Add Elliptic Curve Cryptography Algorithm

src/main/java/com/thealgorithms/ciphers/ECC.java

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+package com.thealgorithms.ciphers;
+
+import java.math.BigInteger;
+import java.security.SecureRandom;
+
+/**
+ * ECC - Elliptic Curve Cryptography
+ * Elliptic Curve Cryptography is a public-key cryptography method that uses the algebraic structure of
+ * elliptic curves over finite fields. ECC provides a higher level of security with smaller key sizes compared
+ * to other public-key methods like RSA, making it particularly suitable for environments where computational
+ * resources are limited, such as mobile devices and embedded systems.
+ *
+ * This class implements elliptic curve cryptography, providing encryption and decryption
+ * functionalities based on public and private key pairs.
+ *
+ * @author xuyang
+ */
+public class ECC {
+
+    private BigInteger privateKey; // Private key used for decryption
+    private ECPoint publicKey; // Public key used for encryption
+    private EllipticCurve curve; // Elliptic curve used in cryptography
+    private ECPoint basePoint; // Base point G on the elliptic curve
+
+    public ECC(int bits) {
+        generateKeys(bits); // Generates public-private key pair
+    }
+
+    public EllipticCurve getCurve() {
+        return curve; // Returns the elliptic curve
+    }
+
+    public void setCurve(EllipticCurve curve) {
+        this.curve = curve;
+    }
+
+    // Getter and Setter for private key
+    public BigInteger getPrivateKey() {
+        return privateKey;
+    }
+
+    public void setPrivateKey(BigInteger privateKey) {
+        this.privateKey = privateKey;
+    }
+
+    /**
+     * Encrypts the message using the public key.
+     * The message is transformed into an ECPoint and encrypted with elliptic curve operations.
+     *
+     * @param message The plain message to be encrypted
+     * @return The encrypted message as an array of ECPoints (R, S)
+     */
+    public ECPoint[] encrypt(String message) {
+        BigInteger m = new BigInteger(message.getBytes()); // Convert message to BigInteger
+        SecureRandom r = new SecureRandom(); // Generate random value for k
+        BigInteger k = new BigInteger(curve.getFieldSize(), r); // Generate random scalar k
+
+        // Calculate point r = k * G, where G is the base point
+        ECPoint rPoint = basePoint.multiply(k, curve.getP(), curve.getA());
+
+        // Calculate point s = k * publicKey + encodedMessage
+        ECPoint sPoint = publicKey.multiply(k, curve.getP(), curve.getA()).add(curve.encodeMessage(m), curve.getP(), curve.getA());
+
+        return new ECPoint[] {rPoint, sPoint}; // Return encrypted message as two ECPoints
+    }
+
+    /**
+     * Decrypts the encrypted message using the private key.
+     * The decryption process is the reverse of encryption, recovering the original message.
+     *
+     * @param encryptedMessage The encrypted message as an array of ECPoints (R, S)
+     * @return The decrypted plain message as a String
+     */
+    public String decrypt(ECPoint[] encryptedMessage) {
+        ECPoint rPoint = encryptedMessage[0]; // First part of ciphertext
+        ECPoint sPoint = encryptedMessage[1]; // Second part of ciphertext
+
+        // Perform decryption: s - r * privateKey
+        ECPoint decodedMessage = sPoint.subtract(rPoint.multiply(privateKey, curve.getP(), curve.getA()), curve.getP(), curve.getA());
+
+        BigInteger m = curve.decodeMessage(decodedMessage); // Decode the message from ECPoint
+
+        return new String(m.toByteArray()); // Convert BigInteger back to String
+    }
+
+    /**
+     * Generates a new public-private key pair for encryption and decryption.
+     *
+     * @param bits The size (in bits) of the keys to generate
+     */
+    public final void generateKeys(int bits) {
+        SecureRandom r = new SecureRandom();
+        curve = new EllipticCurve(bits); // Initialize a new elliptic curve
+        basePoint = curve.getBasePoint(); // Set the base point G
+
+        // Generate private key as a random BigInteger
+        privateKey = new BigInteger(bits, r);
+
+        // Generate public key as the point publicKey = privateKey * G
+        publicKey = basePoint.multiply(privateKey, curve.getP(), curve.getA());
+    }
+
+    /**
+     * Class representing an elliptic curve with the form y^2 = x^3 + ax + b.
