Constructing a non-degenerate n-dimensional hyper chaotic map model over GF(p) with application in elliptic curve-based PRNG

Constructing a non-degenerate n-dimensional (n ≥ 2) integer domain hyper chaotic map (nD-IDHCM) over Galois field with expected dynamic characteristics, is an interesting and challenging topic. First, we design an nD hyper chaotic map generation model over GF(p), give the proof that its phase space satisfies global boundedness, and it owns n positive Lyapunov exponents. The performance evaluations of two instanced examples indicate that, the trajectories of the nD-IDHCM exhibit ergodicity in phase space and good randomness. To evaluate its practical application, we design an elliptic curve-based PRNG (EC-PRNG). First, we transform the initial key into big integer sub-keys through a 2D-IDHCM, then calculate corresponding coordinate points through an efficient computing of multiple point on the elliptic curve over GF(p), further feedback the coordinate points into the 2D-IDHCM, to generate two big integer sequences through specified iterations. The elliptic curve discrete logarithm problem (ECDLP) can ensure that the EC-PRNG is irreversible, and all the multiple points can be calculated in parallel. Experimental results analysis and security evaluation demonstrated the effectiveness and high security of the proposed EC-PRNG.