RSA Encryption: Finding Primes to Make Decryption Difficult

In summary, the conversation discusses the encryption system RSA and its vulnerabilities. The participants mention different techniques for breaking RSA encryption, such as Elliptic Curve Factorisation and Pollard Rho techniques. They also mention that RSA is becoming weaker and people are turning to other encryption systems like Diffie Hellman and El-Gamal. The conversation concludes with a question about the factors needed for decoding RSA.
  • #1
Zurtex
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I'm working on encrypting a small message using RSA. Are there any types of primes or primes of particular property that would make RSA decryption particularly difficult?

Furthermore are there any better ways that just randomly trying to factorise to break RSA encryption or is there some particularly good way?
 
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  • #2
Check here,
http://www.rsasecurity.com/rsalabs/node.asp?id=2213

RSA is getting weaker by the day. There are algos like Elliptic Curve Factorisation and pollards rho techniques (this is getting modified by the day to give more and improved pollard rho techniques ... ). Impressive isn't it ?? once the most hardest encryption system is losing ground ... (People are now reverting to Diffie Hellman and El-Gamal these days ... as u can see from the PGP system)

Check here for,
Elliptic Curve Factorisation :
http://www.alpertron.com.ar/ECM.HTM
(brilliant java piece)

Check here for,
Pollard Rho techniques :
http://mathworld.wolfram.com/PollardRhoFactorizationMethod.html
http://planetmath.org/encyclopedia/PollardsRhoMethod.html

-- AI
 
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  • #3
Wow! Thanks, I don't have to worry too much as I am a Freshmen who is far more into maths than any of my fellow class mates, so with a bit of luck the only algorthm they'll use to test for primes is the very traditional brute force.

The program is very impressive, it can factorise quicker than MATLAB can multiply the factors.

I’m still a little unsure about RSA though, will I be factorising pq or (p-1)(q-1)? Still grappling with the understanding the theory a bit (mind you I’m reading several weeks ahead of the lectures so no big deal yet).

Edit: Dosn't really matter, I'll read it all up. Thanks again :smile:
 
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  • #4
If you want to decode it without knowing the keys you will factorise pq since it is public (p-1)(q-1) is not public.
I'm in the Ib diploma program and I'm thinking of writing an extended essey about RSA. Do you have any tips?
/Andreas
 

Related to RSA Encryption: Finding Primes to Make Decryption Difficult

1. What is RSA encryption and how does it work?

RSA encryption is a form of asymmetric encryption that uses two keys, a public key and a private key, to encrypt and decrypt data. The public key is used to encrypt the data, while the private key is used to decrypt it. The security of RSA encryption lies in the fact that it is extremely difficult to factor large numbers, which is the basis for generating the keys.

2. How does finding prime numbers make decryption difficult in RSA encryption?

In RSA encryption, the security of the algorithm relies on the difficulty of factoring large numbers. The two prime numbers used to generate the public and private keys are crucial in this process. The larger the prime numbers, the harder it is to factor them, making it more difficult for attackers to decrypt the data without the private key.

3. Can any two prime numbers be used in RSA encryption?

No, not all prime numbers can be used in RSA encryption. The two prime numbers used to generate the keys must be relatively prime, meaning they have no common factors other than 1. This ensures that the keys are unique and not easily guessable, providing better security for the encrypted data.

4. How are prime numbers generated for RSA encryption?

Prime numbers used in RSA encryption are typically generated using a primality test, such as the Miller-Rabin test, which determines if a number is prime with a high degree of accuracy. These tests are essential in ensuring that the prime numbers used in RSA encryption are truly prime and not easily factorable.

5. Is RSA encryption still considered secure?

Yes, RSA encryption is still considered secure when implemented correctly. However, as computing power continues to advance, it is important to use sufficiently large prime numbers and regularly update the keys to maintain its security. Additionally, it is crucial to properly store and protect the private key to prevent unauthorized access and decryption of the encrypted data.

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