Class EllipticCurve

java.lang.Object

org.episteme.core.mathematics.cryptography.EllipticCurve

public class EllipticCurve
extends Object

Elliptic Curve Cryptography (ECC).

More efficient than RSA - same security with smaller keys. Based on algebraic structure of elliptic curves over finite fields.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	EllipticCurve.Curve	Elliptic curve parameters: y² = x³ + ax + b (mod p)
static class	EllipticCurve.KeyPair	Generates ECDH key pair.
static class	EllipticCurve.Point	Point on elliptic curve y² = x³ + ax + b (mod p)

Constructor Summary

Constructors

Constructor	Description
EllipticCurve()

Method Summary

Modifier and Type	Method	Description
static EllipticCurve.Point	add(EllipticCurve.Point P, EllipticCurve.Point Q, EllipticCurve.Curve curve)	Point addition on elliptic curve.
static EllipticCurve.Point	computeSharedSecret(BigInteger privateKey, EllipticCurve.Point otherPublicKey, EllipticCurve.Curve curve)	ECDH shared secret computation.
static EllipticCurve.Point	doublePoint(EllipticCurve.Point P, EllipticCurve.Curve curve)	Point doubling: P + P = 2P
static EllipticCurve.KeyPair	generateKeyPair(EllipticCurve.Curve curve)	Generate key pair for ECDH.
static EllipticCurve.Point	multiply(BigInteger k, EllipticCurve.Point P, EllipticCurve.Curve curve)	Scalar multiplication: k * P (adds P to itself k times).

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

EllipticCurve

public EllipticCurve()

Method Details

add

public static EllipticCurve.Point add(EllipticCurve.Point P,
 EllipticCurve.Point Q,
 EllipticCurve.Curve curve)

Point addition on elliptic curve.

doublePoint

public static EllipticCurve.Point doublePoint(EllipticCurve.Point P,
 EllipticCurve.Curve curve)

Point doubling: P + P = 2P

multiply

public static EllipticCurve.Point multiply(BigInteger k,
 EllipticCurve.Point P,
 EllipticCurve.Curve curve)

Scalar multiplication: k * P (adds P to itself k times). Uses double-and-add algorithm for efficiency.

generateKeyPair

public static EllipticCurve.KeyPair generateKeyPair(EllipticCurve.Curve curve)

Generate key pair for ECDH.

computeSharedSecret

public static EllipticCurve.Point computeSharedSecret(BigInteger privateKey,
 EllipticCurve.Point otherPublicKey,
 EllipticCurve.Curve curve)

ECDH shared secret computation.