[Ethereum] How to generate private, public and ethereum addresses using web3.py

1) Follow the instructions in the second answer to implement spongycastle on Android. https://stackoverflow.com/questions/6898801/how-to-include-the-spongy-castle-jar-in-android

2) Download and import the slfj4 logger jar http://www.slf4j.org/android/

3) Download the latest ethereumj jar. Make sure you list the spongycastle jars first in your build.gradle dependencies, followed by slf4j, then ethereumj

4) You'll need to create new ethereum classes using spongy castle instead of bouncycastle. Here's the class I used to create private keys, sign them, etc. It's just a modified version of ethereumj's ECKey.class. Note that I included spongycastle here as a security provider, so don't make yourself a new class that includes it (this was mentioned in step 1)

package com.your.package;
import android.support.annotation.Nullable;

import org.ethereum.config.Constants;
import org.ethereum.crypto.HashUtil;
import org.ethereum.crypto.jce.ECKeyAgreement;
import org.ethereum.crypto.jce.ECKeyFactory;
import org.ethereum.crypto.jce.ECKeyPairGenerator;
import org.ethereum.crypto.jce.ECSignatureFactory;
import org.ethereum.util.BIUtil;
import org.ethereum.util.ByteUtil;
import org.spongycastle.asn1.ASN1InputStream;
import org.spongycastle.asn1.ASN1Integer;
import org.spongycastle.asn1.DLSequence;
import org.spongycastle.asn1.sec.SECNamedCurves;
import org.spongycastle.asn1.x9.X9ECParameters;
import org.spongycastle.asn1.x9.X9IntegerConverter;
import org.spongycastle.crypto.agreement.ECDHBasicAgreement;
import org.spongycastle.crypto.digests.SHA256Digest;
import org.spongycastle.crypto.engines.AESFastEngine;
import org.spongycastle.crypto.modes.SICBlockCipher;
import org.spongycastle.crypto.params.ECDomainParameters;
import org.spongycastle.crypto.params.ECPrivateKeyParameters;
import org.spongycastle.crypto.params.ECPublicKeyParameters;
import org.spongycastle.crypto.params.KeyParameter;
import org.spongycastle.crypto.params.ParametersWithIV;
import org.spongycastle.crypto.signers.ECDSASigner;
import org.spongycastle.crypto.signers.HMacDSAKCalculator;
import org.spongycastle.jcajce.provider.asymmetric.ec.BCECPrivateKey;
import org.spongycastle.jcajce.provider.asymmetric.ec.BCECPublicKey;
import org.spongycastle.jce.spec.ECParameterSpec;
import org.spongycastle.jce.spec.ECPrivateKeySpec;
import org.spongycastle.jce.spec.ECPublicKeySpec;
import org.spongycastle.math.ec.ECAlgorithms;
import org.spongycastle.math.ec.ECCurve.Fp;
import org.spongycastle.math.ec.ECPoint;
import org.spongycastle.util.BigIntegers;
import org.spongycastle.util.encoders.Base64;
import org.spongycastle.util.encoders.Hex;

import java.io.IOException;
import java.io.Serializable;
import java.math.BigInteger;
import java.nio.charset.Charset;
import java.security.InvalidKeyException;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import java.security.PrivateKey;
import java.security.Provider;
import java.security.PublicKey;
import java.security.SecureRandom;
import java.security.Security;
import java.security.Signature;
import java.security.SignatureException;
import java.security.interfaces.ECPrivateKey;
import java.security.interfaces.ECPublicKey;
import java.security.spec.InvalidKeySpecException;
import java.util.Arrays;

import javax.crypto.KeyAgreement;
public class ECKey implements Serializable {
    static {
        Security.insertProviderAt(new org.spongycastle.jce.provider.BouncyCastleProvider(), 1);
    }
    public static final ECDomainParameters CURVE;
    public static final ECParameterSpec CURVE_SPEC;
    public static final BigInteger HALF_CURVE_ORDER;
    private static final SecureRandom secureRandom;
    private static final long serialVersionUID = -728224901792295832L;
    private final PrivateKey privKey;
    protected final ECPoint pub;
    private final Provider provider;
    private transient byte[] pubKeyHash;
    private transient byte[] nodeId;

