Possible plain text needed on a congruence modulo - based encryption

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!

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