Constructing a nondegenerate <i>n</i> D hyperchaotic map based on elliptic curve over GF( <i>p</i> )

To overcome the problem of reversibility in chaotic maps over a Galois field, a model of a nondegenerate nD ([Formula: see text]) hyperchaotic map combined with an elliptic curve (nD-ECHCM) over a Galois field is designed, which is embedded with the Elliptic Curve Discrete Logarithm Problem (ECDLP). First, an nD hyperchaotic map (nD-HCM) over GF([Formula: see text] is designed based on the linear congruential generator (LCG). To compensate for the reversibility of nD-HCM, an irreversible nD-ECHCM model is designed, which can construct any non-degenerate n-dimensional hyperchaotic map. Furthermore, the global boundedness of the Lyapunov exponents and hyperchaotic behavior of nD-ECHCM are proven, and describes ensuring the irreversibility of the nD-ECHCM by embedding the ECDLP. Finally, to verify the effectiveness of nD-ECHCM, two instances are provided to analyze their dynamic behaviors. Experimental results demonstrate that the hyperchaotic maps over the Galois field constructed by nD-ECHCM exhibit ergodicity and irreversibility.