untwisted) Edwards curve related to Curve448 in RFC 7748.
Ed448 has also been approved in the final version of the FIPS 186-5 standard.