<p>Chaotic systems have been widely applied in data encryption to enhance security. This paper proposes a memristive Hopfield neural network-like map (MHLM) by incorporating a discrete memristor into a discrete bi-neuron Hopfield neural network. Theoretical analysis reveals that this map possesses an unstable invariant set under specific parameters. This property enables the offset-control grid coexisting hyperchaotic attractors to be regularly distributed in the phase space, providing excellent pseudo-random sequences for cryptographic applications. Based on Shamir’s secret sharing method, we develop a multi-channel cyclic data encryption scheme that integrates dynamically generated secret sharing, chaotic block-swap scrambling, and cyclic diffusion leveraging the offset-control grid hyperchaos. The scheme can achieve the parallel transmission through multiple channels and support discarding redundant and corrupted data, thereby significantly enhancing security and fault tolerance while improving transmission efficiency. Statistical testing and experimental results validate the excellent randomness of the hyperchaotic sequences and demonstrate the scheme’s effectiveness in resisting cryptographic attacks for secure data communication.</p>