CODEWITHSUNDEEP
encryptionrsa
cud_programmer
cud_programmer

Reputation: 1264

RSA public key encrypts ASCII value to 0, how to decrypt?

I've decided to learn about RSA encryption since learning about the vernal cipher in a comp sci lecture. I grasp the idea behind RSA (it's very clever), however while trying to write my own C program to encrypt and decrypt a string of characters I have run into a few problems.

I am encrypting each character's ASCII value using the public key then decrypting the cipher text. However, I have found that sometimes the public key I have created will encrypt an ASCII value to 0, then there is no way to decrypt it as 0^anything = 0. I surely must be wrong here as binary can be encrypted/decrypted using RSA.

E.g.

Now take the char "T" (ASCII value 84)

Run the encryption, the cipher text is = 0

0^7 (mod 8) = 0 ... not 84!

Can someone point me in the right direction please.

Thanks in advance

Upvotes: 5

Views: 3652

Answers (1)

supercat
supercat

Reputation: 81159

RSA encryption is limited to encrypting positive numbers in the range 1 to (p*q)-1, which are not multiples of p or q. In practical applications, p*q will generally be much bigger than the largest message to be encrypted, and messages will be padded with random bits to fill up the range 1 to (p*q)-1. While it's theoretically possible that the random padding chosen for a message might cause it to be a multiple of p or q, in practice the only way that can happen is if there is something severely wrong with the random number generator.

In "toy applications", however, problematic values represent a much larger portion of the possible message space. Even if you chose p and q to be large enough that the p*q was larger than your message (e.g. 13 and 17) there would still be many possible message values that would fail (e.g. 65 or 85). I would suggest 13 and 17 as reasonable values to use for demonstration purposes, with the caveat that not all message values will work.

Upvotes: 5

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