    public ECKey() {
        this(secureRandom);
    }

    private static ECPoint extractPublicKey(ECPublicKey ecPublicKey) {
        java.security.spec.ECPoint publicPointW = ecPublicKey.getW();
        BigInteger xCoord = publicPointW.getAffineX();
        BigInteger yCoord = publicPointW.getAffineY();
        return CURVE.getCurve().createPoint(xCoord, yCoord);
    }

    public ECKey(Provider provider, SecureRandom secureRandom) {
        this.provider = provider;
        KeyPairGenerator keyPairGen = ECKeyPairGenerator.getInstance(provider, secureRandom);
        KeyPair keyPair = keyPairGen.generateKeyPair();
        this.privKey = keyPair.getPrivate();
        PublicKey pubKey = keyPair.getPublic();
        if(pubKey instanceof BCECPublicKey) {
            this.pub = ((BCECPublicKey)pubKey).getQ();
        } else {
            if(!(pubKey instanceof ECPublicKey)) {
                throw new AssertionError("Expected Provider " + provider.getName() + " to produce a subtype of ECPublicKey, found " + pubKey.getClass());
            }

            this.pub = extractPublicKey((ECPublicKey)pubKey);
        }

    }

    public ECKey(SecureRandom secureRandom) {
        this(new org.spongycastle.jce.provider.BouncyCastleProvider(), secureRandom);
    }

    private static boolean isECPrivateKey(PrivateKey privKey) {
        return privKey instanceof ECPrivateKey || privKey.getAlgorithm().equals("EC");
    }

    public ECKey(Provider provider,  PrivateKey privKey, ECPoint pub) {
        this.provider = provider;
        if(privKey != null && !isECPrivateKey(privKey)) {
            throw new IllegalArgumentException("Expected EC private key, given a private key object with class " + privKey.getClass().toString() + " and algorithm " + privKey.getAlgorithm());
        } else {
            this.privKey = privKey;
            if(pub == null) {
                throw new IllegalArgumentException("Public key may not be null");
            } else {
                this.pub = pub;
            }
        }
    }

    private static PrivateKey privateKeyFromBigInteger(BigInteger priv) {
        if(priv == null) {
            return null;
        } else {
            try {
                return ECKeyFactory.getInstance(new org.spongycastle.jce.provider.BouncyCastleProvider()).generatePrivate(new ECPrivateKeySpec(priv, CURVE_SPEC));
            } catch (InvalidKeySpecException var2) {
                throw new AssertionError("Assumed correct key spec statically");
            }
        }
    }

    public ECKey(@Nullable BigInteger priv, ECPoint pub) {
        this(new org.spongycastle.jce.provider.BouncyCastleProvider(), privateKeyFromBigInteger(priv), pub);
    }

    /** @deprecated */
    public static ECPoint compressPoint(ECPoint uncompressed) {
        return CURVE.getCurve().decodePoint(uncompressed.getEncoded(true));
    }

    /** @deprecated */
    public static ECPoint decompressPoint(ECPoint compressed) {
        return CURVE.getCurve().decodePoint(compressed.getEncoded(false));
    }

    public static ECKey fromPrivate(BigInteger privKey) {
        return new ECKey(privKey, CURVE.getG().multiply(privKey));
    }

    public static ECKey fromPrivate(byte[] privKeyBytes) {
        return fromPrivate(new BigInteger(1, privKeyBytes));
    }

    public static ECKey fromPrivateAndPrecalculatedPublic(BigInteger priv, ECPoint pub) {
        return new ECKey(priv, pub);
    }

    public static ECKey fromPrivateAndPrecalculatedPublic(byte[] priv, byte[] pub) {
        check(priv != null, "Private key must not be null");
        check(pub != null, "Public key must not be null");
        return new ECKey(new BigInteger(1, priv), CURVE.getCurve().decodePoint(pub));
    }

    public static ECKey fromPublicOnly(ECPoint pub) {
        return new ECKey((BigInteger)null, pub);
    }

    public static ECKey fromPublicOnly(byte[] pub) {
        return new ECKey((BigInteger)null, CURVE.getCurve().decodePoint(pub));
    }

