Crypto Key Generate Rsa Modulus

  1. Crypto Key Generate Rsa Modulus 1024

I am newbie in cryptography and pycrypto. I have modulus n and private exponent d. From what I understand after reading some docs private key consists of n and d. I need to sign a message and I can't figure out how to do that using pycrypto. RSA.construct method accepts a tuple. Crypto key generate rsaコマンドの利用例は以下の通りです。 Cisco(config)# crypto key generate rsa The name for the keys will be: test.example.com Choose the size of the key modulus in the range of 360 to 2048 for your General Purpose Keys. Choosing a key modulus greater than 512 may take a few minutes.

You may generate an RSA private key with the help of this tool. Additionally, it will display the public key of a generated or pasted private key.

Description

RSA is an asymmetric encryption algorithm. With a given key pair, data that is encrypted with one key can only be decrypted by the other. This is useful for encrypting data between a large number of parties; only one key pair per person need exist. RSA is widely used across the internet with HTTPS.

To generate a key pair, select the bit length of your key pair and click Generate key pair. Depending on length, your browser may take a long time to generate the key pair. A 1024-bit key will usually be ready instantly, while a 4096-bit key may take up to several minutes. For a faster and more secure method, see Do It Yourself below.

CryptoTools.net does not yet have a tool for facilitating the encryption and decryption of data using RSA, but you may Do It Yourself with the instructions below.

Do It Yourself

For these steps, you will need a command line shell with OpenSSL. Ideally, you should have a private key of your own and a public key from someone else. For demonstration, we will only use a single key pair.

Generate Private Key

Run this command to generate a 4096-bit private key and output it to the private.pem file. If you like, you may change the key length and/or output file.

Derive Public Key

Given a private key, you may derive its public key and output it to public.pem using this command. (You may also paste your OpenSSL-generated private key into the form above to get its public key.)

Encrypt Data

We can now use this key pair to encrypt and decrypt a file, data.txt.

Decrypt Data

Given the encrypted file from the previous step, you may decrypt it like so.

RSA is a first successful public key cryptographic algorithm. It is also known as an asymmetric cryptographic algorithm because two different keys are used for encryption and decryption. RSA is named after Rivest, Shamir and Adleman the three inventors of RSA algorithm. The algorithm was introduced in the year 1978.

In this section, we will discuss, RSA algorithm along with an example. We will also study the reason for the evolution of the RSA algorithm along with its advantages and disadvantages.

Content: RSA Algorithm in Cryptography

What is RSA Algorithm?

RSA is a public key cryptographic algorithm in which two different keys are used to encrypt and decrypt the message. That’s why it is also called an asymmetric key algorithm.

But what was the need of this asymmetric key cryptography? Why it evolved? Let us discuss the reason behind the evolution of asymmetric key cryptography. The Asymmetric key cryptography evolves due to the two problems of symmetric key cryptography.

The first problem with symmetric key cryptography is the key distribution. The two communicating parties may already be sharing the key which has been distributed to them by any means or the key must be shared with the help of a key distribution centre. But, using of key distribution centre compromises the secrecy of the key which hampers confidentiality of the message.

The second problem with symmetric key cryptography is digital signatures. That is, there was a requirement of digital signatures which would assure all the parties that message has been sent from a particular individual. So, there was a lack of authentication.

Both of these problems of symmetric key cryptography lead to the evolution of asymmetric key cryptography. In the year 1978 the three inventors at MIT; Rivest, Shamir and Adleman introduced RSA public key algorithm which follows the essential steps below:

  • In RSA public key cryptography each user has to generate two keys a private key and a public key.
  • The public key is circulated or published to all and hence others are aware of it whereas, the private key is secretly kept with the user only.
  • A sender has to encrypt the message using the intended receivers public key.
  • Only the intended receiver can crack the message. In between the communication no one can harm to the confidentiality of the message as the message can only be decrypted by the intended receiver’s private key which is only known to that receiver.

M’= E(PUr, M) ……….Encryption

Download game clash of clans mod apk versi lama. M = D(PRr, M’) ……….Decryption

Mis the original message
M’ is encrypted message
Eis an encryption algorithm
D is a decryption algorithm
PUr is the receivers public key
PRr is the receivers private key
PUs is the senders public key
PRs is the senders private key

The two problems of symmetric key cryptography i.e. confidentiality and authentication can be overcome by the double use of public key cryptography.

