Generate Rsa Key Online With P And Q

Generate Rsa Key Online With P And Q Download 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. Generating Public Key: Select two prime no's. Suppose P = 53 and Q = 59. Now First part of the Public key: n = P.Q = 3127. We also need a small exponent say e: But e Must be. Not be a factor of n. 1 Key is made of n and e.

Directions are at the bottom.

• ∟ Introduction of RSA Algorithm ∟ Illustration of RSA Algorithm: p,q=5,7. This section provides a tutorial example to illustrate how RSA public key encryption algorithm works with 2 small prime numbers 5 and 7. ﻿ To demonstrate the RSA public key encryption algorithm, let's start it with 2 smaller prime numbers 5 and 7.
• Truth Table Generator This tool generates truth tables for propositional logic formulas. You can enter logical operators in several different formats. For example, the propositional formula p ∧ q → ¬r could be written as p / q - r, as p and q = not r, or as p && q -!r.

To use this, enter the parts of the key required for the operationyou intend to do (in hexadecimal), enter your plaintext or ciphertext,and click the appropriate button. Plaintexts are limited to 128characters, so don't try to encrypt an essay. You can also generate arandom key, but be advised that the random number generator used isnot cryptographically strong (not to mention the fact that the privatekeys are sent over an unencrypted connection) so this should not beused for generating keys to be used in sensitiveapplications. Detailed directions for the more patient below.

Encryption

Fill in the public exponent and modulus (e and n) and yourplaintext message. Click Encrypt. Your key must be a single number inhexadecimal, but your plaintext can be ASCII text or a series of bytesin hexadecimal. If you don't know what this means, keep the'CharacterString' radio button selected. 0x31 0x32 0x33 0x34 in hexmode is equivalent to 1234 in string mode.

Decryption

Fill in the public and private exponents and the modulus (e, d, andn) as well as the cryptotext. The key and cryptogram must both be inhex. The parts of the key should each be a single hex number, whilethe cryptotext should be a sequence of bytes. Here are some acceptable(equivalent) examples for the cryptotext:

• 0x12 0x34 0x56 0x78
• 12 34 56 78

Key Generation

To generate a key pair, just click the Generate button. This willgenerate a 1024 bit key. Other key sizes are on the bottom of my todolist. Keys generated this way are not suitable for keeping thingssecret. I claim no responsibility if you go to jail or are foiledbecause you decided to encrypt your plans to take over the world usinga key generated here.

Signing

To generate a signature of a hash, enter the hash in the text fieldand click the sign button. The hash should be entered as hex valueslike the rest of the stuff on here. If you just want to do a signingoperation on a string, use the character string radio button and itshould work.

Verification

To verify a signature, put the signature in the text field andclick verify. If you signed an ascii string instead of a hash, you canuse the character string mode to see the original.

Cracking

To crack a key, enter the public modulus and exponent in hex andclick the crack button. This function will only crack keys 40 bitslong or shorter. Please do not use 40 bit keys to encrypt yoursensitive data.

Interesting historical note: The export policies of the UnitedStates did not allow encryption schemes using keys longer than 40 bitsto be exported until 1996. By that point, 40 bit keys could easily becracked in under 4 hours by a cluster of workstations. The method usedbehind the scenes on this site is a simple brute force search of203,280,221 sorted primes. I could probably get it going faster bychanging the order but it's just not worth it. As it stands, my testkey can be cracked in less than 4 tenths of a second.

Standalone

I hacked this into a standalone program that you can runlocally. It's still not suitable for real cryptographic work, since ituses your computer's pseudorandom number generator, but it's here.

page generated in 0.00251889228821 seconds

RSA (step-by-step)

This module demonstrates step-by-step encryption or decryption with the RSA method. The sender uses the public key of the recipient for encryption; the recipient uses his associated private key to decrypt.

Prime factors

The security of RSA is based on the fact that it is easy to calculate the product n of two large primes p and q. However, it is very difficult to determine only from the product n the two primes that yield the product. This decomposition is also called the factorization of n.

As a starting point for RSA choose two primes p and q.

