how does private key contain modulus? - algorithm

In RSA, we got public/private key.
let's say I have a private key. How can I get public key ? to get public key, i would need to know private key pairs(q and N), but private key seems one long thing only.

Related

Test which public keys were generated by a specific private key

Let's say I've used near keys foo.near to identify all the keys for a given account and I want to understand which of those public keys were generated by a particular private key. How would I do that most easily?
If you know the private key in question, this is a pretty trivial problem. You can use near-api-js to generate the KeyPair and get the public key. A quick code-snippet:
const { KeyPair } = require("near-api-js");
let keyPair = KeyPair.fromString(secretKey);
let publicKey = keyPair.getPublicKey().toString();
At this point, you have the Public Key and can compare with the keys returned from the CLI.

Generate a private key from public key

I am try to generate a private key from rsa public key. My attempts to use the formulas from this solution were unfortunately unsuccessful, because the codes never matched. My target is to calculate an RSA 1024 bit private key from this public key.
Edit: I have now added the public key, because the previous one was an entire certificate.
-----BEGIN PUBLIC KEY-----
MIGdMA0GCSqGSIb3DQEBAQUAA4GLADCBhwKBgQD1cJDUjO87H/eM+VxtUxB5gHIH
W2Q1wniS6kxXPzaEnPPzaQflsEHOV2mrCnXd2qsa9Soqpl5U0x3OlzjXnaYRfck7
0BsppFRnEFfhPFmXOKxv4pCx30O9O+yAD69Z8h+OGJtL2DQfPpcTuOxxwYS77BfG
rSymPSF0gLFV1mn4AwIBAw==
-----END PUBLIC KEY-----

Spring Data Cassandra: How to define a Repository for a table with composite primary key?

This is my table;
#Table
public class Opinion {
private String text;
#PrimaryKeyColumn(type = PrimaryKeyType.PARTITIONED)
private String topic;
#PrimaryKeyColumn(type = PrimaryKeyType.PARTITIONED)
private String owner;
#PrimaryKeyColumn(type = PrimaryKeyType.CLUSTERED)
private LocalDateTime createdDate;
...
}
How can I declare a Repository for this table with a composite primary key? This is what I have now but it does not work, probably because of the ID part, since my id is not just a string but a composite one.
#Repository
public interface OpinionRepository extends CassandraRepository<Opinion, String> {
....
}
By the way I would be glad to hear your experiences whether Cassandra plays nicely with Spring Data or not.. Actually I have been using Spring Data for a while, and I have to say that this time with Cassandra was everything different. Even for some very simple stuff which one can deal with easily on other databases, I have hard time figuring it out. And some of the stuff was not supported at all.. So I am actually very disappointed about Cassandra-Spring Boot interplay.

How to check if a public key matches a given private key?

I would like to use Ruby and its OpenSSL module to check whether a public key matches a given private key. Basically a user enters both a private key and a public key and I want to make sure that they match (they belong to the same key pair).
How can I achieve that?
The solution I have found is to sign a message with the private key and then try to verify the message with the public key:
public_key.verify(OpenSSL::Digest::SHA256.new, private_key.sign(OpenSSL::Digest::SHA256.new, 'message'), 'message')

OpenSSL RSA Public Key encryption in Java in Server and decryption with Private Key in Client in OSX

I have an application which is client/server based. The client is developed for both iOS and OSX. The server is common for both the clients (and server's implementation cannot be changed).
The client developed in iOS generates an RSA public/private key pair and send the public key in base64 encoding to the server. The server (implemented in Java) encrypts some secure data and sends the same to the client who is required to decrypt data with the private key. The RSA key pair is generated on iOS using the Crypto Exercise Sample provided by apple.
The public and private key generated (of key length 1024) in base64Encoding is of length 216 and 844 bytes respectively and of the form provided below.
Private Key:
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
Public Key:
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADkIJlKBgQDQ1dz/te8wiMP2SMIzP+auw3hBIuAFWBNkkz527gKb3NCYwt4Mfhfpi7Qn0fpcYtEwFqnRSujJIxmTFzjXBB0VsQP+5bRQtUZYBFs8Zna+JDhC+Q1eg0XqeGJIeILrxn9wODdQPO3KJtK0ozqFkfvjfRwphsa5xIYFe4G/cJJ6EQIDAQAB
Things are working fine in the iOS world.
I am trying to implement this in the MAC using Objective-c and find that the Crypto Exercise sample is not working as expected. The SecItemCopyMatching is returning failure.
While investigating for the solution found that the public/private key using Open SSL met the criteria of private and public key except for the header and footer that is appended to the generated key pair.
I used the SSCrypto OpenSSL wrapper (http://septicus.com/products/opensource/) to generate the public and private key pair using OpenSSL which is of the form.
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
-----BEGIN PUBLIC KEY-----
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCrEgoLjG34pNLj4ahpWlvXZZEh
zimg/mJoKJLdrjE3Fg817Qf2+iXTPMWAtmCkYgHn9Y99VJSdJzrb0/E1JnxMPva5
2ZMS8ilS/hSZnXRAlq2OPFMj64SU9XDu/eWqJMULELNkBcTtPgTCAkjrDU6Qt2Ab
wNUwrgufJC8WJEhWdQIDAQAB
-----END PUBLIC KEY-----
To extract the public key, I stripped of the "-----BEGIN PUBLIC KEY-----" and "-----END PUBLIC KEY-----" footer and white spaces to extract the public key to be sent to the server.
The problem is that when I strip the header and footer the sent the public key to the server, though the server successfully encrypts the data (using the public key) and sent encrypted data to the client, the decryption using private key (in PEM format) using OpenSSL fails.
I think the decryption has failed as when i modify the public key's content (by stripping of the header/fooders), the public and private key seize to be key pairs.
Can somebody help me with the solution such that I am able to use the private key to decrypt the received encrypted data.
Alternatively, can somebody help me in generation of public key/private key pair of abovementioned lengths using objective-c api's (pair as generated by OpenSSL) which will fix the issue I am facing?
Thanks & Regards.
The data encrypted by server using Public Key is an AES key. The size of the AES key after encryption using public key is 176 characters. Here is the code snippet which does it.
public static String encryptAESKey(byte[] aesKeyBytes, String publicKeyStr) {
String cipherStr = null;
try {
PublicKey pkey = getPublicKey(publicKeyStr);
final Cipher cipher = Cipher.getInstance(RSA_ALGORITHM);
cipher.init(Cipher.ENCRYPT_MODE, pkey);
byte[] cipherBytes = cipher.doFinal(aesKeyBytes);
cipherStr = Base64.encodeBase64String(cipherBytes);
} catch (Exception e) {
e.printStackTrace();
}
return cipherStr;
}
private static PublicKey getPublicKey(String publicKey) throws InvalidKeySpecException, NoSuchAlgorithmException {
KeyFactory rsaKeyFac = KeyFactory.getInstance(RSA_ALGORITHM);
byte[] keyBytes = Base64.decodeBase64(publicKey.getBytes());
X509EncodedKeySpec keySpec = new X509EncodedKeySpec(keyBytes);
RSAPublicKey rsaPubKey = (RSAPublicKey)rsaKeyFac.generatePublic(keySpec);
return rsaPubKey;
}

Resources