Stuck on Decrypting with RSA and SHA256 in Encryption Task

Amir Hassan

5/28/24, 12:19 AM

I'm working on solving a encryption task, and I'm a bit stuck. I want to clarify that I'm only seeking hints and not direct answers since I want to solve it myself. The goal is to solve it on my own; otherwise, it wouldn't make sense. Therefore, I'm just looking for hints to help me progress from where I'm stuck or any comments suggesting that I might be missing an aspect or something.

The task started with an image that had text in the background. From the information in the background of the image, I managed to obtain N, e, d, p, and q related to RSA encryption. There are also two formulas for a variable called "key." One formula is based on d and N, which I have. The other formula is a condition that should be satisfied, and my results reveal that it is satisfied.

There is also a given hint about a value of c, which is c = d7a7e396df976cf6c59adce5d1381ea020a35af126efd0d5d380e4ccb74758e0f05e86a0bed61ac75d5a1dfd029c8792ced99c5abf33354505e288f0b9bda280c9099506be3c3ee818b5e405e1fbf45903708cd067cafa34aa5f5b88958ae6603b4a427ab2.

Additionally, it is mentioned that m = decrypt(sha256("%d" % key), c), and this is where I'm primarily stuck. I'm coding in Python, and that's where I've made the most progress so far. I've coded two separate programs: one that encrypts text using the public key and another program that decrypts the text using the calculated private key. It works, and I can encrypt and decrypt text with the values I have. I'm just stuck regarding m = decrypt(sha256("%d" % key), c). Maybe there are some steps I'm overlooking or missing information?

I hope someone can provide a comment or hint on what considerations I should make.

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fgrieu

5/28/24, 8:01 AM

Is $c/N$ in range $[0.0001, 0.9999]$ making it plausible that $c$ is encrypted per RSA with $N$ the public modulus? Especially if so, my bets are that `m = decrypt(h, c)` means one of $m=c^h\bmod N$ or $c=m^h\bmod N$ ; and that `sha256("%d" % key)` is the string with the decimal representation of integer `key`, converted to bytestring, hashed per SHA-256, with the resulting hash then converted to the integer $h$ (likely per big-endian binary convention). Notice that if the right interpretation is $c=m^h\bmod N$, then $h$ is a public encryption exponent, not directly usable for decryption.

Elon Musk

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EN: Stuck on Decrypting with RSA and SHA256 in Encryption Task

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