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I am trying to decrypt a message which its ciphertext in Hex A3 BB 05 00. The original plain text is 8 bits and it is encrypted by a 32 bits RSA key.

I have successfully found the public key is $(e=947,n=2671079)$ and the private key is $(d=713604)$.

Then, I try to convert the Hex string to integer 00 05 BB A3 (Little Endian) $=375715$.

Finally, I calculate $C^d \mod n = 375715^{713604} \mod 2671079 = 544824$.

Calculate in python: C**d % n

My problem:

1) what does $544824$ mean? Is it the original plain text or I need to further converting this number?

2) The plain text should be 8 bits, why the result I get is larger than 8 bits?

thanks!

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    $\begingroup$ In Python don't use ** % n use pow(c,d,n) this is more effective. $\endgroup$
    – kelalaka
    Nov 9, 2019 at 14:35

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Your ciphertext is A3 BB 05 00

In RSA, the ciphertext is always larger than the original data. In this case, the keys are 32 bits, which is 4 bytes, and A3 BB 05 00 is four bytes

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  • $\begingroup$ How about the plain text I get after the decryption? It will be 4 byte too? $\endgroup$
    – JC234
    Nov 9, 2019 at 14:51
  • $\begingroup$ Can you prove this statement ` the ciphertext is always larger than the original data`. What if my plaintext is $n\hbox{-}1$ $\endgroup$
    – kelalaka
    Nov 9, 2019 at 19:39
  • $\begingroup$ This is wrong. $N$ is an upper bound for both the message and the ciphertext - there is no asymmetry. At least as long as plain RSA is concerned ( and not something like RSA-OAEP. $\endgroup$
    – tylo
    Nov 9, 2019 at 23:40

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