The RSA key generator uses the provided public exponent as parameter, and selects appropriate p and q. This rules out even values. Any odd integer (except 1) can be used as public exponent; using a prime only makes it slightly simpler for the key generator. Jun 03, 2016  Rsa algorithm key generation 1. RSAAlgorithm is the first public key algorithm discovered by a group of three scientists namely Ron Rivest,Adi Shamir and Len Adleman and was first published in 1978. RSAAlgorithm is based on the original work of Diffie. RSA Function Evaluation: A function (F), that takes as input a point (x) and a key (k) and produces either an encrypted result or plaintext, depending on the input and the key. Key Generation The key generation algorithm is the most complex part of RSA. The aim of the key generation algorithm is to generate both the public and the private RSA keys. Sounds simple enough! RSA(Rivest-Shamir-Adleman) is an Asymmetric encryption technique that uses two different keys as public and private keys to perform the encryption and decryption. With RSA, you can encrypt sensitive information with a public key and a matching private key is used to decrypt the encrypted message.

Contents

• 3. Saving the Keys in Binary Format
• Source Code

1. Introduction

Let us learn the basics of generating and using RSA keys in Java.

Java provides classes for the generation of RSA public and private key pairs with the package java.security. You can use RSA keys pairs in public key cryptography.

Public key cryptography uses a pair of keys for encryption. Distribute the public key to whoever needs it but safely secure the private key.

Public key cryptography can be used in two modes:

Encryption: Only the private key can decrypt the data encrypted with the public key. /mssql-insert-return-generated-keys.html.

Authentication: Data encrypted with the private key can only be decrypted with the public key thus proving who the data came from.

2. Generating a Key Pair

First step in creating an RSA Key Pair is to create a KeyPairGeneratorfrom a factory method by specifying the algorithm (“RSA” in this instance):

Initialize the KeyPairGenerator with the key size. Use a key size of 1024 or 2048. Currently recommended key size for SSL certificates used in e-commerce is 2048 so that is what we use here.

From the KeyPair object, get the public key using getPublic() and the private key using getPrivate().

3. Saving the Keys in Binary Format

Save the keys to hard disk once they are obtained. This allows re-using the keys for encryption, decryption and authentication.

What is the format of the saved files? The key information is encoded in different formats for different types of keys. Here is how you can find what format the key was saved in. On my machine, the private key was saved in PKCS#8 format and the public key in X.509 format. We need this information below to load the keys.

3.1. Load Private Key from File

After saving the private key to a file (or a database), you might need to load it at a later time. You can do that using the following code. Note that you need to know what format the data was saved in: PKCS#8 in our case.

3.2 Load Public Key from File

Load the public key from a file as follows. The public key has been saved in X.509 format so we use the X509EncodedKeySpec class to convert it.

4. Use Base64 for Saving Keys as Text

Save the keys in text format by encoding the data in Base64. Java 8 provides a Base64 class which can be used for the purpose. Save the private key with a comment as follows:

And the public key too (with a comment):

Key Generation Using Rsa Algorithms

5. Generating a Digital Signature

As mentioned above, one of the purposes of public key cryptography is digital signature i.e. you generate a digital signature from a file contents, sign it with your private key and send the signature along with the file. The recipient can then use your public key to verify that the signature matches the file contents.

Here is how you can do it. Use the signature algorithm “SHA256withRSA” which is guaranteed to be supported on all JVMs. Use the private key (either generated or load from file as shown above) to initialize the Signatureobject for signing. It is then updated with contents from the data file and the signature is generated and written to the output file. This output file contains the digital signature and must be sent to the recipient for verification.

6. Verifying the Digital Signature

The recipient uses the digital signature sent with a data file to verify that the data file has not been tampered with. It requires access to the sender’s public key and can be loaded from a file if necessary as presented above.

The code below updates the Signature object with data from the data file. It then loads the signature from file and uses Signature.verify() to check if the signature is valid.

And that in a nutshell is how you can use RSA public and private keys for digital signature and verification.

Source Code

Go here for the source code.

Key Generation Using Rsa Algorithm Code

Key Generation Using Rsa Algorithm Free

I. Choose two distinct prime numbers p and q.

II. Find n such that n = pq.

n will be used as the modulus for both the public and private keys.

Example Of Rsa Algorithm

III. Find the totient of n, ϕ(n)
ϕ(n)=(p-1)(q-1).
IV. Choose an e such that 1 < e < ϕ(n), and such that e and ϕ(n) share no divisors other than 1 (e and ϕ(n) are relatively prime).
e is kept as the public key exponent.
V. Determine d (using modular arithmetic) which satisfies the congruence relation
de ≡ 1 (mod ϕ(n)).
In other words, pick d such that de - 1 can be evenly divided by (p-1)(q-1), the totient, or ϕ(n).
This is often computed using the Extended Euclidean Algorithm, since e and ϕ(n) are relatively prime and d is to be the modular multiplicative inverse of e.
d is kept as the private key exponent.
The public key has modulus n and the public (or encryption) exponent e. The private key has modulus n and the private (or decryption) exponent d, which is kept secret.

I. Person A transmits his/her public key (modulus n and exponent e) to Person B, keeping his/her private key secret.
II. When Person B wishes to send the message 'M' to Person A, he first converts M to an integer such that 0 < m < n by using agreed upon reversible protocol known as a padding scheme.
III. Person B computes, with Person A's public key information, the ciphertext c corresponding to
c ≡ me (mod n).

IV. Person B now sends message 'M' in ciphertext, or c, to Person A.

Key Generation Using Rsa Algorithm Examples

Rsa Algorithm

I. Person A recovers m from c by using his/her private key exponent, d, by the computation
m ≡ cd (mod n).
II. Given m, Person A can recover the original message 'M' by reversing the padding scheme.
This procedure works since
c ≡ me (mod n),
cd ≡(me)d (mod n),
cd ≡ mde (mod n).
By the symmetry property of mods we have that
m^de≡ m^de (mod n).

Since de = 1 + kϕ(n), we can write
mde ≡ m^{1 + kϕ(n)} (mod n),
m^de≡ m(m^k)^ϕ(n) (mod n),
m^de ≡ m (mod n).
From Euler's Theorem and the Chinese Remainder Theorem, we can show that this is true for all m and the original message
c^d ≡ m (mod n), is obtained.
Why RSA Encryption is secure
References
1. http://www.di-mgt.com.au/rsa_alg.html