下面的完整示例代码取自我的私有跨平台项目，应该可以使用。它使用带有2048密钥对的rsa加密对字符串进行加密，并使用带有sha-1的oaep填充作为散列。
加密数据采用base64编码。出于演示的目的，我使用pem格式的静态（硬编码）密钥-在生产中永远不要这样做。
您可以在此处联机运行代码：https://repl.it/@javacrypto/cpcjavarsaencryptionoaepsha1string
这是输出：

RSA 2048 encryption OAEP SHA-1 string
plaintext: The quick brown fox jumps over the lazy dog

* * * encrypt the plaintext with the RSA public key * * *

ciphertextBase64: pSPayOK79NMPLpaQOp8L7dOTdLeS+jVU5cKPF5mDOvuKtnOjf/NYfgsf1JWa5Ud/fzsXrSN8I/8KAs/freagOYflv6PGUHZ7cYk1iX6sO5cmdD0Mfglj39NxczbqCK3FG20hQfa01ZaOu/dV8+QvVx851ph1nEl8arNML5ohhjIdZTxR3olGouGzDJmuJkDlv2fJICP7sdMnvl7t21QI701I2xR01eatD5src5fY//EIOEjSoTesCBZwEUz1S3UpclNqGONAqaYqlscdTyAlY3Hg8smJRqKWk7ZWKSTYsocBbFeTvcNy75LG/xyILM0l4U+NnwGUypkjR2vJRGVQtw==

* * * decrypt the ciphertext with the RSA private key * * *

ciphertextReceivedBase64: pSPayOK79NMPLpaQOp8L7dOTdLeS+jVU5cKPF5mDOvuKtnOjf/NYfgsf1JWa5Ud/fzsXrSN8I/8KAs/freagOYflv6PGUHZ7cYk1iX6sO5cmdD0Mfglj39NxczbqCK3FG20hQfa01ZaOu/dV8+QvVx851ph1nEl8arNML5ohhjIdZTxR3olGouGzDJmuJkDlv2fJICP7sdMnvl7t21QI701I2xR01eatD5src5fY//EIOEjSoTesCBZwEUz1S3UpclNqGONAqaYqlscdTyAlY3Hg8smJRqKWk7ZWKSTYsocBbFeTvcNy75LG/xyILM0l4U+NnwGUypkjR2vJRGVQtw==
decryptedtext: The quick brown fox jumps over the lazy dog

安全警告：代码没有任何异常处理，使用静态（硬编码）密钥，仅用于教育目的。
代码：

import javax.crypto.BadPaddingException;
import javax.crypto.Cipher;
import javax.crypto.IllegalBlockSizeException;
import javax.crypto.NoSuchPaddingException;
import javax.crypto.spec.OAEPParameterSpec;
import javax.crypto.spec.PSource;
import java.io.IOException;
import java.nio.charset.StandardCharsets;
import java.nio.file.Files;
import java.nio.file.Paths;
import java.security.*;
import java.security.spec.MGF1ParameterSpec;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;
import java.util.Base64;

public class Main {
    public static void main(String[] args) throws GeneralSecurityException, IOException {
        System.out.println("RSA 2048 encryption OAEP SHA-1 string");

        String dataToEncryptString = "The quick brown fox jumps over the lazy dog";
        byte[] dataToEncrypt = dataToEncryptString.getBytes(StandardCharsets.UTF_8);
        System.out.println("plaintext: " + dataToEncryptString);

        // # # # usually we would load the private and public key from a file or keystore # # #
        // # # # here we use hardcoded keys for demonstration - don't do this in real programs # # #
        String filenamePrivateKeyPem = "privatekey2048.pem";
        String filenamePublicKeyPem = "publickey2048.pem";

        // encryption
        System.out.println("\n* * * encrypt the plaintext with the RSA public key * * *");
        PublicKey publicKeyLoad = getPublicKeyFromString(loadRsaPublicKeyPem());
        // use this in production
        //PublicKey publicKeyLoad = getPublicKeyFromString(loadRsaKeyPemFile(filenamePublicKeyPem));
        String ciphertextBase64 = base64Encoding(rsaEncryptionOaepSha1(publicKeyLoad, dataToEncrypt));
        System.out.println("ciphertextBase64: " + ciphertextBase64);

