Alice claims to know the message m. This was encrypted with rsa scheme with public parameters n, e and ciphertext c was obtained. She offers to convince Victor of this by the following set-up. She selects two random numbers r1 , r2 in [2, n - 1] and then forms
c1 = r1^e (mod n),
c2 = r2^e(mod n)
and sends c1 and c2 to Victor. Victor then selects to see r1 or r2 and checks that ci = ri^e(mod n).
This is repeated as many times as Victor wishes.
Should Victor be convinced?
Is there a security leak for Alice?
In each case justify your answer and if there is an issue, offer a solution alternative.