A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: For any prime p, reduce its coefficients mod p and consider its action on the field Fp. We say a subset of Z[x] is dynamically distinguishable mod p if the associated mod p dynamical systems are pairwise non-isomorphic. For any k, M ∈ Z>1, we prove that there are infinitely many sets of int...

Abstract Grain is one of the simplest ECRYPT Stream Cipher project Candidates which deals with key and IV of length 80 and 64 respectively. Using the linear sequential circuit approximation method, introduced by Golic in 1994, we derive a linear function of consecutive keystream bits which is held with correlation coefficient of about 2. Then using the concept of so-called generating function, ...