        // transport the encrypted data to recipient

        // receiving the encrypted data, decryption
        System.out.println("\n* * * decrypt the ciphertext with the RSA private key * * *");
        String ciphertextReceivedBase64 = ciphertextBase64;
        //String ciphertextReceivedBase64 = "l4G3O42LtjI9KkzvcF7SQcpqrkOMJw1sWVuI3FCZ1g+Sp/t05E3ZEXyVV/FnadkKVgmpWBifaYPEdKNBTbuts2F1DfrDz1v14lKlMOcqkJB8OmJUAiKJ1ic414R7M5fECKruqkzOdKlTtdb3MI49Ygrzd/cJxOGEvONo3DAOq1kZvZdmyW+K8m807g2qoy833EHyj9NjVZHuDzXi8fMxbIAI5MrN8ykXZBxkFOAGiITEFbGPxu6gBOPJKsPWJ0SVU53CiI1YwGc76/ov4c7FIA1ZeVsJXKo8CEfYuUc7PKIJ3e5Z7CbiNgr4Z5720Xbi0drUBk/LlYq6m8s/zEIMaQ==";
        System.out.println("ciphertextReceivedBase64: " + ciphertextReceivedBase64);
        PrivateKey privateKeyLoad = getPrivateKeyFromString(loadRsaPrivateKeyPem());
        // use this in production
        //PrivateKey privateKeyLoad = getPrivateKeyFromString(loadRsaKeyPemFile(filenamePrivateKeyPem));
        byte[] ciphertextReceived = base64Decoding(ciphertextReceivedBase64);
        byte[] decryptedtextByte = rsaDecryptionOaepSha1(privateKeyLoad, ciphertextReceived);
        System.out.println("decryptedtext: " + new String(decryptedtextByte, StandardCharsets.UTF_8));
    }

    public static byte[] rsaEncryptionOaepSha1 (PublicKey publicKey, byte[] plaintextByte) throws NoSuchAlgorithmException,
            InvalidKeyException, IllegalBlockSizeException, BadPaddingException, NoSuchPaddingException, InvalidAlgorithmParameterException {
        byte[] ciphertextByte = null;
        Cipher encryptCipher = Cipher.getInstance("RSA/ECB/OAEPWITHSHA-1ANDMGF1PADDING");
        //OAEPParameterSpec oaepParameterSpecJCE = new OAEPParameterSpec("SHA-256", "MGF1", MGF1ParameterSpec.SHA256, PSource.PSpecified.DEFAULT);
        // note: SHA1 is the default for Java
        OAEPParameterSpec oaepParameterSpecJCE = new OAEPParameterSpec("SHA1", "MGF1", MGF1ParameterSpec.SHA1, PSource.PSpecified.DEFAULT);
        encryptCipher.init(Cipher.ENCRYPT_MODE, publicKey, oaepParameterSpecJCE);
        ciphertextByte = encryptCipher.doFinal(plaintextByte);
        return ciphertextByte;
    }

    public static byte[] rsaDecryptionOaepSha1 (PrivateKey privateKey, byte[] ciphertextByte) throws NoSuchAlgorithmException,
            NoSuchPaddingException, InvalidKeyException, BadPaddingException, IllegalBlockSizeException, InvalidAlgorithmParameterException {
        byte[] decryptedtextByte = null;
        Cipher decryptCipher = Cipher.getInstance("RSA/ECB/OAEPWITHSHA-1ANDMGF1PADDING");
        //OAEPParameterSpec oaepParameterSpecJCE = new OAEPParameterSpec("SHA-256", "MGF1", MGF1ParameterSpec.SHA256, PSource.PSpecified.DEFAULT);
        OAEPParameterSpec oaepParameterSpecJCE = new OAEPParameterSpec("SHA1", "MGF1", MGF1ParameterSpec.SHA1, PSource.PSpecified.DEFAULT);
        decryptCipher.init(Cipher.DECRYPT_MODE, privateKey, oaepParameterSpecJCE);
        decryptedtextByte = decryptCipher.doFinal(ciphertextByte);
        return decryptedtextByte;
    }