    /** @deprecated */
    public ECKey decompress() {
        return !this.pub.isCompressed()?this:new ECKey(this.provider, this.privKey, decompressPoint(this.pub));
    }

    /** @deprecated */
    public ECKey compress() {
        return this.pub.isCompressed()?this:new ECKey(this.provider, this.privKey, compressPoint(this.pub));
    }

    public boolean isPubKeyOnly() {
        return this.privKey == null;
    }

    public boolean hasPrivKey() {
        return this.privKey != null;
    }

    public static byte[] publicKeyFromPrivate(BigInteger privKey, boolean compressed) {
        ECPoint point = CURVE.getG().multiply(privKey);
        return point.getEncoded(compressed);
    }

    public static byte[] computeAddress(byte[] pubBytes) {
        return HashUtil.sha3omit12(Arrays.copyOfRange(pubBytes, 1, pubBytes.length));
    }

    public static byte[] computeAddress(ECPoint pubPoint) {
        return computeAddress(pubPoint.getEncoded(false));
    }

    public byte[] getAddress() {
        if(this.pubKeyHash == null) {
            this.pubKeyHash = computeAddress(this.pub);
        }

        return this.pubKeyHash;
    }

    public static byte[] pubBytesWithoutFormat(ECPoint pubPoint) {
        byte[] pubBytes = pubPoint.getEncoded(false);
        return Arrays.copyOfRange(pubBytes, 1, pubBytes.length);
    }

    public byte[] getNodeId() {
        if(this.nodeId == null) {
            this.nodeId = pubBytesWithoutFormat(this.pub);
        }

        return this.nodeId;
    }

    public static ECKey fromNodeId(byte[] nodeId) {
        check(nodeId.length == 64, "Expected a 64 byte node id");
        byte[] pubBytes = new byte[65];
        System.arraycopy(nodeId, 0, pubBytes, 1, nodeId.length);
        pubBytes[0] = 4;
        return fromPublicOnly(pubBytes);
    }

    public byte[] getPubKey() {
        return this.pub.getEncoded(false);
    }

    public ECPoint getPubKeyPoint() {
        return this.pub;
    }

    public BigInteger getPrivKey() {
        if(this.privKey == null) {
            throw new ECKey.MissingPrivateKeyException();
        } else if(this.privKey instanceof BCECPrivateKey) {
            return ((BCECPrivateKey)this.privKey).getD();
        } else {
            throw new ECKey.MissingPrivateKeyException();
        }
    }

    public boolean isCompressed() {
        return this.pub.isCompressed();
    }

    public String toString() {
        StringBuilder b = new StringBuilder();
        b.append("pub:").append(Hex.toHexString(this.pub.getEncoded(false)));
        return b.toString();
    }

    public String toStringWithPrivate() {
        StringBuilder b = new StringBuilder();
        b.append(this.toString());
        if(this.privKey != null && this.privKey instanceof BCECPrivateKey) {
            b.append(" priv:").append(Hex.toHexString(((BCECPrivateKey)this.privKey).getD().toByteArray()));
        }

        return b.toString();
    }

    public ECKey.ECDSASignature doSign(byte[] input) {
        if(input.length != 32) {
            throw new IllegalArgumentException("Expected 32 byte input to ECDSA signature, not " + input.length);
        } else if(this.privKey == null) {
            throw new ECKey.MissingPrivateKeyException();
        } else if(this.privKey instanceof BCECPrivateKey) {
            ECDSASigner ex1 = new ECDSASigner(new HMacDSAKCalculator(new SHA256Digest()));
            ECPrivateKeyParameters derSignature1 = new ECPrivateKeyParameters(((BCECPrivateKey)this.privKey).getD(), CURVE);
            ex1.init(true, derSignature1);
            BigInteger[] components = ex1.generateSignature(input);
            return (new ECKey.ECDSASignature(components[0], components[1])).toCanonicalised();
        } else {
            try {
                Signature ex = ECSignatureFactory.getRawInstance(this.provider);
                ex.initSign(this.privKey);
                ex.update(input);
                byte[] derSignature = ex.sign();
                return ECKey.ECDSASignature.decodeFromDER(derSignature).toCanonicalised();
            } catch (InvalidKeyException | SignatureException var5) {
                throw new RuntimeException("ECKey signing error", var5);
            }
        }
    }

