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How can I generate an EC KeyPair from a PrivateKey string?

I generated a KeyPair like this:
ECGenParameterSpec ecSpec = new ECGenParameterSpec("secp256k1");
KeyPairGenerator generator = KeyPairGenerator.getInstance("EC");
generator.initialize(ecSpec, new SecureRandom());
KeyPair kp = generator.generateKeyPair();
Then I generate Strings from the KeyPair:
String privateKeyString = Base64.getEncoder().encodeToString(kp.getPrivate().getEncoded();
So my first Question is how can I generate a PrivateKey object from privateKeyString and my second question is how can I generate a PublicKey / KeyPair from the PrivateKey object?

Java: Converting between Key type and String

Is it possible to take a public key that I have generated, convert it into a string, reverse the process and use it as a key again?
generator = KeyPairGenerator.getInstance("RSA");
generator.initialize(2048);
KeyPair keyPair = generator.generateKeyPair();
RSAPublicKey publicKey = (RSAPublicKey) keyPair.getPublic();
RSAPrivateKey privateKey = (RSAPrivateKey) keyPair.getPrivate();
Then convert this to a string:
String public = someMethod(publicKey)
and then Reverse it at a later time:
RSAPublicKey newPublicKey = someMethod(public)

You can convert the Public Key to a String as follows.
String publicKeyString = Base64.getEncoder().encodeToString(publicKey.getEncoded());
Then that String can be converted back to a public key as follows.
byte[] publicKeyBytes = Base64.getDecoder().decode(publicKeyString);
X509EncodedKeySpec spec = new X509EncodedKeySpec(publicKeyBytes);
KeyFactory keyFactory = KeyFactory.getInstance("RSA");
PublicKey publicKey2 = keyFactory.generatePublic(spec);

String to Public key using Base64.getEncoder() [duplicate]

I've used the following code to convert the public and private key to a string
KeyPairGenerator keyPairGen = KeyPairGenerator.getInstance("RSA");
keyPairGen.initialize(2048);
KeyPair keyPair = keyPairGen.genKeyPair();
PublicKey publicKey = keyPair.getPublic();
PrivateKey privateKey = keyPair.getPrivate();
String publicK = Base64.encodeBase64String(publicKey.getEncoded());
String privateK = Base64.encodeBase64String(privateKey.getEncoded());
Now I'm trying to convert it back to public ad private key
PublicKey publicDecoded = Base64.decodeBase64(publicK);
I'm getting error of cannot convert from byte[] to public key. So I tried like this
PublicKey publicDecoded = new SecretKeySpec(Base64.decodeBase64(publicK),"RSA");
This leads to error like below
java.security.spec.InvalidKeySpecException: java.security.InvalidKeyException: Neither a public nor a private key
Looks like I'm doing wrong key conversion here. Any help would be appreciated.

I don't think you can use the SecretKeySpec with RSA.
This should do:
byte[] publicBytes = Base64.decodeBase64(publicK);
X509EncodedKeySpec keySpec = new X509EncodedKeySpec(publicBytes);
KeyFactory keyFactory = KeyFactory.getInstance("RSA");
PublicKey pubKey = keyFactory.generatePublic(keySpec);
And to decode the private use PKCS8EncodedKeySpec

How to use RSAPublicKey and RSAPrivateKey classes in Java?

I am trying to use [Java JWT] library(https://github.com/auth0/java-jwt) to generate JWT and I require to make instances of private key and public key i.e. RSAPrivateKey and RSAPublicKey.
//RSA
RSAPublicKey publicKey = //Get the key instance
RSAPrivateKey privateKey = //Get the key instance
Algorithm algorithmRS = Algorithm.RSA256(publicKey, privateKey);
How do I create the instances of RSAPrivateKey and RSAPublicKey?
I have created .pem files using OpenSSL (if that helps) but I am not able to use that too.

First create the KeyPairGenerator to create the KeyPairs.
KeyPairGenerator kpg = KeyPairGenerator.getInstance("RSA");
This will give you a KeyPairGenerator using RSA. Next you initialize the generator with the amount of bytes you want it to use and then create the KeyPair.
kpg.initialize(1024);
KeyPair kp = kpg.generateKeyPair();
Get the PublicKey and PrivateKey from the KeyPair kp using their Getters and than because RsaPublicKey is just a a SubClass of Key and we made these keys with RSA we can safely cast the PublicKey and PrivateKey classes to RSAPublicKey and RSAPrivateKey
RSAPublicKey rPubKey = (RSAPublicKey) kp.getPublic();
RSAPrivateKey rPriKey = (RSAPrivateKey) kp.getPrivate();

Asymmertic key encryption not working

Below mentioned is a code which is showing exception while running. Wanted to understand the public key / private key working.
KeyPairGenerator generator = KeyPairGenerator.getInstance("RSA");
KeyPair keyPair = generator.generateKeyPair();
PublicKey publicKey = keyPair.getPublic();
PrivateKey privateKey = keyPair.getPrivate();
Cipher aes = Cipher.getInstance("AES/ECB/PKCS5Padding");
aes.init(Cipher.ENCRYPT_MODE,publicKey);
byte[] cipherText = aes.doFinal("my password".getBytes());
System.out.println(new String(cipherText));
Below mentioned is exception.
Exception in thread "main" java.security.InvalidKeyException: Illegal key size or default parameters