@return a parameter specification representing the EdDSA domain parameters for the key.

GroupElement addition using the twisted Edwards addition law with extended coordinates (Hisil2008). <p> this must be in $P^3$ representation and $q$ i

Converts the group element to the P3 representation. @return The group element in the P3 representation.

Encode a FieldElement in its $(b-1)$-bit encoding. @return the $(b-1)$-bit encoding of this FieldElement.

Constant-time byte comparison. @param b a byte @param c a byte @return 1 if b and c are equal, 0 otherwise.

Converts a hex string to bytes. @param s the hex string to be converted. @return the byte[]

Constant-time conditional move. <p> Replaces this with $u$ if $b == 1$.<br> Replaces this with this if $b == 0$. <p> Method is package private only so

Converts the group element to the P2 representation. @return The group element in the P2 representation.

Creates a new group element in P1P1 representation. @param curve The curve. @param X The $X$ coordinate. @param Y The $Y$ coordinate. @param Z The $Z

Creates a new group element in PRECOMP representation. @param curve The curve. @param ypx The $y + x$ value. @param ymx The $y - x$ value. @param xy2

Verify an Ed25519 signature against the message @param signature [String] 64-byte string containing an Ed25519 signature @param message [String] stri

Doubles a given group element $p$ in $P^2$ or $P^3$ representation and returns the result in $P \times P$ representation. $r = 2 p$ where $p = (X : Y

@return the base (generator)

Convert in to big endian @param in the $(b-1)$-bit encoding of a FieldElement. @return the decoded value as a BigInteger

Converts the group element to the CACHED representation. @return The group element in the CACHED representation.

Gets the curve of the group element. @return The curve.

GroupElement addition using the twisted Edwards addition law with extended coordinates (Hisil2008). <p> this must be in $P^3$ representation and $q$ i

Creates a new group element in P2 representation. @param curve The curve. @param X The $X$ coordinate. @param Y The $Y$ coordinate. @param Z The $Z$

Sign the given message, returning an Ed25519 signature @param message [String] message to be signed @return [String] 64-byte Ed25519 signature

Convert a GroupElement from one Representation to another. TODO-CR: Add additional conversion? $r = p$ <p> Supported conversions: <p><ul> <li>P3 $\rig

@return the public key

@return the hash of the seed

@return will be null if constructed from a spec which was directly constructed from H

@return the private key

$h = f g$ <p> Can overlap $h$ with $f$ or $g$. <p> Preconditions: </p><ul> <li>$|f|$ bounded by $1.65 2^{26},1.65 2^{25},1.65 2^{26},1.65 2^{25},$ etc

Creates a new group element in P3 representation. @param curve The curve. @param X The $X$ coordinate. @param Y The $Y$ coordinate. @param Z The $Z$

Precomputes several tables. <p> The precomputed tables are used for {@link #scalarMultiply(byte[])} and {@link #doubleScalarMultiplyVariableTime(Group

Reduce the given scalar mod $l$. <p> From the Ed25519 paper:<br> Here we interpret $2b$-bit strings in little-endian form as integers in $\{0, 1,...,

$h = a B$ where $a = a[0]+256 a[1]+\dots+256^{31} a[31]$ and $B$ is this point. If its lookup table has not been precomputed, it will be at the start

Converts the group element to an encoded point on the curve. @return The encoded point as byte array.

Return a compressed twisted Edwards coordinate representing the public key @return [String] bytestring serialization of this public key

Creates a new group element in CACHED representation. @param curve The curve. @param YpX The $Y + X$ value. @param YmX The $Y - X$ value. @param Z Th

Create a SigningKey from a 64-byte Ed25519 keypair (i.e. public + private) @param keypair [String] 64-byte keypair value containing both seed + publi

Generate a random Ed25519 signing key (i.e. private scalar)

@return the public key

Returns the public key in its canonical encoding. <p> This implements the following specs: <ul><li> General encoding: https://tools.ietf.org/html/draf