Attacking a polynomial-based cryptosystem: Polly Cracker

Abstract.

We describe several attacks on Polly Cracker, a public key cryptosystem proposed by Fellows and Koblitz. The first kind of attack shows that variations in the CPU time needed for evaluating polynomials can leak significant information about the secret key. This kind of attack might also be of interest when dealing with other cryptosystems using polynomial evaluations, like Patarin’s hidden fields equations.

Next, we exhibit some “structural” weaknesses in Polly Cracker’s encryption procedure. In particular, we demonstrate that with the parameters considered in a book by Koblitz it is often possible to reveal the private key easily.