Why does some key pair for RSA return same value

In summary, the RSA algorithm generates the same key pair every time because it uses a deterministic process. It is highly unlikely for two different key pairs to return the same value. The same key pair can be used for any type of data and multiple encryption and decryption processes. It is important to keep the key pair safe and secure to maintain the confidentiality and integrity of the encrypted data.
  • #1
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There are certain key pairs of RSA that will return the same exact value when encrypt and decrypt, for example (5,7) and (13,19)

is there a mathematical pattern that describes this behavior?

Any advice would be appreciated
 
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  • #2
What convention are you using? The only one I've seen is (encoding exponent, modulus), but [itex]2^5 \equiv 4 \pmod 7[/itex] and [itex]2^7 \equiv 3 \pmod 5[/itex], so I presume I have misunderstood your question. Can you give a more specific example?
 

Related to Why does some key pair for RSA return same value

1. Why does the same key pair for RSA return the same value every time?

The RSA algorithm, like many other encryption algorithms, uses a deterministic process to generate the key pair. This means that given the same inputs, the algorithm will always produce the same output. In the case of RSA, the key pair is generated using a specific mathematical formula that ensures the same value is produced each time.

2. Can two different key pairs for RSA return the same value?

No, it is extremely unlikely that two different key pairs for RSA will return the same value. The RSA algorithm uses very large prime numbers to generate the key pair, and the probability of two different pairs of large prime numbers resulting in the same value is incredibly low. This is one of the reasons why RSA is considered a secure encryption method.

3. Does the same key pair for RSA work for all types of data?

Yes, the same key pair for RSA can be used to encrypt and decrypt any type of data, as long as it is within the size limit of the key. This is because the RSA algorithm works on binary data, so any type of data can be converted into binary form and encrypted using the same key pair.

4. Can the same key pair for RSA be used for multiple encryption and decryption processes?

Yes, the same key pair for RSA can be used for multiple encryption and decryption processes. This is one of the advantages of using RSA, as it allows for secure communication between two parties without the need for constantly changing keys.

5. Why is it important to keep the key pair for RSA safe and secure?

The security of the RSA encryption depends on the secrecy of the key pair. If an attacker gains access to the key pair, they can decrypt any message encrypted with that key. Therefore, it is crucial to keep the key pair safe and secure to ensure the confidentiality and integrity of the encrypted data.

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