const type: ecPoint

Type to describe a point at an elliptic curve. A point is either the neutral element or it is defined by x and y.

const type: ellipticCurve

Type to describe the elliptic curve y**2 = x**3 + a*x + b (mod p). The value p defines the finite field F. The values a and b specify the elliptic curve.

const type: jacobianPoint

Alternate type to describe a point at an elliptic curve. The curve points are on the elliptic curve y**2 = x**3 + a*x + b (mod p). This coordinates eliminate the need for expensive inversions mod p.

const type: eccKeyPair

Type to describe a pair of ECC keys (private key and public key).

const type: ecdsaSignatureType

Structure to hold an ECDSA signature. ECDSA is the Elliptic Curve Digital Signature Algorithm.

const ecPoint: neutralEcPoint

The neutral point of an elliptic curve.

const ellipticCurve: secp192k1

The elliptical curve secp192k1.

const ellipticCurve: secp192r1

The elliptical curve secp192r1.

const ellipticCurve: secp224k1

The elliptical curve secp224k1.

const ellipticCurve: secp224r1

The elliptical curve secp224r1.

const ellipticCurve: secp256k1

The elliptical curve secp256k1.

const ellipticCurve: secp256r1

The elliptical curve secp256r1.

const ellipticCurve: secp384r1

The elliptical curve secp384r1.

const ellipticCurve: secp521r1

The elliptical curve secp521r1.

const func boolean: (in ecPoint: point1) = (in ecPoint: point2)

Check if two elliptic curve points are equal.

Returns:

TRUE if the two points are equal, FALSE otherwise.

const func boolean: (in ecPoint: point1) <> (in ecPoint: point2)

Check if two elliptic curve points are not equal.

Returns:

FALSE if both numbers are equal, TRUE otherwise.

const func ecPoint: ecPoint (in bigInteger: x, in bigInteger: y)

Create an elliptic curve point from the given coordinates x and y.

const func ellipticCurve: ellipticCurve (in integer: bits, in string: name, in bigInteger: p, in bigInteger: a, in bigInteger: b, in ecPoint: g, in bigInteger: n)

Create an elliptic curve from the given parameters. Creates the elliptic curve y**2 = x**3 + a*x + b (mod p).

Parameters:

bits - Number of bits in the elliptic curve.

name - Name of the elliptic curve.

p - In the finite field F all computations are (mod p).

a - Possible negative factor from the curve formula.

b - Possible negative constant from the curve formula.

g - Base point of the elliptic curve.

n - Order of g (mult(g, n) = neutralEcPoint).

const func integer: getSizeInBytes (in ellipticCurve: curve)

Get the size of an elliptic curve in bytes. This is the number of bytes necessary to represent the x or y coordinate of an ecPoint.

const func boolean: element (in ecPoint: point, in ellipticCurve: curve)

Test, whether 'point' is on the given elliptic curve.

const func ecPoint: double (in ellipticCurve: curve, in ecPoint: p)

Double the point p over given curve. Double point in y**2 = x**3 + a*x + b (mod p).

const func ecPoint: add (in ellipticCurve: curve, in ecPoint: p1, in ecPoint: p2)

Add the points p1 and p2 over given curve. Addition of points in y**2 = x**3 + a*x + b (mod p).

const func ecPoint: mult (in ellipticCurve: curve, in var ecPoint: p1, in var bigInteger: c)

Multiply point p1 by scalar c over given curve. Scalar multiplication p1 * c = p1 + p1 + ... + p1 (c times).

const func jacobianPoint: toJacobian (in ecPoint: p)

Transform point p given as (x, y) to jacobian coordinates.

const func ecPoint: fromJacobian (in jacobianPoint: jp, in bigInteger: n)

Transform a point from jacobian coordinates to (x, y) mod n.

const func jacobianPoint: double (in ellipticCurve: curve, in jacobianPoint: jp)

Double the point jp in jacobian coordinates over given curve. Double point in y**2 = x**3 + a*x + b (mod p).

const func jacobianPoint: add (in ellipticCurve: curve, in jacobianPoint: jp1, in jacobianPoint: jp2)

Add the points jp1 and jp2 in jacobian coordinates over given curve. Addition of points in y**2 = x**3 + a*x + b (mod p).

const func jacobianPoint: mult (in ellipticCurve: curve, in var jacobianPoint: jp1, in var bigInteger: c)

Multiply point jp1 by scalar c in jacobian coordinates over given curve. Scalar multiplication jp1 * c = jp1 + jp1 + ... + jp1 (c times).

const func ecPoint: multFast (in ellipticCurve: curve, in var ecPoint: p1, in var bigInteger: c)

Multiply point p1 by scalar c over given curve. Scalar multiplication p1 * c = p1 + p1 + ... + p1 (c times). Encapsulates the multiplication that is done with jacobian coordinates.

const func ecPoint: multAddFast (in ellipticCurve: curve, in var ecPoint: p1, in var bigInteger: c1, in var ecPoint: p2, in var bigInteger: c2)

Compute the sum of two products (ecPoint times scalar). Encapsulates the computation that is done with jacobian coordinates.

const func string: ecPointCompress (in ellipticCurve: curve, in ecPoint: point)

Encode an ecPoint in compressed form.

const func string: ecPointEncode (in ellipticCurve: curve, in ecPoint: point)

Encode an ecPoint in uncompressed form.

const func ecPoint: ecPointDecode (in ellipticCurve: curve, in string: encoded)

ecode an ecPoint, which can be compressed or uncompressed.

const func bigInteger: genPrivateKey (in ellipticCurve: curve)

Generate a private key for elliptic curve cryptography (ECC).

const func eccKeyPair: genEccKeyPair (in ellipticCurve: curve)

Generate a new ECC keyPair (private key and public key).

const func boolean: verifyKeyPair (in ellipticCurve: curve, in eccKeyPair: keyPair)

Verify that public and private key of an ECC keyPair fit together.

const func ecdsaSignatureType: sign (in ellipticCurve: curve, in var bigInteger: message, in bigInteger: privateKey)

Compute the ECDSA signature of 'message'. ECDSA is the Elliptic Curve Digital Signature Algorithm.

const func boolean: verify (in ellipticCurve: curve, in var bigInteger: message, in ecdsaSignatureType: signature, in ecPoint: publicKey)

Verify that 'signature' is a valid ECDSA signature of 'message'. ECDSA is the Elliptic Curve Digital Signature Algorithm.