# Breaking RSA if you know m^k = 1 mod n

• nudan
In summary, the conversation discusses the lack of clear definitions and understanding of modular arithmetic in relation to RSA encryption. It suggests looking into Euler's Theorem as a generalized form of Fermat's Little Theorem and emphasizes the importance of carefully choosing keys in RSA.

#### nudan

Hello I'm looking for some guidance:

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You seem to assume that everyone knows what you are talking about--why?

You certainly have not defined terms, but when I look into this, it is my impression that you have no understanding of modular arithmetic. Why not check that out?

Look, RSA is built on the fact in the private key (d,n) and the public key (e,n) d and e are exponential inverses of each other mod n. If x^d or x^e are congruent to 1 then d = phi(n) or e = phi(n) respectively... Take a look at Euler's Theorem which is a generalize form of Fermat's Little Theorem. This is why in RSA there is so much care taken in picking keys.

## 1. How does the RSA algorithm work?

The RSA algorithm is a popular encryption method used to securely transmit data over the internet. It involves the use of public and private keys to encrypt and decrypt messages. The public key is used to encrypt the message, while the private key is used to decrypt it. The algorithm relies on the difficulty of factoring large numbers to ensure the security of the encrypted message.

## 2. What is the significance of knowing m^k = 1 mod n in breaking RSA?

Knowing m^k = 1 mod n allows for the decryption of the message by finding the value of k. This value is then used to calculate the private key, which can be used to decrypt the message. This is known as a "plaintext attack" and is one way to break RSA encryption.

## 3. Can the RSA algorithm be broken without knowing m^k = 1 mod n?

Yes, there are other ways to break RSA encryption without knowing m^k = 1 mod n. These include factoring large numbers, using a side-channel attack, or exploiting weaknesses in the implementation of the algorithm.

## 4. Is it possible to break RSA encryption if the public key is known?

No, it is not possible to break RSA encryption solely with the knowledge of the public key. The whole purpose of the public key is to be shared and used for encryption, while the private key remains secret and is used for decryption.

## 5. What are the implications of breaking RSA encryption?

Breaking RSA encryption would have significant implications for data security and privacy. It would mean that encrypted messages could potentially be intercepted and decrypted, compromising the confidentiality of sensitive information. This is why it is crucial to constantly improve and update encryption methods to prevent attacks on data security.