Suppose m is a positive integer converted from the plain text in bytes.

And there are two positive integers a, b which satisfies $a^2=1+4919b^2$ in the encryption process. (a and b are both unknown)

The cipher text is x which satisfies $x = (am+b) mod p$ where p is known and is a large prime number.

For some reasons, the cipher texts are shuffled by group. And so I got several possible values of x (which are all very large)

Given the cues above, how to get the possible integer number m? The possible m can be checked by deciding if the plain text converted from the m makes sense.

Any detailed solution would be appreciated, thank you!

  • $\begingroup$ Could you be more verbose as to what you mean by ciphertexts were shuffled by a group? $\endgroup$
    – Lev
    Jan 12, 2023 at 21:10


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