    private static String base64Encoding(byte[] input) {
        return Base64.getEncoder().encodeToString(input);
    }
    private static byte[] base64Decoding(String input) {
        return Base64.getDecoder().decode(input);
    }

    private static String loadRsaPrivateKeyPem() {
        // this is a sample key - don't worry !
        return "-----BEGIN PRIVATE KEY-----\n" +
                "MIIEvgIBADANBgkqhkiG9w0BAQEFAASCBKgwggSkAgEAAoIBAQDwSZYlRn86zPi9\n" +
                "e1RTZL7QzgE/36zjbeCMyOhf6o/WIKeVxFwVbG2FAY3YJZIxnBH+9j1XS6f+ewjG\n" +
                "FlJY4f2IrOpS1kPiO3fmOo5N4nc8JKvjwmKtUM0t63uFFPfs69+7mKJ4w3tk2mSN\n" +
                "4gb8J9P9BCXtH6Q78SdOYvdCMspA1X8eERsdLb/jjHs8+gepKqQ6+XwZbSq0vf2B\n" +
                "MtaAB7zTX/Dk+ZxDfwIobShPaB0mYmojE2YAQeRq1gYdwwO1dEGk6E5J2toWPpKY\n" +
                "/IcSYsGKyFqrsmbw0880r1BwRDer4RFrkzp4zvY+kX3eDanlyMqDLPN+ghXT1lv8\n" +
                "snZpbaBDAgMBAAECggEBAIVxmHzjBc11/73bPB2EGaSEg5UhdzZm0wncmZCLB453\n" +
                "XBqEjk8nhDsVfdzIIMSEVEowHijYz1c4pMq9osXR26eHwCp47AI73H5zjowadPVl\n" +
                "uEAot/xgn1IdMN/boURmSj44qiI/DcwYrTdOi2qGA+jD4PwrUl4nsxiJRZ/x7PjL\n" +
                "hMzRbvDxQ4/Q4ThYXwoEGiIBBK/iB3Z5eR7lFa8E5yAaxM2QP9PENBr/OqkGXLWV\n" +
                "qA/YTxs3gAvkUjMhlScOi7PMwRX9HsrAeLKbLuC1KJv1p2THUtZbOHqrAF/uwHaj\n" +
                "ygUblFaa/BTckTN7PKSVIhp7OihbD04bSRrh+nOilcECgYEA/8atV5DmNxFrxF1P\n" +
                "ODDjdJPNb9pzNrDF03TiFBZWS4Q+2JazyLGjZzhg5Vv9RJ7VcIjPAbMy2Cy5BUff\n" +
                "EFE+8ryKVWfdpPxpPYOwHCJSw4Bqqdj0Pmp/xw928ebrnUoCzdkUqYYpRWx0T7YV\n" +
                "RoA9RiBfQiVHhuJBSDPYJPoP34kCgYEA8H9wLE5L8raUn4NYYRuUVMa+1k4Q1N3X\n" +
                "Bixm5cccc/Ja4LVvrnWqmFOmfFgpVd8BcTGaPSsqfA4j/oEQp7tmjZqggVFqiM2m\n" +
                "J2YEv18cY/5kiDUVYR7VWSkpqVOkgiX3lK3UkIngnVMGGFnoIBlfBFF9uo02rZpC\n" +
                "5o5zebaDImsCgYAE9d5wv0+nq7/STBj4NwKCRUeLrsnjOqRriG3GA/TifAsX+jw8\n" +
                "XS2VF+PRLuqHhSkQiKazGr2Wsa9Y6d7qmxjEbmGkbGJBC+AioEYvFX9TaU8oQhvi\n" +
                "hgA6ZRNid58EKuZJBbe/3ek4/nR3A0oAVwZZMNGIH972P7cSZmb/uJXMOQKBgQCs\n" +
                "FaQAL+4sN/TUxrkAkylqF+QJmEZ26l2nrzHZjMWROYNJcsn8/XkaEhD4vGSnazCu\n" +
                "/B0vU6nMppmezF9Mhc112YSrw8QFK5GOc3NGNBoueqMYy1MG8Xcbm1aSMKVv8xba\n" +
                "rh+BZQbxy6x61CpCfaT9hAoA6HaNdeoU6y05lBz1DQKBgAbYiIk56QZHeoZKiZxy\n" +
                "4eicQS0sVKKRb24ZUd+04cNSTfeIuuXZrYJ48Jbr0fzjIM3EfHvLgh9rAZ+aHe/L\n" +
                "84Ig17KiExe+qyYHjut/SC0wODDtzM/jtrpqyYa5JoEpPIaUSgPuTH/WhO3cDsx6\n" +
                "3PIW4/CddNs8mCSBOqTnoaxh\n" +
                "-----END PRIVATE KEY-----";
    }