    public ECKey.ECDSASignature sign(byte[] messageHash) {
        ECKey.ECDSASignature sig = this.doSign(messageHash);
        int recId = -1;
        byte[] thisKey = this.pub.getEncoded(false);

        for(int i = 0; i < 4; ++i) {
            byte[] k = recoverPubBytesFromSignature(i, sig, messageHash);
            if(k != null && Arrays.equals(k, thisKey)) {
                recId = i;
                break;
            }
        }

        if(recId == -1) {
            throw new RuntimeException("Could not construct a recoverable key. This should never happen.");
        } else {
            sig.v = (byte)(recId + 27);
            return sig;
        }
    }

    public static byte[] signatureToKeyBytes(byte[] messageHash, String signatureBase64) throws SignatureException {
        byte[] signatureEncoded;
        try {
            signatureEncoded = Base64.decode(signatureBase64);
        } catch (RuntimeException var4) {
            throw new SignatureException("Could not decode base64", var4);
        }

        if(signatureEncoded.length < 65) {
            throw new SignatureException("Signature truncated, expected 65 bytes and got " + signatureEncoded.length);
        } else {
            return signatureToKeyBytes(messageHash, ECKey.ECDSASignature.fromComponents(Arrays.copyOfRange(signatureEncoded, 1, 33), Arrays.copyOfRange(signatureEncoded, 33, 65), (byte)(signatureEncoded[0] & 255)));
        }
    }

    public static byte[] signatureToKeyBytes(byte[] messageHash, ECKey.ECDSASignature sig) throws SignatureException {
        check(messageHash.length == 32, "messageHash argument has length " + messageHash.length);
        int header = sig.v;
        if(header >= 27 && header <= 34) {
            if(header >= 31) {
                header -= 4;
            }

            int recId = header - 27;
            byte[] key = recoverPubBytesFromSignature(recId, sig, messageHash);
            if(key == null) {
                throw new SignatureException("Could not recover public key from signature");
            } else {
                return key;
            }
        } else {
            throw new SignatureException("Header byte out of range: " + header);
        }
    }

    public static byte[] signatureToAddress(byte[] messageHash, String signatureBase64) throws SignatureException {
        return computeAddress(signatureToKeyBytes(messageHash, signatureBase64));
    }

    public static byte[] signatureToAddress(byte[] messageHash, ECKey.ECDSASignature sig) throws SignatureException {
        return computeAddress(signatureToKeyBytes(messageHash, sig));
    }

    public static ECKey signatureToKey(byte[] messageHash, String signatureBase64) throws SignatureException {
        byte[] keyBytes = signatureToKeyBytes(messageHash, signatureBase64);
        return fromPublicOnly(keyBytes);
    }

    public static ECKey signatureToKey(byte[] messageHash, ECKey.ECDSASignature sig) throws SignatureException {
        byte[] keyBytes = signatureToKeyBytes(messageHash, sig);
        return fromPublicOnly(keyBytes);
    }

    public BigInteger keyAgreement(ECPoint otherParty) {
        if(this.privKey == null) {
            throw new ECKey.MissingPrivateKeyException();
        } else if(this.privKey instanceof BCECPrivateKey) {
            ECDHBasicAgreement ex1 = new ECDHBasicAgreement();
            ex1.init(new ECPrivateKeyParameters(((BCECPrivateKey)this.privKey).getD(), CURVE));
            return ex1.calculateAgreement(new ECPublicKeyParameters(otherParty, CURVE));
        } else {
            try {
                KeyAgreement ex = ECKeyAgreement.getInstance(this.provider);
                ex.init(this.privKey);
                ex.doPhase(ECKeyFactory.getInstance(this.provider).generatePublic(new ECPublicKeySpec(otherParty, CURVE_SPEC)), true);
                return new BigInteger(1, ex.generateSecret());
            } catch (InvalidKeyException | InvalidKeySpecException | IllegalStateException var3) {
                throw new RuntimeException("ECDH key agreement failure", var3);
            }
        }
    }

