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Chaos distributes with a covert method to condense the dynamic of complexity and satisfies the security requirements of a cryptographic system. This study gives an ability online/offline (O/O) ID-based short signature (IBSS) scheme using conformable fractional chaotic maps. Furthermore, we establish its security under IBSS existential unforgeability of identity-based short signature (IBSS) under chosen message attack (EUF-IBSS-CMA) in the random oracle model (ROM). Some of the stimulating preparations of obtainable processes are that they give a multiperiod application of the offline storage, which licenses the agent to recycle the offline pre-registered data in time series (especially the polynomial time), rather than one-period usage in all past IBSS processes.