How to solve "Data must not be longer than 256 bytes." in Java? I want to implement without using AES algorithm

Question

I'm working with Java, and my colleague is working with .NET. We each have to link to a page on each other's websites. When connecting, SSO processing is required, and at this time, 'current time (yyyy-MM-dd HH:mm:ss)' must be sent and received through RSA encryption.

First of all, I'm testing whether RSA encryption and decryption work properly. My colleague shared a public key. When I encrypt and decrypt with this, I keep getting the error "Data must not be longer than 256 bytes". What's wrong with my code?

I read other similar posts. But those are not what I'm looking for. I want to implement this function without using AES algorithm.

The shared public key is like this: (I can't show you all, so I'll show you some.)

-xml type

<RSAKeyValue><Modulus>0Lvg8dDJA5z0VbYLVfzXT1pC7PJIY[...]AHuFqh/TQSuDENoLlOYfk4MSiNq2P5J6HMrj4MQ==</Modulus><Exponent>AQAB</Exponent><P>+IvTFBd3ldPsx5MYvxV[...]+kJQ==</D></RSAKeyValue>

-pem type

MIIBIjANBgkqhkiG9w0BAQ[...]5J6HMrj4MQIDAQAB

Encryption Code

    @RequestMapping(value="/ezConn/getEncryptedAkey1.do")
    @ResponseBody
        public String getEncryptedAkey1(@RequestParam String userId, HttpServletRequest request, HttpServletResponse response) {
        logger.debug("getEncryptedAkey1 started. userId=" + userId);
        
        String encryptedAkey = "";
        
        try {
            //Modulus
            String modulusInBase64 = "0Lvg8dDJA5z0VbYLVfzXT1pC7PJIY[...]AHuFqh/TQSuDENoLlOYfk4MSiNq2P5J6HMrj4MQ==";
            //Exponent
            String exponentInBase64 = "AQAB";

            java.util.Base64.Decoder decoder = java.util.Base64.getDecoder();
            String modulusInHex = toHexString(decoder.decode(modulusInBase64));
            String exponentInHex = toHexString(decoder.decode(exponentInBase64));

            BigInteger modulus = new BigInteger(modulusInHex, 16);
            BigInteger pubExp = new BigInteger(exponentInHex, 16);

            KeyFactory keyFactory = KeyFactory.getInstance("RSA");
            RSAPublicKeySpec pubKeySpec = new RSAPublicKeySpec(modulus, pubExp);
            RSAPublicKey key = (RSAPublicKey) keyFactory.generatePublic(pubKeySpec);
            Cipher cipher = Cipher.getInstance("RSA");
            cipher.init(Cipher.ENCRYPT_MODE, key);

            //the current time
            String now = new SimpleDateFormat("yyyy-MM-dd HH:mm:ss").format(new Date());

            byte[] cipherData = cipher.doFinal(now.getBytes());
            
            encryptedAkey = toHexString(cipherData);
                                                            
        } catch (Exception e) {
            logger.error(e.getMessage(), e);
        }
        
        logger.debug("encryptedAkey=" + encryptedAkey);
        logger.debug("getEncryptedAkey1 ended.");
        
        return encryptedAkey;
    }
    
    private String toHexString(byte[] array) {
        return DatatypeConverter.printHexBinary(array);
    }

Decryption Code

    @RequestMapping(value = "/ezConn/getDecryptedAkey.do")
    public String getDecryptedAkey(@RequestParam String Akey, HttpServletRequest request, HttpServletResponse response) throws Exception {
        logger.debug("getDecryptedAkey started");
        
        logger.debug("Akey=" + Akey);
        String decryptedAkey = "";

        try {
            String modulusInBase64 = "0Lvg8dDJA5z0VbYLVfzXT1pC7PJIY[...]AHuFqh/TQSuDENoLlOYfk4MSiNq2P5J6HMrj4MQ==";
            String exponentInBase64 = "AQAB";

            java.util.Base64.Decoder decoder = java.util.Base64.getDecoder();
            String modulusInHex = toHexString(decoder.decode(modulusInBase64));
            String exponentInHex = toHexString(decoder.decode(exponentInBase64));

            BigInteger modulus = new BigInteger(modulusInHex, 16);
            BigInteger pubExp = new BigInteger(exponentInHex, 16);
            
            KeyFactory keyFactory = KeyFactory.getInstance("RSA");
            RSAPrivateKeySpec privateKeySpec = new RSAPrivateKeySpec(modulus, pubExp);
            RSAPrivateKey key = (RSAPrivateKey) keyFactory.generatePrivate(privateKeySpec);
            Cipher cipher = Cipher.getInstance("RSA");
            cipher.init(Cipher.DECRYPT_MODE, key);

            byte[] cipherData = cipher.doFinal(Akey.getBytes());                        
            descryptedAkey = toHexString(cipherData);
            
        }
        catch (Exception e) {
            logger.error(e.getMessage(), e);
        }
        
        logger.debug("decryptedAkey=" + decryptedAkey);
        logger.debug("getDecryptedAkey ended");
        return decryptedAkey;
    }

Error Code

2023-08-03 13:53:10,221 ERROR [http-nio-8080-exec-111] [egovframework.ezEKP.ezConn.web.EzConnController] Data must not be longer than 256 bytes
javax.crypto.IllegalBlockSizeException: Data must not be longer than 256 bytes
    at com.sun.crypto.provider.RSACipher.doFinal(RSACipher.java:347) ~[sunjce_provider.jar:1.8.0_332]
    at com.sun.crypto.provider.RSACipher.engineDoFinal(RSACipher.java:404) ~[sunjce_provider.jar:1.8.0_332]
    at javax.crypto.Cipher.doFinal(Cipher.java:2168) ~[?:1.8.0_332]
    at egovframework.ezEKP.ezConn.web.RsaTestController.getDecryptedAkey(RsaTestController.java:165) [classes/:?]