+     */
+    public static class EllipticCurve {
+        private final BigInteger a; // Coefficient a in the curve equation
+        private final BigInteger b; // Coefficient b in the curve equation
+        private final BigInteger p; // Prime number p, defining the finite field
+        private final ECPoint basePoint; // Base point G on the curve
+
+        // Constructor with explicit parameters for a, b, p, and base point
+        public EllipticCurve(BigInteger a, BigInteger b, BigInteger p, ECPoint basePoint) {
+            this.a = a;
+            this.b = b;
+            this.p = p;
+            this.basePoint = basePoint;
+        }
+
+        // Constructor that randomly generates the curve parameters
+        public EllipticCurve(int bits) {
+            SecureRandom r = new SecureRandom();
+            this.p = BigInteger.probablePrime(bits, r); // Random prime p
+            this.a = new BigInteger(bits, r); // Random coefficient a
+            this.b = new BigInteger(bits, r); // Random coefficient b
+            this.basePoint = new ECPoint(BigInteger.valueOf(4), BigInteger.valueOf(8)); // Fixed base point G
+        }
+
+        public ECPoint getBasePoint() {
+            return basePoint;
+        }
+
+        public BigInteger getP() {
+            return p;
+        }
+
+        public BigInteger getA() {
+            return a;
+        }
+
+        public BigInteger getB() {
+            return b;
+        }
+
+        public int getFieldSize() {
+            return p.bitLength();
+        }
+
+        public ECPoint encodeMessage(BigInteger message) {
+            // Simple encoding of a message as an ECPoint (this is a simplified example)
+            return new ECPoint(message, message);
+        }
+
+        public BigInteger decodeMessage(ECPoint point) {
+            return point.getX(); // Decode the message from ECPoint (simplified)
+        }
+    }
+
+    /**
+     * Class representing a point on the elliptic curve.
+     */
+    public static class ECPoint {
+        private final BigInteger x; // X-coordinate of the point
+        private final BigInteger y; // Y-coordinate of the point
+
+        public ECPoint(BigInteger x, BigInteger y) {
+            this.x = x;
+            this.y = y;
+        }
+
+        public BigInteger getX() {
+            return x;
+        }
+
+        public BigInteger getY() {
+            return y;
+        }
+
+        @Override
+        public String toString() {
+            return "ECPoint(x=" + x.toString() + ", y=" + y.toString() + ")";
+        }
+
+        /**
+         * Add two points on the elliptic curve.
+         */
+        public ECPoint add(ECPoint other, BigInteger p, BigInteger a) {
+            if (this.x.equals(BigInteger.ZERO) && this.y.equals(BigInteger.ZERO)) {
+                return other; // If this point is the identity, return the other point
+            }
+            if (other.x.equals(BigInteger.ZERO) && other.y.equals(BigInteger.ZERO)) {
+                return this; // If the other point is the identity, return this point
+            }
+
+            BigInteger lambda;
+            if (this.equals(other)) {
+                // Special case: point doubling
+                lambda = this.x.pow(2).multiply(BigInteger.valueOf(3)).add(a).multiply(this.y.multiply(BigInteger.valueOf(2)).modInverse(p)).mod(p);
+            } else {
+                // General case: adding two different points
+                lambda = other.y.subtract(this.y).multiply(other.x.subtract(this.x).modInverse(p)).mod(p);
+            }
+
+            BigInteger xr = lambda.pow(2).subtract(this.x).subtract(other.x).mod(p);
+            BigInteger yr = lambda.multiply(this.x.subtract(xr)).subtract(this.y).mod(p);
+
+            return new ECPoint(xr, yr);
+        }
+
+        /**
+         * Subtract two points on the elliptic curve.
+         */
+        public ECPoint subtract(ECPoint other, BigInteger p, BigInteger a) {
+            ECPoint negOther = new ECPoint(other.x, p.subtract(other.y)); // Negate the Y coordinate
+            return this.add(negOther, p, a); // Add the negated point
+        }
+
+        /**
+         * Multiply a point by a scalar (repeated addition).
+         */
+        public ECPoint multiply(BigInteger k, BigInteger p, BigInteger a) {
+            ECPoint result = new ECPoint(BigInteger.ZERO, BigInteger.ZERO); // Identity point
+            ECPoint addend = this;
+
+            while (k.signum() > 0) {
+                if (k.testBit(0)) {
+                    result = result.add(addend, p, a); // Add the current point
+                }
+                addend = addend.add(addend, p, a); // Double the point
+                k = k.shiftRight(1); // Divide k by 2
+            }
+
+            return result;
+        }
+    }
+}

src/test/java/com/thealgorithms/ciphers/ECCTest.java

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+package com.thealgorithms.ciphers;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertNotEquals;
+
+import java.math.BigInteger;
+import org.junit.jupiter.api.Test;
+
+/**
+ * ECCTest - Unit tests for the ECC (Elliptic Curve Cryptography) implementation.
+ * This class contains various test cases to validate the encryption and decryption functionalities.
+ * It ensures the correctness and randomness of ECC operations.