    /** @deprecated */
    public byte[] decryptAES(byte[] cipher) {
        if(this.privKey == null) {
            throw new ECKey.MissingPrivateKeyException();
        } else if(!(this.privKey instanceof BCECPrivateKey)) {
            throw new UnsupportedOperationException("Cannot use the private key as an AES key");
        } else {
            AESFastEngine engine = new AESFastEngine();
            SICBlockCipher ctrEngine = new SICBlockCipher(engine);
            KeyParameter key = new KeyParameter(BigIntegers.asUnsignedByteArray(((BCECPrivateKey)this.privKey).getD()));
            ParametersWithIV params = new ParametersWithIV(key, new byte[16]);
            ctrEngine.init(false, params);
            int i = 0;
            byte[] out = new byte[cipher.length];

            while(i < cipher.length) {
                ctrEngine.processBlock(cipher, i, out, i);
                i += engine.getBlockSize();
                if(cipher.length - i < engine.getBlockSize()) {
                    break;
                }
            }

            if(cipher.length - i > 0) {
                byte[] tmpBlock = new byte[16];
                System.arraycopy(cipher, i, tmpBlock, 0, cipher.length - i);
                ctrEngine.processBlock(tmpBlock, 0, tmpBlock, 0);
                System.arraycopy(tmpBlock, 0, out, i, cipher.length - i);
            }

            return out;
        }
    }

    public static boolean verify(byte[] data, ECKey.ECDSASignature signature, byte[] pub) {
        ECDSASigner signer = new ECDSASigner();
        ECPublicKeyParameters params = new ECPublicKeyParameters(CURVE.getCurve().decodePoint(pub), CURVE);
        signer.init(false, params);

        try {
            return signer.verifySignature(data, signature.r, signature.s);
        } catch (NullPointerException var6) {
            return false;
        }
    }

    public static boolean verify(byte[] data, byte[] signature, byte[] pub) {
        return verify(data, ECKey.ECDSASignature.decodeFromDER(signature), pub);
    }

    public boolean verify(byte[] data, byte[] signature) {
        return verify(data, signature, this.getPubKey());
    }

    public boolean verify(byte[] sigHash, ECKey.ECDSASignature signature) {
        return verify(sigHash, signature, this.getPubKey());
    }

    public boolean isPubKeyCanonical() {
        return isPubKeyCanonical(this.pub.getEncoded(false));
    }

    public static boolean isPubKeyCanonical(byte[] pubkey) {
        if(pubkey[0] == 4) {
            if(pubkey.length != 65) {
                return false;
            }
        } else {
            if(pubkey[0] != 2 && pubkey[0] != 3) {
                return false;
            }

            if(pubkey.length != 33) {
                return false;
            }
        }

        return true;
    }

    @Nullable
    public static byte[] recoverPubBytesFromSignature(int recId, ECKey.ECDSASignature sig, byte[] messageHash) {
        check(recId >= 0, "recId must be positive");
        check(sig.r.signum() >= 0, "r must be positive");
        check(sig.s.signum() >= 0, "s must be positive");
        check(messageHash != null, "messageHash must not be null");
        BigInteger n = CURVE.getN();
        BigInteger i = BigInteger.valueOf((long)recId / 2L);
        BigInteger x = sig.r.add(i.multiply(n));
        Fp curve = (Fp)CURVE.getCurve();
        BigInteger prime = curve.getQ();
        if(x.compareTo(prime) >= 0) {
            return null;
        } else {
            ECPoint R = decompressKey(x, (recId & 1) == 1);
            if(!R.multiply(n).isInfinity()) {
                return null;
            } else {
                BigInteger e = new BigInteger(1, messageHash);
                BigInteger eInv = BigInteger.ZERO.subtract(e).mod(n);
                BigInteger rInv = sig.r.modInverse(n);
                BigInteger srInv = rInv.multiply(sig.s).mod(n);
                BigInteger eInvrInv = rInv.multiply(eInv).mod(n);
                org.spongycastle.math.ec.ECPoint.Fp q = (org.spongycastle.math.ec.ECPoint.Fp)ECAlgorithms.sumOfTwoMultiplies(CURVE.getG(), eInvrInv, R, srInv);
                return q.getEncoded(false);
            }
        }
    }

