Asymmetric Encryption: Overview & Techniques

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In summary, the conversation discusses the use of asymmetric encryption, particularly the RSA algorithm, for demonstration purposes. One person expresses concern about the complexity of the algorithm, specifically the use of modular multiplicative inverses, but is encouraged to further study and utilize the RSA algorithm as it is relatively simple.
  • #1
Krushnaraj Pandya
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Homework Statement
With a project I'm trying to demonstrate the key distribution problem on top of an Enigma machine encryption (I'm thinking about naming the project 'Enigmatic Encryption'). For that I'm trying to demonstrate asymmetric encryption, now it seems to me that the 'one-way' functions used in RSA encryption are too complex for me to demonstrate that. So I was thinking I'd have something like a quintic polynomial which takes in a value of x then goes through g(x)=x^5-x+1 and produces an encrypted message- which is sent to the person who has the inverse of this function (and the only person to know the inverse function since he's the only person who knows of g(x) in the first place) and gets back the original x by plugging in the encrypted x through the inverse.

I'm having two issues with this-

1) how would the function g(x) be hidden for the person who has the original message and wants to encrypt it? A key feature of asymmetric encryption is that even the person who encrypted the message can't decrypt it and so it becomes necessary that this function is hidden but can still be used- something like a magical vending machine where you put in something and get something out but have no idea how it works.

2) Another major problem seems to be that quintic functions don't have inverses which makes it impossible to reverse the encryption. Ideally I want a way so that, say, Joe has a function (in a sense his public key) and the inverse of a function (his private key) and he can distribute his public key for use without allowing people to know what the function is (so they can't find its inverse) but can still use that function. Do you know of any good functions I could use, which have an inverse and can be used in this sense.
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  • #2
Krushnaraj Pandya said:
For that I'm trying to demonstrate asymmetric encryption, now it seems to me that the 'one-way' functions used in RSA encryption are too complex for me to demonstrate that.
No, the RSA algorithm is remarkably simple, see this example on Wikipedia, so why not just use that?
 
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  • #3
pbuk said:
No, the RSA algorithm is remarkably simple, see this example on Wikipedia, so why not just use that?
I was looking at the algorithm at earlier but got scared looking at modular multiplicative inverses; I still can't fully wrap my head around it but I'll try to learn more about it since you suggest that it's simple enough. Thank you very much.
 
  • #4
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1. What is asymmetric encryption?

Asymmetric encryption is a type of encryption where a pair of keys, a public key and a private key, are used to encrypt and decrypt data. The public key can be shared with anyone, while the private key is kept secret and used by the owner to decrypt the data.

2. How does asymmetric encryption work?

Asymmetric encryption works by using a mathematical algorithm to generate a pair of keys. The public key is used to encrypt the data, and the private key is used to decrypt the data. This allows for secure communication between two parties without the need to share a secret key.

3. What are the advantages of using asymmetric encryption?

One of the main advantages of asymmetric encryption is that it provides a higher level of security compared to symmetric encryption. This is because the private key is never shared, making it harder for hackers to intercept and decrypt the data. Asymmetric encryption also allows for secure communication between two parties who have not previously communicated and exchanged a secret key.

4. What are some common techniques used in asymmetric encryption?

Some common techniques used in asymmetric encryption include RSA, Diffie-Hellman, and Elliptic Curve Cryptography. RSA is the most widely used technique and is based on the difficulty of factoring large numbers. Diffie-Hellman is used for key exchange, and Elliptic Curve Cryptography is used for both encryption and key exchange.

5. Can asymmetric encryption be cracked?

Asymmetric encryption, like any other encryption, can be cracked given enough time and computing power. However, the level of difficulty in cracking asymmetric encryption is much higher compared to symmetric encryption. It is also constantly evolving, with new techniques and algorithms being developed to increase its security.

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