For the algorithm to work, the two primes must be different.

For demonstration we start with small primes. To make the factorization difficult, the primes must be much larger. Currently, values of n with several thousand binary digits are used for secure communication.

Public key

The product n is also called module in the RSA method. The public key consists of the module n and an exponent e. This e may even be pre-selected and the same for all participants.

Secret key

RSA uses the Euler φ function of n to calculate the secret key. This is defined as

Here it is used that p and q are different. Otherwise, the φ function would calculate differently.

It is important for RSA that the value of the φ function is coprime to e (the largest common divisor must be 1).

To determine the value of φ(n), it is not enough to know n. Only with the knowledge of p and q we can efficiently determine φ(n).

The secret key also consists of n and a d with the property that e × d is a multiple of φ(n) plus one.

Expressed in formulas, the following must apply:

e × d = 1 (mod φ(n))

In this case, the mod expression means equality with regard to a residual class. It is x = y (mod z) if and only if there is an integer a with xy = z × a.

For the chosen values of p, q, and e, we get d as:

This d can always be determined (if e was chosen with the restriction described above)—for example with the extended Euclidean algorithm.

Encryption and decryption

Internally, this method works only with numbers (no text), which are between 0 and n.

Encrypting a message m (number) with the public key (n, e) is calculated:

m' := me (mod n)

Decrypting with the private key (n, d) is done analogously with

m' := m'd (mod n).

This is

m' = me × d (mod n).

RSA now exploits the property that

xa = xb (mod n)

if

a = b (mod φ(n))

As e and d were chosen appropriately, it is

m' = m.

The order does not matter. You could also first raise a message with the private key, and then power up the result with the public key—this is what you use with RSA signatures.

Messages

In the following two text boxes, you can see how the encryption and decryption works for concrete input (numbers).

Used library

As a result, you can calculate arbitrarily large numbers in JavaScript, even those that are actually used in RSA applications.

CTOAUTHORS: Timm Knape (thanks to Bernhard Esslinger for the review)

The security of RSA is based on the fact that it is not possible at present to factorize the product of two large primes in a reasonable time. However, this is only a reasonable assumption, but no certain knowledge: So far, there is no known fast method. We do not know if factoring is at least as severe as other severe problems, and whether it is NP-complete.

Attack with quantum computers

Due to the principle, a quantum computer with a sufficient number of entangled quantum bits (Qbits) can quickly perform a factorization because it can simultaneously test every possible factor simultaneously. So far, however, there is no known quantum computer, which has just an approximately large computing capacity. Thus, effective quantum computers are currently a myth that will probably not be ready for production in the next few years. However, factoring may be over in 20 years and RSA loses its security.

Size of prime factors

The larger the prime factors are, the longer actual algorithms will take and the more Qbits will be needed in future quantum computers. At the moment, the product should consist of at least 4096 binary digits to be secure.

Reuse of primes

Prime numbers may not be reused! If you have two products each consisting of two primes and you know that one of the primes used is the same, then this shared prime can be determined quickly with the Euclidean algorithm. And by dividing the products by this shared prime, one obtains the other prime number.

Early implementations of RSA made this mistake to reduce the time it takes to find a prime number. Also on resource-constrained devices it came in recent times due to lack of entropy. Current implementations should not commit this error anymore.

Choice of primes

Basically, the primes have to be selected randomly enough. If only n/2-bit numbers are used for an n-bit number, this considerably reduces the search space for attackers. However, neither of the two primes may be too small to avoid an early hit via a brute-force attack with all primes. A clever choice between the two extremes is necessary and not trivial. The two primes should not be too close to each other, but also not too far apart.

Generate Rsa Private Key From P And Q

This let the user see how (N, e, d) can be chosen (like we do here too), but also translates text messages into numbers.

Generate Rsa Key Online With P And Qs

Here you can input the message as text (it is assumed the user already has chosen N, e, and d).

Both are from 2012, use no arbitrary long-number library (but pure JavaScript), and look didactically very well.

References

• The CrypTool book, chap. 4 with further references

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