    @Nullable
    public static byte[] recoverAddressFromSignature(int recId, ECKey.ECDSASignature sig, byte[] messageHash) {
        byte[] pubBytes = recoverPubBytesFromSignature(recId, sig, messageHash);
        return pubBytes == null?null:computeAddress(pubBytes);
    }

    @Nullable
    public static ECKey recoverFromSignature(int recId, ECKey.ECDSASignature sig, byte[] messageHash) {
        byte[] pubBytes = recoverPubBytesFromSignature(recId, sig, messageHash);
        return pubBytes == null?null:fromPublicOnly(pubBytes);
    }

    private static ECPoint decompressKey(BigInteger xBN, boolean yBit) {
        X9IntegerConverter x9 = new X9IntegerConverter();
        byte[] compEnc = x9.integerToBytes(xBN, 1 + x9.getByteLength(CURVE.getCurve()));
        compEnc[0] = (byte)(yBit?3:2);
        return CURVE.getCurve().decodePoint(compEnc);
    }

    @Nullable
    public byte[] getPrivKeyBytes() {
        return this.privKey == null?null:(this.privKey instanceof BCECPrivateKey?ByteUtil.bigIntegerToBytes(((BCECPrivateKey)this.privKey).getD(), 32):null);
    }

    public boolean equals(Object o) {
        if(this == o) {
            return true;
        } else if(o != null && o instanceof ECKey) {
            ECKey ecKey = (ECKey)o;
            return this.privKey != null && !this.privKey.equals(ecKey.privKey)?false:this.pub == null || this.pub.equals(ecKey.pub);
        } else {
            return false;
        }
    }

    public int hashCode() {
        return Arrays.hashCode(this.getPubKey());
    }

    private static void check(boolean test, String message) {
        if(!test) {
            throw new IllegalArgumentException(message);
        }
    }

    static {
        X9ECParameters params = SECNamedCurves.getByName("secp256k1");
        CURVE = new ECDomainParameters(params.getCurve(), params.getG(), params.getN(), params.getH());
        CURVE_SPEC = new ECParameterSpec(params.getCurve(), params.getG(), params.getN(), params.getH());
        HALF_CURVE_ORDER = params.getN().shiftRight(1);
        secureRandom = new SecureRandom();
    }

    public static class MissingPrivateKeyException extends RuntimeException {
        public MissingPrivateKeyException() {
        }
    }

    public static class ECDSASignature {
        public final BigInteger r;
        public final BigInteger s;
        public byte v;

        public ECDSASignature(BigInteger r, BigInteger s) {
            this.r = r;
            this.s = s;
        }

        private static ECKey.ECDSASignature fromComponents(byte[] r, byte[] s) {
            return new ECKey.ECDSASignature(new BigInteger(1, r), new BigInteger(1, s));
        }

        public static ECKey.ECDSASignature fromComponents(byte[] r, byte[] s, byte v) {
            ECKey.ECDSASignature signature = fromComponents(r, s);
            signature.v = v;
            return signature;
        }

        public boolean validateComponents() {
            return validateComponents(this.r, this.s, this.v);
        }

        public static boolean validateComponents(BigInteger r, BigInteger s, byte v) {
            return v != 27 && v != 28?false:(BIUtil.isLessThan(r, BigInteger.ONE)?false:(BIUtil.isLessThan(s, BigInteger.ONE)?false:(!BIUtil.isLessThan(r, Constants.getSECP256K1N())?false:BIUtil.isLessThan(s, Constants.getSECP256K1N()))));
        }

        public static ECKey.ECDSASignature decodeFromDER(byte[] bytes) {
            ASN1InputStream decoder = null;

            ECKey.ECDSASignature e1;
            try {
                decoder = new ASN1InputStream(bytes);
                DLSequence e = (DLSequence)decoder.readObject();
                if(e == null) {
                    throw new RuntimeException("Reached past end of ASN.1 stream.");
                }

                ASN1Integer r;
                ASN1Integer s;
                try {
                    r = (ASN1Integer)e.getObjectAt(0);
                    s = (ASN1Integer)e.getObjectAt(1);
                } catch (ClassCastException var15) {
                    throw new IllegalArgumentException(var15);
                }

                e1 = new ECKey.ECDSASignature(r.getPositiveValue(), s.getPositiveValue());
            } catch (IOException var16) {
                throw new RuntimeException(var16);
            } finally {
                if(decoder != null) {
                    try {
                        decoder.close();
                    } catch (IOException var14) {
                        ;
                    }
                }