+ *
+ * @author xuyang
+ */
+public class ECCTest {
+    ECC ecc = new ECC(256); // Generate a 256-bit ECC key pair. Calls generateKeys(bits) to create keys including privateKey and publicKey.
+
+    /**
+     * Test the encryption functionality: convert plaintext to ciphertext and output relevant encryption data.
+     */
+    @Test
+    void testEncrypt() {
+        String textToEncrypt = "Elliptic Curve Cryptography";
+
+        ECC.ECPoint[] cipherText = ecc.encrypt(textToEncrypt); // Perform encryption
+
+        // Output private key information
+        System.out.println("Private Key: " + ecc.getPrivateKey());
+
+        // Output elliptic curve parameters
+        ECC.EllipticCurve curve = ecc.getCurve();
+        System.out.println("Elliptic Curve Parameters:");
+        System.out.println("a: " + curve.getA());
+        System.out.println("b: " + curve.getB());
+        System.out.println("p: " + curve.getP());
+        System.out.println("Base Point G: " + curve.getBasePoint());
+
+        // Verify that the ciphertext is not empty
+        assertEquals(cipherText.length, 2); // Check if the ciphertext contains two points (R and S)
+
+        // Output the encrypted coordinate points
+        System.out.println("Encrypted Points:");
+        for (ECC.ECPoint point : cipherText) {
+            System.out.println(point); // Calls ECPoint's toString() method
+        }
+    }
+
+    /**
+     * Test the decryption functionality: convert ciphertext back to plaintext using known private key and elliptic curve parameters.
+     */
+    @Test
+    void testDecryptWithKnownValues() {
+        // 1. Define the known private key
+        BigInteger knownPrivateKey = new BigInteger("28635978664199231399690075483195602260051035216440375973817268759912070302603");
+
+        // 2. Define the known elliptic curve parameters
+        BigInteger a = new BigInteger("64505295837372135469230827475895976532873592609649950000895066186842236488761"); // Replace with known a value
+        BigInteger b = new BigInteger("89111668838830965251111555638616364203833415376750835901427122343021749874324"); // Replace with known b value
+        BigInteger p = new BigInteger("107276428198310591598877737561885175918069075479103276920057092968372930219921"); // Replace with known p value
+        ECC.ECPoint basePoint = new ECC.ECPoint(new BigInteger("4"), new BigInteger("8")); // Replace with known base point coordinates
+
+        // 3. Create the elliptic curve object
+        ECC.EllipticCurve curve = new ECC.EllipticCurve(a, b, p, basePoint);
+
+        // 4. Define the known ciphertext containing two ECPoints (R, S)
+        ECC.ECPoint rPoint = new ECC.ECPoint(new BigInteger("103077584019003058745849614420912636617007257617156724481937620119667345237687"), new BigInteger("68193862907937248121971710522760893811582068323088661566426323952783362061817"));
+        ECC.ECPoint sPoint = new ECC.ECPoint(new BigInteger("31932232426664380635434632300383525435115368414929679432313910646436992147798"), new BigInteger("77299754382292904069123203569944908076819220797512755280123348910207308129766"));
+        ECC.ECPoint[] cipherText = new ECC.ECPoint[] {rPoint, sPoint};
+
+        // 5. Create an ECC instance and set the private key and curve parameters
+        ecc.setPrivateKey(knownPrivateKey); // Use setter method to set the private key
+        ecc.setCurve(curve); // Use setter method to set the elliptic curve
+
+        // 6. Decrypt the known ciphertext
+        String decryptedMessage = ecc.decrypt(cipherText);
+
+        // 7. Compare the decrypted plaintext with the expected value
+        String expectedMessage = "Elliptic Curve Cryptography"; // Expected plaintext
+        assertEquals(expectedMessage, decryptedMessage);
+    }
+
+    /**
+     * Test that encrypting the same plaintext with ECC produces different ciphertexts.
+     */
+    @Test
+    void testCipherTextRandomness() {
+        String message = "Elliptic Curve Cryptography";
+
+        ECC.ECPoint[] cipherText1 = ecc.encrypt(message);
+        ECC.ECPoint[] cipherText2 = ecc.encrypt(message);
+
+        assertNotEquals(cipherText1, cipherText2); // Ensure that the two ciphertexts are different
+    }
+
+    /**
+     * Test the entire ECC encryption and decryption process.
+     */
+    @Test
+    void testECCEncryptionAndDecryption() {
+        String textToEncrypt = "Elliptic Curve Cryptography";
+        ECC.ECPoint[] cipherText = ecc.encrypt(textToEncrypt);
+        String decryptedText = ecc.decrypt(cipherText);
+        assertEquals(textToEncrypt, decryptedText); // Verify that the decrypted text matches the original text
+    }
+}