1. First, encrypt the message by the sender’s private key which can be decrypted by the sender’s public key(known to all). This provides a digital signature to the sender’s message and thus authentication is achieved.

E(PRs, M)

2. In the next step, encrypt again with the receiver’s public key. This will allow only the intended receiver to decrypt the message, this provides the confidentiality to the message.

M’= E(PUr, E(PRs, M)

The Decryption is shown by the following expression:

M= D(PUs, E(PRr, M’)

Key Generation

Till now we have seen that every sender or a receiver must have two keys a public key and a private key. In this section, we will discuss the steps to derive a public and a private key.

In RSA, the encryption and decryption expressions are in the exponential form:

M’= Me mod n …………. Encryption, Public key (e, n)

M= M’d mod n …………. Decryption, Private key (d, n)

Steps to generate public key (e, n) & private key (d, n)

  1. First, select two prime numbers p=7 and q=11.
  2. Now calculate n= p X q = 7 X 11
    n = 77
  3. Calculate Ø(n)= Ø(pXq)
    = Ø(p) X Ø(q)
    = (p-1) X (q-1) ……. Ø (a) = (a-1) if a is a prime number.
    =(7-1) X (11-1)
    = 6X10
    Ø(n) = 60
  4. Select e such that 1 ≤ e < Ø(n) and also ‘e’ should be coprime to Ø(n).
    So, I select e=7.
    Our Public Key for this particular example is (7,77).
  1. Now we will determine the value of d. The value of d can be calculated from the formula given below:

In the expression above we know that and e and Ø(n) are the coprime numbers so in this case d is the multiplicative inverse of e. To calculate the value of d use the formula below:

In this equation above we know the value of Ø(n), e, the value of i is unknown. First, we have to put the value of i=1.

If the result is in decimals then we have to compute the equation again but this time we have to increment the value of i by 1 so we will compute the equation with i=2. Keep on incrementing the value of i till the above equation results in a proper integer.

So, by trial and error method, for i=5 we get the result 43 i.e.

Now we have generated both the private and public key.

Private Key (43, 77)
Public Key (7, 77)

RSA Encryption

Crypto Key Generate Rsa Modulus

Now, after generating the private and public key we will now encrypt the message. In RSA the plain text is always encrypted in blocks. The binary value of each plain text block should be <n. Encryption is done with the intended receiver’s public key. The expression to calculate cipher text is as follow:

M’= Me mod n

In our example, the value of e=7 and n=77 i.e. public key (e, n) and we have to take the value of M such that M<n. We will take the value of M=15. So, the expression becomes

M’= 157 mod 77

M’= [ (154 mod 77)*(152 mod 77)*
( 151 mod 77) ]mod77

M’= [(36)*(71)*(15)] mod77

M’=71 ……… Cipher Text

RSA Decryption

Done with the encryption now its time to decrypt the message. For decryption in RSA, we require a cipher text and the private key of the corresponding public key used in encryption.

In our example the cipher text we have M’=71 and the private key we have (43, 77). The expression to calculate plain text is as follow:

M= M’d mod n

M= 7143 mod 77

Crypto

M= 15

So, this is the method to encrypt and decrypt the message in RSA. It is very important to remember that in RSA we have to encrypt the message using the intended receiver’s public key. So, the message can only be decrypted by the intended receiver private key. This provides confidentiality to our message.

Advantages and Disadvantages

Advantage

  1. RSA is stronger than any other symmetric key algorithm.
  2. RSA has overcome the weakness of symmetric algorithm i.e. authenticity and confidentiality.

Disadvantage

  1. RSA has too much computation.

Key Takeaways

  • RSA is a public key or asymmetric key algorithm.
  • RSA stands for Rivest, Shamir and Adleman the three inventors of RSA algorithm.
  • Each user has to generate two keys public key known to all and private key only known to him.
  • Encryption is done using the public key of the intended receiver.
  • A receiver cracks the message using its private key.
  • Encrypting the message using receivers public key assures confidentially of the message as no third party would be able to crack the message because the message can only be decrypted by using receivers private key which is only known to him.
  • Using the double public key scheme, we can also achieve authenticity.

So, this is all about the RSA algorithm. So far, we have discussed the methods of generating a public key and a private key. We have also studied encryption and decryption in RSA using these keys.

Crypto Key Generate Rsa Modulus 1024

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