            }

            return e1;
        }

        public ECKey.ECDSASignature toCanonicalised() {
            return this.s.compareTo(ECKey.HALF_CURVE_ORDER) > 0?new ECKey.ECDSASignature(this.r, ECKey.CURVE.getN().subtract(this.s)):this;
        }

        public String toBase64() {
            byte[] sigData = new byte[65];
            sigData[0] = this.v;
            System.arraycopy(ByteUtil.bigIntegerToBytes(this.r, 32), 0, sigData, 1, 32);
            System.arraycopy(ByteUtil.bigIntegerToBytes(this.s, 32), 0, sigData, 33, 32);
            return new String(Base64.encode(sigData), Charset.forName("UTF-8"));
        }

        public boolean equals(Object o) {
            if(this == o) {
                return true;
            } else if(o != null && this.getClass() == o.getClass()) {
                ECKey.ECDSASignature signature = (ECKey.ECDSASignature)o;
                return !this.r.equals(signature.r)?false:this.s.equals(signature.s);
            } else {
                return false;
            }
        }

        public int hashCode() {
            int result = this.r.hashCode();
            result = 31 * result + this.s.hashCode();
            return result;
        }
    }
}

To actually get this going in your app, try something like this:

        ECKey key = new com.your.package.ECKey();
        byte[] addr = key.getAddress();
        byte[] priv = key.getPrivKeyBytes();
        String addrBase16 = Hex.toHexString(addr);
        String privBase16 = Hex.toHexString(priv);
        Log.d("address",addrBase16);
        Log.d("priv",privBase16);

Your calculations are right, except there aren't exactly 2^256 private keys -- there are "FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141" (this number is named N in the ETH source code, and is the order of the generator of the elliptic curve secp256k1, from which Ethereum key pairs are generated).

In answer to your question, yes, private keys mapping to the same address will both be able to spend the money in that address on a first come first served basis. They will create the same public key, which the ECDSA verification algorithm is performed against, and so signatures generated by either private key will verify against the same address!

In go-ethereum/accounts/key.go, we have a private key generated from S256 which is secp256k1's curve, meaning they will be less than N be default.

func newKeyFromECDSA(privateKeyECDSA *ecdsa.PrivateKey) *Key {
    id := uuid.NewRandom()
    key := &Key{
        Id:         id,
        Address:    crypto.PubkeyToAddress(privateKeyECDSA.PublicKey),
        PrivateKey: privateKeyECDSA,
    }
    return key
}

func newKey(rand io.Reader) (*Key, error) {
    privateKeyECDSA, err := ecdsa.GenerateKey(secp256k1.S256(), rand)
    if err != nil {
        return nil, err
    }
    return newKeyFromECDSA(privateKeyECDSA), nil
}

go-ethereum/crypto/secp256k1/secp256 also generates the key pairs in accordance with secp2656k1 albeit in a slightly different way :)

Cool illustrative explanation for what N really is and why 2 keys will be able to spend money from the same account

Imagine private keys are miles driven in your car, and public keys are number of miles on your car's odometer. If the odometer rolls over from 999,999 to 000,000, a person with miles driven = 1,000,001 will have the same 'public key', and hence the same address, as a person with miles driven = 1.

EC group arithmetic is surprisingly similar to this, but rather than 999,999, we have the seemingly arbitrary number given above! Due to this property, even with your different 'private keys', you will be able to create signatures that verify against the same public key, and hence spend ETH from the same address!!

Boring math explanation

Private keys are 256 bit numbers, and to calculate the public key from a private key you multiply by the generator, g, of the elliptic curve group. The generator in use is defined in the parameters of the secp256k1 libraries being used in ETH. It itself is also an elliptic curve point, and as elliptic curves are cyclic, there exists an n such that n.g = 1 (this is called the generator order).

With this equation we can see that if we had a private key k with k>n, we would have k.g = (k-n).g = k'.g, for a k' that is possibly someone else's private key! So we have keys generated at random modulo n, rather than 2^256.