    private static String loadRsaPublicKeyPem() {
        // this is a sample key - don't worry !
        return "-----BEGIN PUBLIC KEY-----\n" +
                "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEA8EmWJUZ/Osz4vXtUU2S+\n" +
                "0M4BP9+s423gjMjoX+qP1iCnlcRcFWxthQGN2CWSMZwR/vY9V0un/nsIxhZSWOH9\n" +
                "iKzqUtZD4jt35jqOTeJ3PCSr48JirVDNLet7hRT37Ovfu5iieMN7ZNpkjeIG/CfT\n" +
                "/QQl7R+kO/EnTmL3QjLKQNV/HhEbHS2/44x7PPoHqSqkOvl8GW0qtL39gTLWgAe8\n" +
                "01/w5PmcQ38CKG0oT2gdJmJqIxNmAEHkatYGHcMDtXRBpOhOSdraFj6SmPyHEmLB\n" +
                "ishaq7Jm8NPPNK9QcEQ3q+ERa5M6eM72PpF93g2p5cjKgyzzfoIV09Zb/LJ2aW2g\n" +
                "QwIDAQAB\n" +
                "-----END PUBLIC KEY-----";
    }

    public static PrivateKey getPrivateKeyFromString(String key) throws GeneralSecurityException {
        String privateKeyPEM = key;
        privateKeyPEM = privateKeyPEM.replace("-----BEGIN PRIVATE KEY-----", "");
        privateKeyPEM = privateKeyPEM.replace("-----END PRIVATE KEY-----", "");
        privateKeyPEM = privateKeyPEM.replaceAll("[\\r\\n]+", "");
        byte[] encoded = Base64.getDecoder().decode(privateKeyPEM);
        KeyFactory kf = KeyFactory.getInstance("RSA");
        PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(encoded);
        PrivateKey privKey = (PrivateKey) kf.generatePrivate(keySpec);
        return privKey;
    }

    public static PublicKey getPublicKeyFromString(String key) throws GeneralSecurityException {
        String publicKeyPEM = key;
        publicKeyPEM = publicKeyPEM.replace("-----BEGIN PUBLIC KEY-----", "");
        publicKeyPEM = publicKeyPEM.replace("-----END PUBLIC KEY-----", "");
        publicKeyPEM = publicKeyPEM.replaceAll("[\\r\\n]+", "");
        byte[] encoded = Base64.getDecoder().decode(publicKeyPEM);
        KeyFactory kf = KeyFactory.getInstance("RSA");
        PublicKey pubKey = (PublicKey) kf.generatePublic(new X509EncodedKeySpec(encoded));
        return pubKey;
    }

    private static String loadRsaKeyPemFile(String filename) throws IOException {
        return new String(Files.readAllBytes(Paths.get(filename)), StandardCharsets.UTF_8);
    }
}